Interview Questions | MAT livestream 2025

Category: Education

Tags: InterviewsMathematicsOxfordPreparationTips

Entities: CaliJamesNew CollegeOxford Mathematics PlusOxford University

Transcript

00:00

Hello and welcome back to a bonus episode of the Oxford Maths live stream. Uh my name is James and today we're looking at Oxford interview information for maths and or computer science.

Um

00:15

good to see you here. Welcome back after the after the mat again.

This is a bit of a different one uh because not only are we not getting ready for the mat, we're not even talking about the mat. Uh we're talking about some other maths uh that might happen at a maths interview.

uh if shortlisted for interviews for

00:31

math or computer science at Oxford. Hello people in chat.

Hello. Is actually the last one this time.

Hi James. I'm at the gym right now.

Hello everyone at the gym. There you go.

Uh brilliant. The gym's got a shout out.

What what what a

00:46

world we're living in. Yep.

Last one. You know, there we go.

Um we've done quite a few this year. Uh but uh this is a a finite sequence uh which is going to be this one and it's sort of included in the Matt live stream thing partly for

01:02

clicks because I know you know what that is. Um but also partly because you know we're looking at similar skills really.

Now two things I want to do at the start. Uh firstly wanted to thank Cali who's moderating chat again.

Right. Is it Cali again today?

Have I got that right? It is Cali.

Hello. Thank thank

01:18

you Callie. Cali has done a bunch of these.

Um, not just this year, but over several years. So, uh, let's put thanks Cali on the screen.

I don't know if they're watching, but they're definitely in chat. Uh, there you go.

01:33

You can say, um, you can say thanks in chat if you like. Uh, and we've had various students moderating things along there as well.

Um, I would like to do the normal stuff we do at the start of stream, uh, which is to, uh, ask you how your day's been. Um, and I want to do some obvious things that I know are going to be frequently asked questions

01:48

in chat. So, I'm going to try and do the front, which are, at the time of recording, no interview invites have gone out yet.

No deselections have gone out yet for maths or computer science at Oxford, I'm expecting those to go out uh starting next week. I'm not expecting

02:04

absolutely all of them to go out next week. Um, but looking at my calendar, it is currently uh the 27th of November.

Uh I am expecting emails to start being sent by the various college colleges of Oxford uh week starting uh 1 of December

02:21

and I'm hoping get most of them out 5th of December uh because interviews are not long after that. Uh maybe I should maybe I am expecting most of them really most of them to be done by Friday the 5th of December um and out there and I

02:37

I've got some what where and how questions to to deal with. So we'll do we'll do more information.

My plan for this is to spend maybe 20 minutes half an hour uh doing the kind of questions about what interviews are like. Um and then uh I have a question

02:53

that I used last year uh in maths interviews and I I'd like to walk through it with you. We could try doing the question uh and maybe we could uh talk about what I'm trying to get out of that.

So the the when question from anonymous and a different anonymous person. Uh, sorry.

Uh, I'm I'm going to

03:11

Let's put it on here as well. Um, then let's zoom in.

So, like, uh, invite emails. Uh, and this is going to be about 01 to 5 of Decemberish approximately.

Um, and

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then actual interviews uh are mostly in the week that starts. Um, mostly in the week that starts 15th of December.

Well, let's go. Mostly um end of Oh, hang on.

How am I going to

03:47

do how am I going to phrase this? Sorry, I've sort of changed my mind halfway through that sentence.

So, mostly um it's week commencing 15th of December uh or the second half of uh the previous week. So there's some happening in that

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week of December for math computer science. Uh maybe even the first half of that.

This is still mostly um so the week uh in Oxford terms it's 9th week of term that doesn't mean anything. So 8th to 12th of December.

Uh

04:19

and just in case anyone's watching the recording it is 2025 at time at time of recording. Um, mostly that week, Wednesday, 15th as Monday, Tuesday, Wednesday, and possibly Thursday, but hopefully not too much on Thursday.

Quick update. Chat is having a terrible day and I'm not ignoring that.

What is

04:37

that? 19% on one star.

That's terrible. That's like the highest proportion of bad days we've ever had.

I wonder if that is I wonder if that's like Wonder if that's like related to the thing that's on the screen right now. Um,

04:54

yeah. Okay, good.

Um, I think I think we've hit when uh let's clear that. Kelly's been Kelly in chat says thanks.

Um, people in chat are hoping that I do my triangle question again because I do my triangle

05:10

question quite a lot. Sorry, I'm ex doing this a lot as well at the moment.

Um, I'm not planning to do the triangle question this time because I've already done it as open days. But now what's happened is that you've mentioned it in chat, which means that the however many

05:25

people who don't know what my triangle question is will want to see it, which now means that we're doing it. Um, so I'll tag that on the end.

Um, let's make a little set list for myself here. Do the triangle question.

Uh, okay. And I also have the uh 2 plus

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3 is five question, right? That's my set list.

Eric says we all know the question which I think is exactly the sort of thing where I did that open day. I've done it in a previous video.

Nope. Shouldn't have seen people have seen things.

Let's do our who, what, where, when, why. Uh I

06:00

hope people have so I saw that people voted one star there. That's pretty that's pretty sad.

Um normally I would say oh I hope thinking about some maths uh cheers you up. Um, that's still 20 minutes away, I think.

So, maybe go make a cup of tea or something and then come

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back and we'll do we'll do a math question together because I want to do the information side of this first. Um, let's work our way through these questions in some order.

Um so where uh the interviews for Oxford are online

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uh we've been doing online interviews for everyone since the pandemic but we've actually been doing online interviews for overseas candidates for about 20 years. So we've done a lot of online interviews.

Um we've worked out I think how I think we've worked out a

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pretty good way of of doing those. Um we found that we can still do all of the stuff that we want to do in an interview um online.

uh asking people questions over a team's call. Uh so we have something like uh teams uh to do the call.

Uh and where possible we use an

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online whiteboard like this one if people can access it. Um if that's not possible, we've got other other plans as well.

Um but uh where possible uh people uh join this in a a separate tab or a separate uh device or on a phone or

07:19

something so that they can see. uh failing that.

Uh [snorts] I've done things like screen share so I can at least show people what I'm doing. Uh I'm failing everything.

There is always write something on a bit of paper and hold it up to the camera. Oh, I was considering switching to um just full

07:35

screen camera there, but it's a bit of a jump scare, I think, if if I'm suddenly the whole screen. Um and there's a question about content in chat.

Um do I prefer So the the setup, the person who's asking about visualizers or an iPad or whatever. Um, to be honest, we

07:51

can work with whatever. I I'm not expecting Visualizer.

I think Visualizer is quite rare. Um, and I haven't I would I wouldn't start an interview by saying get out your visualizers because there was a thing during the pandemic where people were balancing uh balancing phones on top of stacks of books and

08:07

things. And I thought it's quite precarious.

Um, uh, so I've been using these online whiteboards where where I can. Uh, Reuben, if you can't afford paper, we will maybe send you some paper.

Um, right. Okay.

Uh the dates are so the w of it are invite just to

08:24

clarify for Aaron in chat. I think uh uh we tell you when the interviews are.

If you can't make it, then uh please reply to the email. Uh please don't just don't turn up.

Uh what's the way to

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phrase that? Please don't not turn.

Please don't just not turn up. Um uh please reply and try.

We'll try and rearrange if we can. Uh right.

Okay. Uh so online calls, I should the why really quickly.

Uh and maybe this is a little

08:58

bit of the who as well. Um for maths, we're interviewing about three people per place.

Uh which means about almost 600 people uh invited to

09:14

interview. um that's not the same number of people as we have applicants.

Um we're doing the interviews because we want to see people doing maths

09:30

that includes computer science. Um so computer scientists uh I know less about computer science than I know about maths.

I have sometimes interviewed computer scientists and just asked uh maths questions in my role as a maths

09:46

tutor. Uh at New College, we sometimes like to give the computer scientists a maths interview just for just for that um just for that comparison.

Um just for just for more maths fun. Uh

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we want to see what happens when you get stuck. Uh I'm going to put this as a question here.

Now, we have some data on this from

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things like the math submissions test where we've done tricky questions. Uh we've set tricky questions and we've seen what happens when you're stuck on these tricky questions.

But interviews are different because in an interview we can give prompts. Um, the interview is

10:35

usually two interviewers who might take it in turns to talk or who might both talk. Or it might be the case that you have one person talking and one person taking notes.

Uh, that's how I do my interviews at the moment. I

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have me doing all the talking and I have somebody else in the call just to take notes on what's going on and track who said what. Uh [snorts] so usually two interviewers uh who might be uh uh who might be tutors

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uh at the college uh they're almost always involved if they're teaching people on the course they're almost always involved in admissions um but also might be uh defill students who have done training.

11:26

Um there's a range of different uh teams uh interviewing. Um if you're interviewed at Oxford for maths, you almost certainly have two interviews with different colleges.

So let's put that in the that's sort of a how thing I

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think or maybe it's a what. So what is this?

So it's uh at least two. Let's put usually there.

Occasionally someone is in a very distant time zone and we just cannot find a way to find a second time that people can do. So usually

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um to uh 20 to 30 minute and this is usually as well guidelines not a strict rule uh uh calls

12:16

about maths. I'm putting calls because these are online calls.

Let's put online in here. Online calls about maths.

Um where you should expect expect to solve problems.

12:36

I'm being vague about what those problems are. Uh it's not the case that we've got a set syllabus for this.

Um for the math, we can't help you with the questions while you're doing them. We're not there.

Um so for the math, we have a really specific syllabus. You've seen it, I'm sure.

this one page of A4 that

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lists maths topics. Whereas for interview, we can go a little bit wider.

Um, we can bring in new things entirely and maybe teach you something on the spot. We can bring in other topics from maths or further maths or equivalent provided that we've made a plan for what

13:09

we will do when we meet people who haven't yet seen that in school. The interview is happening before the end of school.

So, we know that um we can't expect everyone to have seen every topic that they're going to learn before the end of school. Um that doesn't always stop me because I

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know that um if somebody hasn't met it before, I can get some good information about what happens when they're learning something new on the spot. What happens it's not the same experience, but it's a a useful experience um for me at least doing interviews.

Uh,

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how many students I interviewed? Oh, so Eric wants numbers for computer science.

I think it's about three per place. Something like that.

Yeah, maybe a little bit lower, but I think it's about three per place. Um, so in raw numbers, gosh, I I can't remember off the top of my head, but at most a couple of

14:01

hundred, I think. Was it 60 for CS at the moment or is that 60 for math and computer science?

I should know these numbers. Uh some, not most, not most of the applications, I'm afraid.

Uh short listing down. Uh okay.

So, we're

14:18

applying one year late and you've finished year 13. We could get asked year two content.

Yeah, of course. Why not?

Right. And also, if you haven't finished year 13, you could get asked year two content because you're in year two.

I mean, uh this question is interesting to me, right? Because

14:34

I I don't know if this person is like this person has finished year 13 and they seem slightly nervous about the idea that they know mathematics. But like don't be nervous.

You know mathematics. You finished year 13.

You got the grades, right? Probably.

Like surely I should be allowed to ask you

14:50

about stuff you definitely know. Uh James is having a fourstar day.

Thank you for asking. Uh I'm now looking at chat.

Can you tell? Yeah.

If you say you've never learned something, well, when you had and then shocked them by being insanely good. In general, I think

15:06

I'm quite good at detecting. Well, so firstly, I don't think people actually try this.

Um, and secondly, I think you're going for a maths degree, not an acting degree. So, presumably you're better at maths than you are at acting.

I don't know, maybe you're amazing at

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both. Um, my caution to people considering this is that you're probably not as good at acting as you think.

Uh right. Is it equal number of people invited from both Matt days?

Uh maybe. Uh not something I've counted.

Uh what

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content is expected knowledge? Yeah.

So expected knowledge is an interesting question, right? Because we're not really trying to test what you've learned in school.

Uh let's let's maybe put that on the board somehow. Uh so people are quite nervous in chat at the moment about I think maths topics that

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might come up. uh we're not really here to ask A-level questions at interview in the same way that you get A-level questions on topics.

Uh because well, if you imagine being in my shoes, right? Uh if I spend a day interviewing people and I ask them A-level questions, what I'll learn is mostly whether people have met

16:12

those topics or not. Uh you know, if I ask about tricky A-level topics from the end of Alevel, then mostly I'll learn whether people have seen that topic yet or not.

And that's not really interesting to me because by the time they come to Oxford they will all have seen all of it. Um so in some sense I'm I'm measuring something that is not

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relevant. Um so instead when I'm designing interview questions my preference is to go a bit more basic.

Uh and my preference is to do things where uh I know that everyone has seen it. Some of my colleagues go the other way.

Some of my colleagues like to ask things that they know that nobody has seen. Uh

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so some of my colleagues like to level the playing field by making sure things are challenging for absolutely everybody. That's a different sort of challenge, right?

Uh so I I tend to go towards, you know, triangles and parabas and things which some people have seen one of my example interview questions,

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triangles and parabas, right? Uh and the other way that people sometimes go is to go really hard.

Um the third option is of course to do something where you can adapt it based on students uh to do a question where depending on what they've seen you can ask different things. That's a bit harder to do.

Uh right. Can

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I expect much to be asked about the personal statement? Uh not usually.

I would say uh I want to do some maths. I can read your personal statement whenever I like.

Uh but while I've got you in the interview, that's my chance to actually do some maths with you. Uh is this true?

Have I never asked someone about their personal statement? I think

17:35

I've a few times I've asked people about their personal statement. I find that not very interesting generally.

Uh so I don't do it very much [snorts] personally. And was that a threat?

What did I do? Oh no.

Did I back up? What did

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I do? I was threatening.

Yes, there was a bit where I stared down the barrel of the camera and said that things challenging for everybody which is maybe a bit too a bit too I'll try and tone it down a little bit. Will you asked why you want to study maths?

Uh no. But I think that would be a boring question

18:06

because we already asked you that on the personal statement. Why Oxford is silly.

We know that we're the best. Uh we cannot ask why the college choice because we don't know that you chose the college.

You might have made an open application and been allocated to our college. We don't know.

So we can't ask you why you chose the college because

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you might not have. We can ask you about your personal statement.

Uh personally, I would rather get on with some maths. Uh what have I not done yet?

Uh I haven't done have I done who you know. I've done who have you and I've done a couple of us.

I haven't really talked about the Oxford way of doing multiple

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interviews. It's it's on the board somewhere.

But this idea that we we know that people tend to be a bit nervous in their first interview. Um uh that tends to make me a little bit nervous as well when I know that it's somebody's first interview and I have to set a good impression for what interviews are like.

18:52

Um but in Oxford we interview people at least twice. Almost always if you're in a very distant time zone, we're going to try just so that I can say always.

Um, and because we want to see you, uh, because we're interviewing multiple times, uh, we get a range of, uh, tutor

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opinions, we get a range of experiences. We get to ask people multiple things.

Uh, and I, I think that's good because occasionally people come out their first interview and they might not have got very much done. They might have been quite scared, but now they know what to expect or now they know how it works.

Of course, I'm trying to prime you for what

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to expect, which is people live there and they ask you maths questions. Uh, right.

How important is knowing everything on your personal statement? Well, it's your personal statement, so presumably you wrote it, so you should know what's on it because you wrote it.

Um, you shouldn't be

19:43

surprised if something on your personal statement comes up. Um, some of my uh, colleagues I know try to use the personal statement as a way to make somebody feel comfortable at the start of an interview by saying aha on your personal statement.

You've read this book. Uh, I also read that book.

What

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did you think about the book? Uh, and uh, maybe that will make you comfortable or or maybe not.

Uh, we have different interviews. Something I'm trying to I suppose get across today is that I'm one interviewer.

There are maybe about a hundred people doing interviews with

20:15

maths and computer science and we have a lot of academic freedom to do uh different things. We have obviously some guidelines what we're looking for.

We're all looking for best candidates for the courses. Um but our behavior in interviews and the ways that we might try and surprise candidates by showing them something new mathematical or ask

20:32

them a question they haven't seen before. Um there's a lot of freedom there and I'm not trying to box in my colleagues.

Does Oxford consider teacher reference before the interview? Yes, very much.

We've already looked at uh teacher references of course because we've got those. Often they've got really important information in and

20:48

often they tell us how great you all are at maths or computer science. Oh yes, let's put what thank you.

Math and philosophy student waiting there very patiently. M philosophy students should probably expect uh uh I'm going to say should expect

21:05

separate philosophy interview. Have I mentioned second colleges?

Um, so this is an Oxford thing that if you're interviewed at Oxford, then almost

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always you're interviewed by a second college, which might mean that you get one or more than one interview with a second college. Uh, that's done for everyone or almost.

Uh, it doesn't mean anything about your application. Uh, we just like to get people seen by a second

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team of of people. Um, so that although we're at different colleges and we're each trying to get the best students, if one of our colleges has uh too many good students, then at least they've been seen by second colleges who can then like, you know, hungry hungry hippos,

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right? Can just like gobble up uh grab some extra extra points.

Uh, so math and philosophy students might end up with four interviews. Um, it's not unheard of for it to be more than four.

Um I think at New College we do

22:11

I'm at New College where I think we do I think we do a standard three interviews for first college candidates and then I'm not sure we do three for our for our second college candidates but we do a couple for math and philosophy. I think there's quite a lot of interviews in the end but we think this is a good thing.

22:27

We think this is a lots of opportunities for people to demonstrate that they're the right candidate for the course and lots of opportunities for rather than think about it like that perhaps lots of opportunities to just do some maths with us uh or philosophy with us or just just have those conversations uh and get some

22:42

get some get some experience. Uh, I think my best interview questions are the ones that actually show you a technique or something useful so that even if you don't end up coming to Oxford and even if you didn't really like the overall experience, at least you've learned a thing now.

I I think

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the best math questions are like that. I I know everyone's still grumpy about Matt and this is not the right time, but I think the best math questions actually make you better at maths, right?

Uh, I think feel like I'm not allowed time to think during interviewers. Oh, I think

23:15

So, we're not mind readers and if you don't say anything, we will try and work out what you're thinking by asking you. I try not to give people hints unless I think they need them.

And often I think my best interview strategy is to shut up

23:30

and listen um because I want to see what the candidates doing. So, I know what you mean about having to trying to time to think.

Um it's slightly artificial, but I do encourage you to think out loud. Um, maybe we'll do this.

Where am I going to

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do this? Top tips.

Let's do a top tips column. Top tips.

Top interview tips with James from Oxford. Hello.

Uh,

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uh, uh, top tip number one is listen to the interviewer. Um, we are telling you what the question is.

we can help you. Uh, and if the question is too hard, which is one of the things that I might try to

24:17

do is to make the question too hard, then I might substitute the question with a kind of sub problem or a way to break down the problem. I might suggest a way to um [snorts] attack the question in a different way or or something like what if, you know, what if all of these

24:33

spiders were just there was just one spider, right? I don't know.

Whatever. What is that question?

My goodness. Um, but what if there was less going on?

Um, which might give you a smaller thing to think about. Everyone's thinking about spiders now.

What have I done? Um,

24:48

melons. Watermelons.

Uh, no. Terrible.

What is my question concept? It's always like, oh, Derek has 37 watermelons.

And now that's like a classic math question. Let's go for that one.

Derek's got 37 watermelons. Wow, there's too many watermelons.

I can't think about all of those watermelons. So, the interview

25:04

might say, well, what if it's just one? Uh, and then hopefully your intuition of imagining one automatically might give you a way to imagine lots or or a way to get back to the main problem.

I have gone off on a tangent here, haven't I? This has gone weird.

Um, so listen, because we might be adapting the question, we might be helping you. We

25:20

might be clarifying something. Uh, oh, we don't even make shorts of these.

Maybe we should make shorts of these. If you apply at New College, gosh, if you're at New College, if you're shortlisted at New College, I think I'm interviewing all of the maths candidates

25:36

at New College. Um, you may not use this chat thread to try and influence that experience.

I won't remember who you are. And I, as I say, I'm interviewing all of the maths candidates who are shortlisted by New College.

So, there we go. Right.

Listen.

25:53

Uh, what's this one going to be? Um, say what you're thinking.

Um, this is a bit artificial. I know that, um, normally when you're working on a maths problem, you don't talk out

26:09

loud while you're doing that probably. I mean, maybe you do.

Um but there is something about uh [snorts] if you just start quietly integrating then it's

26:26

a little bit harder for the interviewer to tell what's going on and to help. But if you say I'm going to integrate this with respect to X, then the interviewer can think, hooray, great, and can maybe even say, yeah, carry on.

Let's see what happens. Which is not a hint.

It's just

26:43

you announcing what you might do next. Um, uh, so there's a suggestion in chat that look, what if you start getting a hint and you realize you want to stop them, but they say too much?

Like you can say

26:58

you can say as you can say as soon as you said one watermelon I knew that that we were going to be able to solve the problem because and then yeah you go uh I would not I'm not going to say I recommend making a joke. Uh

27:14

I I seem to have gone quite jokey very suddenly. I don't know what's come over me.

Um good. Right.

Uh ah anonymous. Why are you doing this in why are you doing this in in Slido chat?

My MAT test was affected by the exam center due to my access ranges. I ported this on OA.

So

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you did a special considerations ranking. Um that goes through the special considerations process possibly gets uh assigned a yeah there's a there's a process for considering this.

Um if you did the special considerations it's

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almost logical but if you did the special considerations request then your request will be specially considered. Um, and it might cause you to be shortlisted for interview even though you have a lower score or or no score at all.

I think every year people ask me on

28:01

that those bar charts like what's going on for the the the left end of the tail where you've shortlisted some people with really low scores and I can't comment on individual cases but we do short list people because there was something else going on. Right.

Dude, you did that in the slido chat in the It could have gone right past. I've missed

28:17

so many slido messages. Were they all like this where Oh, right.

Okay. [snorts] Okay.

Right. Uh I'm not going to have a top tip about.

[sighs] So these are like dos. Uh

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[snorts] so this say what you're thinking and say what you're about to do. Um you can ask for help.

So let's put clarification to start off

28:48

with. Maybe ask for help is going to make people like a that sounds that sounds like a trap, right?

But I would rather help somebody than just have them quietly panicking or something like

29:03

ask for clarification. Um, occasionally we're going to use words that aren't words that your teacher used.

Um, but hey, you can ask us what that means. Uh, and we can help and we won't think that.

Oh my goodness, how can you not know what a periodic function is? Uh, because maybe

29:20

your teacher didn't say what a periodic function was. Maybe they did.

Uh, yes. Uh, so like do ask for clarification if needed.

That's not like a blanket. What do you mean squares?

Um, whatever.

29:37

Um, let's have a You don't I'm not to at the top there is asking a question at the end of the interview. You don't have to.

You can if you like. I tried to say this at the end of the interview.

It's not part you can ask us. Uh for some people that's a convenient way for them to ask a question that they

29:53

didn't want to email in or a question that they didn't want to put in somewhere else. Um people have put me on the spot about all sorts of things.

Uh it's our chance maybe to uh tell you about New College if you want to hear about New College. If you're interviewing being interviewed by New

30:09

College, but I I don't need you to ask about New College and there are loads of other ways to find out about New College. If you ask about New College, I'm not going to think, oh, hooray, a question about New College.

I'm going to think tell them about New College. Um, sometimes people ask about me and I think that's I

30:27

don't really like talking about myself, but that's me. Which kind of burrito are you?

Kindly responded by B16. You see, there you go.

That's that's an example. Uh have you struggled with any interviewee has strong non-native English accent?

Uh personally no

30:43

actually um been fine actually. Uh we have some English language requirements published out there right for for studying at Oxford and people are on track for that which is actually quite a high requirement I

30:58

think for international students but that's my hot take on international English language requirements. Uh right.

So I'm going to struggle to translate it into a different into a different into a different language. But maybe I could start defining it in other

31:14

terms until we realize you know the function where x plus l is equal to f ofx for some minimum value of l such that that's true. [snorts] You know we can get there.

How are students chosen for interview? Oh we look at lots of things.

We look at applications. We look

31:29

at matt in particular. Um, we look at GCSE scores where we've got them.

We look at your predicted grades, but everyone's got pretty good predicted grades. Um, we look at lots of different things.

Uh, but we're taking the students that we think have the most potential to succeed. Uh, we can use our

31:46

interviewing resource on uh, joint math computing, same same schedule as the thing I put on the screen. Uh, they work with us, right?

Can I ask about llass transforms or matrices? uh only if I am prepared to

32:02

explain what those things are because not everybody knows them. In fact, the plus transforms, my goodness, almost nobody knows what they are except for the however many people who have told me in their personal statement that they know what a plus transform is.

Okay. Um I know that someone someone I know did

32:17

do a question about lelass transforms in the sense that they essentially they were teaching some theory about lelass transforms. You didn't need to have heard of lelass beforehand.

Um they designed it so that it was just integration based. It was quite fun actually because you you ended up knowing about what the point of doing a

32:33

lelast transform was quite fun. I think there's been a three blue one brown video.

Is that why everyone's talking about the plus transforms now? There's been a three blue one brown video.

It's like it's not in the scale of like mathematics that I think 18year-olds should know about. It's not really up there, but okay, fair enough.

Um,

32:50

how fair would you say the Oxford admissions process is? That is really hard to define.

I'm going to say nine. Um, what's the best question someone has asked me?

generally it's sounds awful. I can't remember

33:05

any of the we do. So at the end of my interviews I say if you've got any questions for ask you can ask us.

You don't have to and it's not part of the interview. And then I just I guess some people do but I I don't I don't memorize them and I do a lot of interviews, right?

Uh I didn't write about little

33:22

astronal statement but now I know what they are. There you go.

I think you're going to like university. I think you're going to like it.

Not because you're going to look things up on Wikipedia, but because you will have other options of ways to learn about new things. Was there three blue, one brown?

Right.

33:38

Okay. Should we do an interview question?

It's about half. I think we've done the kind of like the meta level of theory of like not yet, but soonish.

Oxford is going to send some interview interview invitations to do interviews. We'll say when they are they are online.

Try and use online whiteboards when we can. Um

33:54

uh the how is has turned into top tips. Mostly they're tutors or or default students who have done some training.

I'm also here. I guess I'm a cheater.

I'm a I'm a cheater. Uh that's me, right?

Good. Okay.

I think we're going to do a

34:10

question now. Should we do a question?

I think there's always room. I don't I don't think people would believe me if I said 10 out of 10.

I think there's always room. Like 10 out of 10 would presumably be everyone looks at every application and really has a big

34:25

discussion to make sure we're not missing anything. And 10 out of 10 would maybe be we got more information.

I think we're nine out of 10, but fairness between candidates at different colleges and things. Um maybe that's not what you meant, but [sighs] you know, right?

Okay.

34:44

Uh here's my question that I uh used a bunch uh last year. It works like this.

Sorry, I've just sprung it on you there. My goodness, I didn't warm you up at all.

Right, time for a math question. Let's go.

Um, works like this. Um, I'd like my computer to calculate the sum 1 plus 2 plus 3+ 1 plus 5.

My computer can

35:01

only add two numbers at a time, and it's expensive to use this particular computer. The cost for replacing a plus b.

So it's two numbers a and b and adding those together with the correct value for the sum c. That cost is a * b

35:16

* c. So that could be quite a lot.

For example, adding 2 + 3 and getting five costs me 2 * 3 * 5 is30. Uh because 2 * 3 * 5 really is 30.

Uh and 2 + 3 is 5. Um, we're going to keep

35:33

doing calculations in some order until there's only a single number, which is going to be 15 because it's getting the sum correct. But there are loads of ways we could order the operations.

Um, and I'd like the minimum total cost. Ah, no.

People who have been on the Zoom call. Now, you see people found out about the

35:48

Zoom call as well. So, I did this thing with Braz Cambridge where did an interview question.

People heard about that and I'm doing it again now. Um, if you've seen this question before, then maybe this is your chance to go and make a cup of tea.

We are doing the triangle as well and then maybe I'll try and do

36:05

something else. Uh, the website says 10th, 15th, 18th and maybe also some for the week before I think interview schedule.

Yeah, exactly. So, now some people are saying what's cool.

So, I did I did a webinar they I got invited to do a webinar about

36:20

interviews and I thought I'm doing the same content that I'm doing on that live stream. nothing plus the triangle question.

You want the triangle question in the at the same time, right? Okay.

Okay. So, the idea for this, by the way, is that um we would

36:37

start this one. Oh, by getting to grips with what that means.

Uh I've put this kind of like notation underneath where uh some people would start describing what sums they wanted to do. And if they started, I

36:54

would explain that I've got a calculator and I'm going to do the working out. Um because I'm not trying to test their ability to multiply um even though that's 1* 2 * 3.

So that step costs 6 or so. But maybe you've got your own opinion

37:09

about how we should add these things up. We given the knowledge we know what sum we are trying to do.

We know we're trying to sum 1 plus 2 plus 3+ 4 plus 5. uh we can feed those numbers into the computer and I suppose each time we feed two numbers into the computer we get a number out um so we can feed two numbers

37:26

into the computer but we can choose which two to select to put into the computer add them together charge me charges me loads of money um and then we've got fewer numbers and keep putting things into the computer until I've only got 15 as a number at the end and I've

37:44

spent some Good. Right.

Okay. That's the question.

Uh I'm going to parallel process it. Let's let's be weird about this.

So, while you're thinking about that, [laughter] this is the silliest way to do the interview one. I've done a few of

38:00

these and this is the da way. Uh right.

Okay. So, the the triangle question works like this.

Um, I have a parabola y = x^2 and I have points a, b, and c on the parabola. Uh, a and c are

38:20

fixed and b is somewhere in between. I really like this question.

[sighs] So, somewhere in between a and c. Um uh

38:36

let's so the question is where should I put B to maximize the area of triangle ABC.

38:52

So trying to find a really big triangle uh by moving the point B around um to make that triangle really large. Good.

Right. Okay.

Uh, and you don't have to make tea. There you go.

Right. Parallel process.

Some of you are going

39:08

to think about triangles. Some of you have already seen triangles from I think we did this at the Oxford open day or at least I put it on the screen at the open day and then moved on.

That's how I do the open day. All of this information for the parents and guardians in the room and some maths questions on the

39:23

screen for the the mathematicians in the room. Who can you know you can look up the information on the website afterwards?

You got the internet. [laughter] Here's some maths.

Uh right back over here in numberland. Uh multiplication of one has some impact

39:40

of course. So for example over here, multiplication of one.

Well, I suppose multiplying by one doesn't have much impact, but adding one and two still costs me money. Uh so there's a suggestion in chat that I start with 1 + 5.

So I'm going to try that out. Uh I wonder what they want me to do next

39:56

because this is going to produce the number six and it's going to cost me £30. So now I have two, three, four, and six, and I've got to keep going.

Right. Okay.

40:11

Maybe these are rival strategies. I don't know.

This one was mine. Right.

So what next? Uh let me know in chat how we're going to proceed there.

Um I I think I started this interview always by checking people had understood the concept. There are currently like 60 or

40:27

70 of you, which is quite a lot. I I'm going to try and make sure everyone understands the concept that we keep adding until we get down to 15.

We're trying to apparently minimize the total cost. I'm going to add up a total cost in a moment.

Uh let's keep going. Have we got any suggestions of what next?

40:44

This is a little bit like multi lots of people here. Maybe 2 plus 6 next.

Smallest plus largest. I can do that.

So 2 + 6 2 + 6 is 8. And that step costs me 2 * 6 * 8 is 96

41:02

criy. Um uh so if you're not sure, so if you're not sure, I would start demonstrating and I would maybe explain again that we've got these five numbers to add and we're going to get the computer to add two at

41:19

a time. It can only add two at a time.

So on a normal computer, of course, you just type this in and it just does it by some sort of computer magic. But this is trying to get one level deeper to say, well, what your computer actually does probably is that it has some uh machine

41:38

for adding together two numbers. It probably wasn't coded with, you know, three or four or five wires going into it.

Probably just two wires for the two numbers. Uh and there's some cost for using that machine.

Uh and this is a an approximation or some sort of modeling problem to say well maybe it costs

41:54

something to do with the size of those two numbers and something to do with the size of the number coming out and maybe it's not pounds maybe it's electricity or something suppose that is pounds in the end. Um so people want some people want to use the step one as the last one to work backwards.

42:11

Uh okay let's do let's let's try that one on the left. I suppose the left was me, wasn't it?

And people want to save one for the end. I don't quite know about this work backwards thing, but we want to do this at the end.

Oh, sorry, that's gone off the screen. Just there,

42:26

which will cost as a final step £210. So, where did this where did this 14 come from?

1 plus 2. All right, so we got um Aaron suggesting in chat is the other direction, right?

And occasionally I

42:42

could get the same person to come up with both of these ideas to start with. Maybe we'll save the one for the end or maybe we'll use it uh maybe we'll use it at the start.

Uh so some people have seen the questions before which is a challenge for chat

42:58

where people are parallel processing. Okay, I'm going to let people carry on thinking about this.

Uh maybe they're working backwards to say well where did 14 come from? I have realized, of course, that with one person doing my question, I can use the calculator.

With 70 people doing my question, I cannot do

43:14

the calculator for all of you, which unfortunately means that if you're playing along at home, you might need to do your own multiplication. Maybe we'll finish this one.

Let's work backwards on this one. So if I interpret this as being always

43:30

uh uh doing sort of the largest adding the largest numbers adding kind of from the right uh 4 * 5 * 9 is 180. So this very first step will be to add those ones.

And then

43:46

the total bill here. Oh my goodness.

324 336 2110 is 1,50 at the bottom. 1,50.

Uh so maybe we can do better better than that because that's four figures. Um so over to over

44:04

to you if you're playing this question. Uh that was one idea.

It wasn't everybody's idea. It was a an idea that I sort of worked backwards like this in an interview with one one person.

I would get them to describe that in a lot more details. Not really quite possible over chat with the slideo delay, but you

44:21

know, maybe you've got a different method. Uh let me know.

Keep me posted. Over this side on the triangle question.

This is a stupid way of doing it, but I am having fun. Um over here on the triangle question, uh maybe you have started to work out some I don't know

44:37

lengths or angles. Uh because you know formulas for the area of a triangle, right?

Um you know, what do you know? I suppose you know half AB sin C because it's on the math syllabus.

I think the area of a triangle sort of

44:55

fact. So maybe you're trying to work out the sign of this angle.

That's hard. Uh if you start doing this in an interview, I will try to stop you politely, but I will try to stop you because working out sign C is pretty

45:10

tricky. Uh maximizing sin CB is an interesting question.

So I would try to stop you and I'll try and get you to maximize separately or work out write down a different area formula. So maybe your area formula next would be half a C sin

45:28

b or something. Uh, and there's also half B C sine A.

And actually, all of these are hard. They're just hard to work with because angles are tricky when you have three three points that are just out there.

You might have started by naming some

45:45

points. You might call this A 2, B, B 2, C, C^ 2.

We've got options. If you've already done this question, test your understanding by switching the

46:00

curve to y= x^ 4. That's a test of understanding.

I don't think it's harder. I just want to check, you know, if you've if you've seen this question before and you saw me help you before, uh, then test your understanding.

Here's a different curve. So, I did this question and then got a different

46:16

question. Uh, right.

So someone uh okay so not these not quite a hint but maybe some help that I would give to someone uh is not those formulas. It's quite hard to write this as a math question because if I

46:33

write this as a math question then you really might try and use one of these formulas and it's quite hard to write the question to say by the way don't use any of these formulas for the area. What?

Those are all valid formulas. Why

46:48

can't I use them? Uh, right.

Okay. Meanwhile, in money.

Meanwhile, in money. Uh, I think I've seen a suggestion to try from the left.

I'm going to carry on this one, I think, actually. So, we did 2 plus 3 and then 2 plus No, we did 1 plus 5 and then 2 plus

47:05

6. We've still got three and four.

I think we might do eight and four next. Uh, eight and four gives 12.

uh which is £384. Uh and then there's still three left over, isn't there?

So 3 + 12 finally to

47:20

give 15. Uh 3 * 12 * 15 is 540.

Uh 30 + 9 30 + 96 + 384 at the end there plus 540 is Oh, it's 1,950.

47:40

Good. How are we doing?

Let's add another question. Has everybody seen the 100 factorial question?

I did it. I did it last year.

I kind of do it every year. Let's put in another one.

Um because people here

47:56

people here have now discovered the real question maybe. So somebody said this is it always 1050 and that's the real question.

48:12

And it's a question you're asking, but I'm mirror going to mirror that back to you. Good question.

Is it always 1050? Um, so in uh a test you might just write down, I reckon it's always 1050.

Uh, but

48:28

here we can try and prove that. Uh, and I love getting an element of proof into these questions because if I'm not convinced by the proof, I can ask follow-up questions, which gives the

48:44

candidate more opportunities to explain their reasoning and to explain what they're thinking. So that something that seems obvious to you, if I want you to say a bit more, I can ask you to say a bit more.

Um, there's not a thing for Matt, right? If you type your answer on Matt and it's it's not really good

49:01

enough, you don't really get a popup that says, you know, tell me tell me more. Um, but in an interview, of course, I can ask more.

Uh, I'm not sure you did get £900. Uh, I think it is always 1050.

100 factorial, right? We're running a we're running a three for Here we go.

three for the price of one. Uh,

49:19

the price is free or or possibly £1,50 depending on how you look at it. Uh so this question is stolen is too strong a word but this question is borrowed with love from Cambridge.

Uh I interviewed at Cambridge one time only uh when I was in

49:36

Cambridge. Uh works like this.

Uh it's got several stages at the start. So what I might start by asking you if we're doing it like this would be something like is 100 factorial + 2

49:56

prime uh I'm not even going to wait for you to type that in in chat uh because the followup is going to be is 100 factorial plus 3 prime. Uh quick check.

I don't

50:11

know if this is an international thing, but um factorial here. We sometimes use it on the mat.

It's in the binomial coefficients, but I would check it into view. If somebody said, "What does that exclamation mark mean?" Multiply all the numbers from 100 down to one.

So big product, huge number. Don't work it out.

50:27

Um multiply 1 2 3 4 5 all the way up to 100. All of them together.

Uh no, it's even. Uh and this one is three.

Sorry, three is not a word. It's a multiple of three.

50:47

Multiple of three. Okay.

Uh, keep going. How far can you go?

Is 100 factorial plus 37 prime? That's the number in the thumbnail,

51:04

right? Good.

Okay. Uh, give them a moment to try that one.

Uh, people on the computer question, you've maybe started writing down loads of algebra. And well, that's probably quite messy.

So, probably I'm going to interrupt and say,

51:21

do you think it's true for other sums? Maybe.

Should we check some other sums to see if it's true for other sums? um because some candidates think that it's a special fact about 1 2 3 4 5 being added together and some candidates just intuitively guess that it's true for

51:38

other sums. So I want to get everyone there.

In fact, it's true that it's true for other sums. Uh but I want to get candidates there by by kind of asking do you should we try it?

Um let's find out. Uh because it's kind of good because you can kind of force people to to realize that they don't know and they should try

51:54

and find out. uh in particular if you're trying this uh with algebra I would say uh what happens uh with three numbers being added.

52:12

Uh so if we had numbers uh maybe we call them A, B, and C. Maybe that's not a great choice because they're already in the question.

Uh but whatever. Three numbers A, B, and C.

Uh, there's several different ways I can think of adding them. Several There's several different

52:28

ways I can think of adding those together with this computer. Maybe it always costs the same.

I mean, maybe it costs 10 £1050 £1,50. Maybe it costs that much every time, but maybe not.

Right. Uh, numbers people have got to 100 factorial plus

52:44

100. Uh, these are all no.

Uh so this is 99. Uh let's do a sentence.

Do a sentence. I don't do interviews for English language, I'm afraid.

Let's do a

53:00

sentence. We have 99 consecutive numbers.

Oh, that's sec. No, there is there that is spelled correctly.

There we go. Consecutive numbers.

Uh none of them prime.

53:18

Uh, and I'm going to put some extra caveats in there. Positive whole numbers, right?

And consecutive means in a sequence that's increasing by one each time. 2 + 3+ 4 + 5 whatever.

Okay. Um,

53:35

is there a set of 99 consecutive numbers with exactly one prime?

53:53

So, here's a here's a set of 99 consecutive numbers up to 100, but not + one. Don't think about that too hard.

But here's 99 numbers. You can think about it if you like, but you know, it's a multiple of one is the obvious thing to say, but that's not really saying

54:09

anything, is it? Um, is there a set of 99 consecutive numbers?

And again, I mean positive whole numbers. Oh, this is going to belong.

This belongs over here.

54:24

Consecutive positive whole numbers just in case with exactly one prime. Uh that's your question over that side.

That's significantly harder than the previous parts of the question. Uh that is sort of the idea here.

Um I will come back and help you but I need to know what you're thinking. Uh I know that

54:40

with Slido chat the thing up here is that people only want to put things if they're very confident about them or if they're anonymous. I think that you can switch to being anonymous if you like.

I know that some people have usernames. I think you can switch.

Why have you done this already? I do this every year on

54:56

the live stream. If you've watched a previous YouTube video, you might have seen it.

Um, it's also used been used by I think it's been used by other people on YouTube as well. Um, I think someone told me once that Tom Rocks Maths has used it in a video.

55:12

Uh, or possibly someone else who's interviewing for Cambridge, which would mean they're still using it, which is probably not a good idea. And I feel a bit bad for having put it on the internet every year since then.

Uh, tech issues. So, tech issues.

If you did the special considerations form, then uh if

55:27

you made a request for special considerations, then we'll consider the request for special special considerations. Uh I don't know about 100 factorial plus 101.

Here's this is good. This is good, right?

Because in a in a written test, you would maybe write 100 factorial plus 101 and you would maybe say that's prime

55:45

and I would say is it right? I don't know.

Um, I don't know that's prime. Maybe it is.

Maybe it isn't. But I can tell you it's not a multiple of

56:03

three. It's not very good though, is it?

Right. Okay.

No, because of even numbers. I I want exactly one prime.

Not exactly one not prime.

56:23

I'm sort of not being that greedy, right? Where are we going?

Uh, geometry question hasn't happened for a while. Geometry question.

Maybe you've realized that the area of a triangle could be written as half base height if you cast your mind all the way back to the very first time you learned about the area of a triangle. Um, you will want for this

56:40

to choose a nice steady base for your triangle uh from which to measure the perpendicular height. Now, of course, B is moving around.

So these two sides connected to B are constantly changing. But there is a nice solid base.

It happens to be on the top of the triangle. But if you turn your head

56:57

round, then you can imagine this to be the base of the triangle. I don't think Myro has a rotate option.

So I'm not going to Oh, it does. If you turn it round now, you have a nice solid base of the triangle there.

57:13

Nice solid base of the triangle. Um, and then the question is about moving B around to maximize the perpendicular height, the perpendicular distance away from that fixed line.

Right, there you go. [snorts]

57:29

So, keep going until you find a prime. Right, there we go.

Can we ask the interview to prime factoriize 101 for us? 101 itself is prime.

101 is prime. Okay, they got half side.

They've got an idea about bases now. Um, I don't disagree that 101 is prime.

Uh I think the question that I I wanted to pose

57:46

there briefly was 100 100 factorial plus 101. That might be a multiple of 7,067.

Don't know. It might be this definitely isn't.

That definitely isn't. But if you add them together then as far as I can

58:02

tell all bets are off, right? So maybe maybe is not a great answer to this question.

But people are now saying that people are now saying that you could keep going until you get to a prime. Uh keep going up

58:18

until you find a prime. Uh which is a good moment for us to have a quick discussion about why there are infinitely many primes.

you we are relying a little bit on that fact I think unless you happen to know a

58:34

particular prime number that's bigger than 100 factorial then you're I think relying on the idea that there are infinitely many probably um so you're going to add something on good okay

58:49

uh right keep going till you find a keep going till you find a prime that works that's good uh I am using a stylus I have a very cheap tablet thing that I got during the pandemic. It has held up remarkably

59:04

well. Um, it's one of those graphics tablets that doesn't have a screen.

Uh, it's the thing that makes the scratching noise that plays all the way through the live stream. That's not like a I've been

59:22

told it sounds like I have a sort of small gerbble or something on my desk, but uh some sort of small animal, but that is the scratchy sound of a a stylist that has never had the never had the nib replaced in 5 and a half years

59:39

of Oh gosh. Um okay, it's done a good duty.

Um next question. Is there a set of 99 consecutive positive whole numbers with exactly two primes?

The handwriting got a lot le worse there while I was talking about the handwriting. Uh it is not a whackom.

59:58

Although the second one that I got for myself was a whackom. Just a small one.

Uh if you represent 100 factorial as a gamma function then my follow-up question is going to be what are you going to do with that gamma function?

00:14

Now what I mean you can support what is it gamma of 101 I forget how that works but don't know now what you probably turn it back into factorial right uh or you could go the other way going the other way also works you can go up you can go

00:31

down uh going down you need to use the theorem that there exists a prime number there there exists a prime number so you'll be fine is that why somebody said 67 in chat. That's not why somebody said 67 in chat,

00:48

right? Okay.

Uh we haven't talked about the computer question for a while. Uh let's check in with them.

Uh so I'll just put it on the screen again to see how how's it going. I left you thinking about what happens with three numbers.

And I think I might do that calculation on the screen in a

01:03

second. Um let's read chat.

What are they up to? The theorem that there is a prime.

Yeah, it's like before Uklid proved that there were infinitely many primes. Um, actually ancient mathematicians have known that there exist finitely many

01:18

primes or at least finitely many uh because they had some uh I'm not putting a fourth question up. We are still we have three on the guy.

Um three is three is feeling like too many. I feel like I'm neglecting the middle one.

Um

01:34

yeah, good. Ben and Sophia, hello.

Uh you get the same thing when multiplying simply. Can we extend it?

Um, yeah. Okay.

Okay. Two.

People have got theories about finding two primes. Uh, I've seen lots of people do different

01:51

things. How to prepare.

Um, I honestly so preparation I think might be practice talking about maths a bit. Um, so if you've got a maths question, it doesn't really matter whether the person you're talking to knows what you're talking about.

Um, but practice talking about

02:09

what you're doing or what you did. Uh, I think it helps you with your own awareness of what your problem solving was like.

Um, if you look back at the question you've done and just talk out loud about what you were doing while you were doing it. Um, if you're stuck, try saying what you would do next.

Um, if

02:25

you can get a math teacher or someone to prompt you about what to do next, maybe uh perhaps with a math question where if if there's a math question that you haven't done, but they've got the answer, then maybe they could maybe they could prompt you about how to get through the math question quite quickly.

02:42

Um, that requires them to have looked at the solution to the math question and understood it. And it's quite hard actually to prompt people through.

So, I'm not expecting, you know, it's a skill that we've trained people for and it's sort of difficult. Uh, right.

Can I

02:59

add a dislike button? There is actually an option for dislike.

Uh, there you go. Pretty sure I've turned it on.

There you go. Um, because it's the last one, I'll switch on down votes.

Uh, they don't

03:16

appear on screen. Do I have to refresh?

Oh yeah, popular recent. There you go.

They now go things can now go negative, right? There you go, chat.

We did it. Oh, and I also broke a

03:31

thing. Right.

Technical issues at 6:00. Remember, if you uh There we go.

It's six o'clock. If you've been looking at the screen for the last hour, remember to blink.

Remember to look away. Remember to look at some maths.

No, that's not one of them.

03:46

I'm going to drink some water. Right.

Uh, it's quite hard generalizing from three things to five things. If you've written down ABCDE E, I would probably interrupt.

Uh, I would instead tell you a quick anecdote about how I find it easier to

04:03

go to two things. uh with two things it costs uh and then we know this is like this is a little bit silly but we know what the sum is supposed to be.

It's

04:19

supposed to be a plus b in brackets or something like a single number. Um, so with two things it costs a b a plus oh I'm on to chat a b a plus b which is a 2 b + a 2 and then the

04:38

kind of prompt is where have you seen that before? I'm quite pleased with that prompt because it's really not like a strong hint.

um

04:54

is not very leading. Um but it does lead to I think the right intuition for what's going on here.

Um it does help you get to uh the the kind of mech the mechanism behind the scenes for I guess the question of why is the computer like

05:10

that? What's it doing?

Um same to you. Uh so there's a there's a thing to understand here about where have you seen that before?

What is actually going on here? If I write it out as AB A plus B rather than ABC, what is going on

05:25

there? Ah, I briefly had it set to popular instead of recent and somebody's found out anonymous though.

Most liked comment. Oh, turns out I highlight things negative.

Let me look. It doesn't show it just is that displaying on there for you as well.

It just says less than

05:40

zero. It does not show like how much it enables down votes.

Fun times. Um, oh, but then in my Oh, in my admin panel.

And Cali, can you see this as well? Cali and I can see how many down

05:58

votes things have got. Oh, that's fun.

[laughter] So, if you downvote something that's already been down voted, I've never switched this on before because I thought it would only lead to trolling. Um, but if you downate something more than one, only Cali and I get a

06:16

little counter for for that. fun.

Ah, okay. The number of down votes was six and then it was the number after six.

You can see it. Yes, Cali.

[laughter] Right. Are we having fun?

Oh, right.

06:32

Okay. Have I answered this question of where have you seen this before?

Is there such a thing where you're too good at maths and you never get stuck? Nah.

06:48

If you're too good at maths, then I would expect I don't know. I wildest dream is that somebody has this idea.

I think that's unrealistic, especially in the time available for somebody to work out what's going on and

07:05

kind of do the question the efficient way. um especially because I am in order to make sure that we don't lose time I am spending time at the start to make sure they've understood the question which naturally leads people towards actually calculating

07:20

and you have to discover the real question that's hiding behind the scenes because the question is phrased as how to minimize it and then you start to suspect that you minimize it by doing anything because it's constant. In my wildest dreams, a candidate will then say, "Maybe we should find out what's

07:36

really going on here." And then somehow work it out. Um, I think I said this to they'll get in touch with me if this is not true, but I think I said this to everyone who I interviewed for this.

Everyone who I gave this interview question to. I think we ended up going

07:54

back down to two things. We saw that expression and I said, "Where have you seen this before?" Uh because I need to make sure you don't see it too fast.

Right. Could you do Yes, you could.

Uh right. Okay.

And chat in square brackets. There we go.

Thank you. Cubic.

Yeah, cubic. Uh binomial

08:11

expansion. It's missing the three.

It's got stuff going on. This expression is, and I like this way of writing it, a + b cubed minus a cubed minus b cubed all over 3.

And I think that's good. I would then

08:27

get people to say that in words to explain what that means. Uh, and then we would go back to three things and say, you've got this expression for ABC.

Can you find something like that? What's going on?

Right, when you add A + B and then add C, can you use this new

08:44

formula? It's not as tidy as A * B * C down there.

Look, that's very tidy. It's not tidy, but it is easier to work with.

So, can you work out what what was going on if you write it out like this? Not like that.

What's happening? Right.

Uh primes. What

09:00

if you've never seen this before? Oh, you're not supposed to have seen this before.

This is This is uh Oh, you have seen this before. This is on the math syllabus, right?

This eventually you'll say something about cubing or multiplying a's and b's

09:17

together. We'll get there.

But you really have seen a plus b all cubed before. I'm sure you've you've worked it out yourself.

I'm sure when you know once you've seen that a plus b squared is this a universal experience? Once

09:32

you've seen that a plus b 2 is not just a squ + b squ but in fact has like a secret extra term that you would never guess plus 2 a. Surely it's a universal experience to be like oh I'm a cubit.

What what comes then it's not just a cub b cubed. There's some some magic extra

09:48

stuff right the the true facts out there. And then at some point you learn about Pascal's triangle, right?

Uh and you learn that there's a way to predict what's going to go on without having to multiply everything out. And that's called the binomial theorem which is so

10:03

exciting that it's on the math syllabus. I don't feel like that's an experience that I think people have probably had or at least they've seen the binomial theorem.

Not a square plus b square roo okay. Are you going to do any new questions?

I want to eat dinner. There is pressure on me to do a fourth but we kind of wrap

10:20

some stuff up. Right.

So base times height people, I don't know if there are any of you in chat, but maybe you've realized that you want if you draw on these like lines for Oh, I've done quite well here actually because look um each pink line that's parallel uh gives me examples for what

10:38

the height might be. That's like a height chart.

Uh height away from the base. If B is somewhere on one of those lines, then that gives me those are the points with equal height.

the kind of how the ladder of how high up we are away from that base. So, drawing

10:55

parallel lines. Uh, and I can make this extreme by finding the uh line that's tangent.

Uh, and I've never really got this one to work on uh the YouTube live stream because ideally I want you to say some

11:11

of those words. I'm saying too much, right?

I should I should shut up and listen um and and get the candidate to say some stuff about extremising this by or making it maximizing it by pushing it away from the line and just getting a single point. So a point of tangency and

11:29

then we know loads of things algebraically and now it falls apart and becomes an algebra question and you can do algebra questions right good. Uh that pretty much ruins the well not ruins this one but finishes that one.

Um this one the way you generalize this uh so

11:46

for two things the way you generalize this is is kind of amazing. If you were then to add C the cost for the next step would be A + B + C cubed minus the cubes of the things that you were adding.

12:02

So the general rule here is that the cost is cube of the new thing minus the cubes of the things that you had before divided by three. So if you do this first and then you add on c for this like three step that we talked about briefly a plus b plus cub minus a plus b

12:18

cub minus cubed not quite just a straight substitution but same rule um and brilliantly if you add these there is some cancellation uh where this cancels with this to leave you just a plus b plus cub minus a cub -

12:35

b - cubed and that's brilliant but then that gives you kind of the final Answer should be that the cost is always uh because of that cancellation the cost is always this when you add up all five numbers.

12:55

Uh which is why it's always 150. Somebody likes it.

Thank you anonymous. Um test your understanding.

Um so test your understanding uh is what if I get a cheaper computer? I think this is cheaper.

What if it's What if it What if the cost

13:11

is just a * b? So none of this time c business.

What if it's just a * b? Um, random and amazing.

There you go. Uh,

13:27

random has got more up votes than amazing. Okay, so that's called an invariant.

if you want to look up other problems that are a bit like this but not really much like this if I'm honest. Um invariance are useful in mathematics.

Uh

13:42

because if you can find something that's not changing while everything else is, then you've got a handle on the problem. If you can find something that's not changing while everything else is, then you've got a handle on the problem.

Oh,

13:59

sorry. Back over here.

If you can find something that's not changing uh then over here it's something like the uh what's not changing is it the sums of the cubes of the numbers you've got

14:16

yeah it's invariant as you go through this process there um so you can look that up uh the Oxford student society here is called the invariance because finding invariance is important This doesn't prove that all combinations leads to

14:31

this. Ah right.

Uh so you're right. We haven't quite proved we've proved that if you start from the left then you will get this sum and then uh there's a symmetry argument to say if

14:47

you permute the five things. So you have maybe a machine that will add them from the left.

That's a weird motion to do, isn't it? A machine that will add them from the left.

uh but you can still choose the order that you line them up at the start. Addition is commutative.

So you can take your five things at the top and shuffle

15:03

the order before you put them into such a machine. Well, that's symmetric as a result at the end.

So it means that if I put in uh b c a d e or something like that. So if I shuffle them around a bit uh then so I'm adding B and C first then

15:20

I will get B plus C plus A plus D plus E cubed minus and then each of the cubes in a different order but isn't that so because you can shuffle the order at the start and this answer allows you to permute the letters at the end. It's all okay.

15:37

Uh request to finish the parabola and then we've got to finish the uh primes question as well. So algebra time uh uh parallel to AC we want a line parallel to AC

15:55

uh tangent to the uh curve. Uh so what are we going to do?

Well, we know the gradient of AC which is this and we want that to be equal to 2 * x for for this point x. In

16:12

fact, I'm going to sub in B. I'm going to say so I've differentiated X squ to get 2X.

Sub in B for the coordinate here. I was calling that B.

Um uh and then it's quite nice because this cancels a little bit. Difference of two squares means that this is just

16:29

B is just the arithmetic mean of A and C. It's in the middle.

That's the answer. Which is actually another reason why I can't do that as a pen and paper test because too many people would just write down I don't know.

It's in the middle and I wouldn't know if they'd done anything worth any marks or not.

16:46

You just come on. It's just in the middle.

Like that person in chat ages ago who put a plus c over two and I thought I'm going to ignore that because I don't know whether they've seen the question before. If they've immediately done loads of algebra or if they're just guessing and I don't want to Yeah, I suspect they'd seen it before.

Right.

17:04

Oh, is that how you're vocal? Okay, I'm learning learning today.

Good. parabola.

If you try this with different curves, it's the algebra is a bit more difficult, but not a lot more difficult. So, I reckon

17:19

you'll be all right. Uh, this gives you the the difference of two fourth powers, I think.

Is that true? Yeah, I think it gives you the difference of two fourth powers.

There's a cube on the other side. It's kind of fine.

Difference two fourth powers you can

17:34

handle. It's also the different two squares, right?

And primes. So occasionally people when I've tried this question have told me uh yes keep going up until you find twin primes primes that differ by two and you say oh no we

17:52

don't know if there are infinitely many twin primes. So I don't know if there are going to be infinitely many occasions where you find uh two primes together.

And also worse news, what if those twin primes are actually surrounded by a constellation of even

18:08

more primes? So that even once you found them, oh no, uh it might have some other primes around so that it's not exactly two.

There are these other ones on either side further away. We're expecting the twin prime on the side, but then twin

18:24

primes on their own others. So yes, the rumor says keep going until you find a prime after you find another prime.

But the problem is as you're searching you might see a prime and then lose that one before you gain another one. So the

18:40

question I suppose is if you keep going that way and then do you ever get two? And sometimes people would tell me something vague about um the gaps between primes getting larger, but that's not known

18:57

either because such a fact would rule out the existence of twin primes. And we don't know there's not infinitely many twin primes either.

We we just we don't know either way. Um but moving down so moving down towards zero uh that

19:15

works because well it's not just that there exists two primes but we know there's lots of primes quite close together down there. Um let's try and make that argument more precise.

I kind of want someone to tell it back to me. Ideally someone who hasn't seen this before.

I've done this question every

19:31

year for well I suppose it's everybody's first year. It's everybody's first.

It's my last Matt live stream, but it's it's everybody somebody else's first live stream. Um, hi.

Uh, the argument that I'm trying to get towards is something like here's an interval with no primes.

19:50

If I move all of the numbers left one to smaller numbers, well, that's left for me, isn't it? Yeah, I go left one, then I'll have 99 numbers.

They'll be slightly smaller. Maybe I've got a prime or maybe not.

I'd like to keep going

20:07

until well eventually there are loads of primes down here somewhere. Um I'm looking well I'd like to know is there a set where it's exactly two the number of primes that I've got.

It's the last one because it's the last one on the on the calendar. Um means it's the last one of

20:25

the year. Uh there exist two primes just the theorem there exist two primes wouldn't be enough because as I move

20:40

down when you see a prime but maybe it's gone away by the time you get down to the other prime the fact that you know lots of primes that are close together is kind of important. Yeah.

Yes. If you keep going until second prime, you might Yeah.

You might you might see one and then lose it and

20:56

then see another. The fact that you know three is prime thousand and three is prime.

But kind of that's just too far apart. All the primes underneath 99 multiplied together.

So 99 factorial or just primes apart from one prime with value greater than 50. Then there's a

21:13

gap in the 99 consecutive numbers. Well, I I Is it exactly two primes though?

Because there's some other numbers in there, right? All primes under 99 multiply together apart from one prime with value greater than 50.

Uh it's not

21:29

obvious to me that any of those numbers are prime. Uh you're talking about huge numbers there.

Um two primes with a difference lower than 99. Well, is that is that good enough?

21:45

Again, I'm worried that those two primes that are quite close together, it's not obvious to me that there isn't a third one in the interval. I would like exactly two primes.

So, two that are quite close together. Maybe

22:01

they're very close together. Maybe they maybe they only differ by 37.

In which case, maybe there's another one that differs by more. You said to keep going until I get to ones that differ by not very much.

But maybe there's another one which differs by more but you in there as well. I say less than 99.

The first

22:17

two parts the gap is does that work? Gap is less than 99 because if there's a third in there then that gap would also be less than 99.

So you should have gone to that one instead. Maybe that does work.

Okay, I

22:33

think that works. Is that Does that definitely exist?

Well, you know, there are some primes where the difference is less than 99. You know, there some where it's not.

So, in between, you know, there's a case where it was like the last time that it happened. Finite interval.

Yeah, sure. I'm having that.

Good. It's not what I thought you were going to say, but yes.

22:50

Uh, good. I liked that.

That was that that felt novel. I felt like I talked too much and I read I read one chat message and then talked too much, but yeah.

Okay, cool. The formulas are hard.

Uh from 1 to 99 there are 25 primes and you can only go

23:07

up or down one prime at a time. Yeah.

So as you move three things might happen. Kind of four things might happen.

You might gain a prime, you might lose a prime at this and you you might gain a prime. What am I saying?

You the proposed shift is something like

23:25

oh dear let's draw this. The proposed shift is that we shift left one in which case you might gain a prime.

It might be a non-p prime and simultaneously over here we might lose a prime or it

23:40

might not not be a prime. So I don't care.

Uh last one is uh don't care. Um so my emotions about how many primes we've got, right?

We might gain one, we might not. We might gain one, we might not.

And then sorry, I've got to lay it out carefully, haven't I? So then there's

23:58

the other cases that we might lose a prime. I'll try to do all four combinations.

or we might not care. We might not care.

Uh and in that first case, we gained one and we lost one. So overall, don't care.

That's like plus zero for primes. In the

24:14

second case, well, I didn't gain one and in fact I lost one. So number of primes has gone down by one.

In the third case, we gain a prime and we didn't lose one over here. So we actually go up by one.

24:30

And then in the in the last case, true neutral, we didn't gain the prime. We didn't lose one, so no one minds.

But the number of primes can only go up by one or down by one. Which means that if it goes from zero out there at these huge numbers on the screen, zero all the

24:45

way up to like 20 something. When you have small numbers, then at some point in between, it's only going up or down by one.

It can't skip two. So it can't skip the number two.

Good. Right.

Thumb. Okay.

Let's do some Q&A. I think that's the right way to go.

If we had three

25:01

interview questions in parallel, which was a fun way to do it, if not meant the most effective way. But, you know, in a real interview, I would only do one questions at a time, but I'd only have one of you at a time.

So, [laughter] maybe this was a good way at splitting the audience into separate activities so

25:20

that you weren't all doing them. I don't know.

There's something in this, right? Give you six questions, maybe multiscreen.

See what happens next year. Twice as many questions.

Don't hold me to that. Six questions.

Off we go then. Choose

25:36

your choose your question. I mean, that's not how interviews work, though.

I would never like throw six questions at someone, right? Uh, if we don't get interviews, are we disadvantaged for applying to study master Oxford?

No. We will in the nicest possible way forget all about your application.

Um, we we

25:54

don't even link them if you were to apply for undergrad again. um we don't connect applications together like that and I mean I I do talk to the people on I mean the people who do masters applications they they are in a different office and I talk to them like

26:09

in the kitchen but I don't talk to them about applications where to apply for masters uh oh the end of the computer question yeah didn't quite finish that can you show how any permutation of five can correspond to one sequence building from the left yeah sure okay

26:27

I do want to change the layout. I want I'm just trying to change the layout a little bit.

So one way of adding is like this. Okay, which is um a plus b plus c plus d

26:43

plus e cubed minus a b cub cub d cubed and e cubed all over three. Um and then a different way of adding them is to rotate them first uh and then add like this.

So this is adding them in a different

26:59

order. I suppose I need to go one better, don't I?

So I let people do this in the interview and I'm now remembering that actually it's a little bit harder than that because you might do a branch. Thank you for doing this.

I didn't hold

27:14

people to this in interview. You might add a pair and a separate pair.

My dream for this really, which I shouldn't talk about dreams too much. My dream for this really, which I didn't really hold people to in the interview,

27:30

would be that we would actually talk about how the computer assigns a value to different numbers, to different inputs and outputs. Um, so it's sort of taking your raw materials, the numbers one, two, three, four, and five, and it's

27:46

charging you for those raw materials when you use them. But the um the value of intermediate products always gets cancelled out when a number is produced by a process in here.

So as the computer adds whenever a number is produced like

28:03

nine or five over here whenever a number is produced it will later be consumed unless it's the final answer. Um and the production involves a term that is plus uh the cube of that number over three

28:21

like this a plus b cubed whenever it's produced and the use of a number whenever it gets consumed uh has a cost associated with it of minus that number cubed over 3. That's where the separate terms of this expression come from.

the positive

28:38

product a plus b cubed over three and negative the inputs a cubed and b cubed separately over three. Um and because we're going to keep going until we get to one single number, every intermediate thing we produce is also consumed.

So every time we have this like plus 9

28:53

cubed over 3, we also have at this step here where the 9 is being used, we have - 9 cubed over 3 plus a new product which is also doomed until we get to 15 cubed over 3. You can tell the story to say it doesn't matter how you combine them together.

Everything you produce along the way, whether you did it in two

29:08

pairs or as a separate snake of numbers, doesn't matter. Anything you produce will be consumed until you get down to the final answer.

Cool. There's more prime stuff in there.

Let's have a look. Uh, yes, I don't think any maths or joint

29:24

honors or math and philosophy or computer science and philosophy interview invites are going to go out before Monday. Um, if a college is really prompt and if some admin processing happens extraordinarily quickly tomorrow, then I guess technically Friday tomorrow, but I don't

29:40

think that's I'm I'm not even going to say that that's going to happen. And then it can be a nice surprise if it does, right?

Okay. Uh, lower bound is not the one I often get asked about an upper bound, right?

Where we try and give people a week's notice for interviews, but we're better than that usually. uh

29:58

our math and CS short list created together or independently uh together we we work together but we have um we have separate uh intake numbers for how many places we've got uh and we have separate short list we consider the applicants

30:15

what do you mean together independent we consider the short lists separately because they've applied for different courses so we look at the applications separately for the courses they've gone for but we work together and we say we look we have a spreadsheet That's got everybody in, right? But we

30:31

we know they're applying for different courses. What does it mean if you get your invite earlier?

Uh thanks for shouting. Uh that got my attention.

Uh it means that your college uh sent the email out earlier. Uh there are 29 different colleges that admit for maths and they are each responsible for

30:47

emailing candidates. Uh they don't all do it at the same time because there are 29 people pressing go on emails.

It doesn't mean anything about you. It hardly means anything about them.

Good number of applications. Have we published this?

I don't think we

31:03

published this. It's not an unusual number of applications.

Not like I'm not going to give a number, but it's not. If I told you the number, you would immediately lose interest.

We publish the number every year. You

31:18

can look previous years. Do interviewers prefer logic to something like cal?

Interesting question, isn't it? What have I done?

Done a question with a bunch of logic. I've done a question

31:34

with some calculations. I've done a question with some calculus, if that's what calc.

Why does the MSC I I don't do admissions for M's courses. I definitely don't do course fees for M's courses.

the mathematical and computational finance £50,000.

31:56

Has the meme math score? I'm definitely not doing me at that school.

Sorry. Any colleges harder to get into?

Um, my friends keep telling me I've applied to the hardest college to get into for maths. Um, each year some colleges have more

32:11

applications than average. Uh, there are maybe some patterns, but it's a bit transient.

It changes for most colleges their like number of applicants changes year on year quite a bit. I would not be comfortable advising applicants based on those numbers because it changes how

32:28

many applications they get. Um and also we have lots of processes to make sure we're taking the best students overall.

One of those is the second college interviews that I talked about where oh I didn't write it on the board. I zoomed in.

There's nothing there. um the second college interviews that I made sure made

32:44

that I talked about so that if a college does have lots of strong applications then sure just mathematically that means that uh there's more competition for places at that college but good students who have applied to that college might get taken by other colleges

33:01

instead and that means that overall I'm pretty sure it's it's fair so that whichever college you've put maybe you'll get that college but if like if there are 20 people who deser deserve to be at Oxford and they've all put that college then there isn't room at that college. Uh so

33:17

maybe that's maybe that's what your friends meant by hard to get into that they looked at some ratios or something. Um but that's not the end of the story for those 20 people.

Um some of them in bedrooms of that college stay at that college accommodation in first year at least. Uh and

33:34

and either third or fourth year usually anyway what [laughter] check the colleges for accommodation offers. Anyway, whatever.

um colleges where you live in first year, maybe some other years is is an important part, but lots of them get offers at other colleges. normally in

33:50

that hypothetical situation. Uh which then this is weird effect where once they've made friends at their new college uh once they've got to know the tutors at that college and done some

34:05

maths with those people uh they sometimes realize that they were at the best college after all. Yeah.

Okay. Okay.

Thanks Steve. So numerically Worcester and St.

John's

34:21

I think got the most applications last year. I don't know how that's supposed to affect your decision making this year.

Like if you want to study at Worcester or St. John's then you you kind of put those down on the form and then if you're strong but they don't pick you and this goes for all colleges.

34:37

If you're strong but they don't pick you then second college. Will the interview be friendly or put on a harsh approach?

That's a good question. Um, I try to be friendly.

Uh, but I am also trying to ask trath questions which some people don't enjoy at all. So, I try and do my best.

We're

34:55

not trying to scare people. I am getting mathematicians to do these mostly.

Am I getting to do these? Colleges are getting mathematicians to do these mostly.

I don't employ them. I'm certainly not paying them.

Uh, colleges find interviewers. I think

35:10

harsh approach is too much. Should I do maths if I am scared of competition or apply for a less competitive course like engineering?

Well, hello. Um, I think you must be applying next year or something.

Um, so welcome to talks with math liveream. Uh, I said it was the last one.

I meant this year. Uh,

35:27

I have bad news about engineering. Um, but let's save that because I think doing a course that you want to do is probably more important than doing it at your absolute top choice university.

I don't know, maybe I'm wrong about this. Um but I think if you want to do maths

35:43

then turning up to engineering practicals and doing all the engineering certification and learning about material stress compounds I just worry that you won't like it. uh and however competitive it might be for different universities.

Um at the

36:01

moment my belief is that across the sector if you want to do maths and if you've got good grades then lots of universities uh will take your application right okay uh are we going to be increasing the

36:17

places uh there has been a rise in the number of uh computer science tutors at Oxford recently which has led to a rise in places for things like maths and computer science andor computer science. It's a bit hazy on the two of those at

36:32

the moment. Um so the number of places has been going up.

Uh not quite as fast as the applications over the last 15 years been going up. Uh but we have now got a bit of motion on that.

I believe that uh which college is it? Is it Wom?

I think

36:48

Wom is offering computer science this year having not offered it before. There's like the number of colleges offering computer science is going up which is kind of exciting.

They're now at I think 26 doing some varieties of maybe just maths, computer science, but 26 out of the 29 that do maths. Pretty

37:06

exciting times. First app next year.

Check check the list, right? Numbers true as of 2025, right?

Good. Okay.

Uh I'm going to scroll a little bit. Shall I look at top questions?

Let's look at popular. Quick look at top.

Oh, look. It's Steve at the

37:21

top. Uh bound.

Still no leaks. A blessing.

Still no leaks. Oh, sorry, Eric.

Uh, so random. This was a different person before.

37:37

This was a different person. They're changing their username to be anonymous but with different usernames.

Uh, Timur advice. You come to the M live stream, you get advice on TMUA.

There you go. Uh, how did you get a formula?

How do you generalize it? That's kind of sticking

37:53

together. We know had a couple of looks.

I haven't told you the answer for a time b, but maybe you've started working out some expressions and seeing where have you seen AB before. The expression AB before we saw it was something to do with cubes.

Have you seen anything to do with squares? A will the interview have

38:09

any further not content? Could do uh last one I missed the tamua.

Do people say tamua or tmua? I say both.

38:25

Matt live stream come to the official place you're like let us know what's going on. Uh oh should build a new college new college too we should call it um for undergrads number of applications keeps

38:41

increasing. Yeah I'm not opposing that.

Sounds great. Sign me up.

Uh yeah sounds sounds good. T.

That's what I say. Tamua like there's

38:56

Okay. Like it's short for the Yes.

Okay. I said to Yeah.

Tu has got a Greek letter in the middle, hasn't it? That's fun.

Okay. TM UR.

39:14

This is fun. And we've now entered the phrase where we've now entered the phase where James is reading out chat messages without thinking about what they say.

So, I'm going to stop doing that. Right.

Okay. I'm running out of content, I think.

Uh I'll show you an interview question that

39:29

I didn't I decided in the end it hadn't gone that well. Um partly to give you the context that we're interviewing people multiple times.

Not all of them I I say not all of them do I learn something. Um, sometimes I do

39:45

an interview and I decide didn't really learn very much there. Um, there was a year a few years ago where I did a question and I wasn't very happy with it in the end in the in the way that uh in the way that went.

I guess I'm doing this so that you know that

40:03

well obviously you're trying to do well at things in your interview. In some sense so am I when I'm coming up with an interview question and then using it on people.

Uh, and because we're interviewing multiple times, there's this effect where it's not the

40:19

end of the world if I take a risk and it doesn't really work out. Uh, maybe I'm saying this so that if someone has a terrible interview with me in the future, they can be shown this clip of video and say, "Well, he's probably screwed up again then, hasn't he?" That's probably just about him, not you.

40:37

Right. Uh, here's the question.

I wanted to ask people about an eclipse. uh where you have maybe a moon that is smaller than the sun.

You know, famously our our solar system, the moon looks the same size as the sun. So, it tends to block out the whole sun.

Um but there's

40:55

this thing in physics where you're um you're looking at the light you're receiving from a distant star. Maybe color this in a distant star as something moves past uh some sort of moon.

uh and the light that you get from that star dips because

41:12

the moon has got in the way uh until eventually it leaves. And the question was, can you sketch a graph please of the amount of light that we get from that star?

You know, there and then it's down a bit and then it's up a bit. Uh so people would draw something like this

41:28

and then they join the dots to make this kind of bathtub shape. I think some people even do this in physics or something.

So already people thought this was a bit of an odd question because I think some people in physics draw this um and oh look IPA

41:45

they can't do titrics you can't do um the corrupted text if you've applied for a joint honest group. Oh hang on there are serious questions going on.

How is second college chosen? Uh random algorithm.

Don't overthink it. Uh I'm we use it to

42:01

kind of move people around based on how many applicants there are at different colleges. It doesn't mean we don't take into consideration your preferences.

Sorry. Uh apply for joint honors degree.

Uh if it involves philosophy then you might expect some philosophy interviews

42:16

as well as the other half. If it's math and computer science then they might be combined together or they might be separate uh separate degrees separate interviews.

I have not seen the dust this with two squares. A1 is rotated 45 degrees.

I do the graph. Anyway, the the

42:32

thing I wanted to do was to talk about the shape here at the corners where it's not actually sharp. Now, unfortunately, actually doing that calculation involves thinking about the area.

We've done this, I think, on the show

42:48

before, the area of intersection between two circles, which is really difficult. Uh, it's one of those calculations that I think I got everyone to do in the Matt live stream earlier where we had I think two equal sized circles and that was hard enough.

Uh, they were nicely spaced

43:03

as well, but still finding that area in the middle was tough work. So, I gave people a kind of different uh question.

And the thing I think I was unsuccessful in really was in convincing people that this was at all the same question where

43:22

related at all where from the side view you could imagine that this is um if the moon is much much smaller. I'm going to set them back to being sun and moon.

Um if the moon is much much smaller than the star

43:40

then you can approximate this situation with a straight line for the sun and a parabola for the moon where the moon uh moves up and down

43:59

uh and then you can find the area by integrating that parabola. So we would set this up as like x^2 over a perhaps for this kind of shape of that kind of curved section of the moon like this.

You can sort of approximate it with a parabola and approximate the sun with a

44:14

straight line. I don't think I did a great job of convincing people this was a sensible thing to try.

uh but then we would do the sum uh and then we would get a result uh and that would tell us that would tell us some area and then the challenge is to remember what we were doing and what I want that to be uh

44:31

as a sort of halfway step people often had to draw the graph of x to the 3 over2 I've set the pen to be comically comically thick

44:47

comically thick is also my the act that I'm doing sometimes for talking about how not to do questions. Anyway, uh I have to sketch the graph of y= x 3 over2 because that's the answer.

The the curve the way it curves in is

45:03

like x 3 over2 but reflected twice or something. Uh people were surprisingly bad at this.

I'm never going to do this question again, but you might like to think about how to sketch x to the 3 over2 because people were surprisingly unprepared for doing that. I like a

45:19

graph sketch. Uh I'm never doing this one again.

You might like this. I prefer the expensive calculator.

Me too. The expensive calculator was fun and people actually at the end felt like they'd done something.

Whereas this one, they kind of drew it right the first time and then I went, "But what if this was a

45:36

strange technique for discovering exactly exactly approximately what the corner like? I know it's a good approximation, but I never really convinced anyone it was a good approximation." So, oh well.

Did I

45:52

do straight edge? I might have even done two parabas, which would be a bit insane, but the star surf is also a parabola.

That's a bit That's a bit silly, right?

46:08

Maybe just x squ plus a. What did I actually do?

I did I try I did not love doing this question anyway. Right.

Good. Okay.

Anyone apply for oral? There we go.

Yes, from my side I can confirm. Yes, some people did apply for oral.

How do you

46:26

make sure you ask a question that candidates might have seen before? I try to invent my own things um or remix things uh or just disguise things uh or make things weird or mash two things together.

Um if I ask something that I think people

46:41

might have seen before, I asked them to tell me at the start. What's my favoriteest interview question of all time?

I mean currently recency bias but I do think the calculator one is strong. I

46:58

haven't really done the debrief right where you get to see people form the hypothesis form the idea. There's this moment in the interview where they realize that maybe it's the same every time which is nice.

Uh and then we get to sort of prove it. I have to help but

47:14

there's some stuff going on about how you might try and prove it. I get to see them do some algebra.

So, I get a bit of a sense of have they ever cubed a plus b a plus b cubed. Have they ever done that before?

If not, I'm a bit surprised. But, you know, to get to know how much

47:30

familiarity they have with some core bit a bit of core content and then depending on how much time we've got, we get to get into this kind of like why does that always work? The kind of in words description of what's going on.

um let's not use the phrase word problem,

47:45

but this starts as a block of text that you need to interpret. It turns into algebra and then by the end I would if anything quite like some description in words about what was really going on all along.

Um turn it back in. What if you

48:01

have seen it before? Please say.

Uh and then we'll switch to something else. Uh yes.

Right. Good.

Okay. Um, right.

And you shouldn't be people using the down vote for subject or college.

48:17

That's rude. This is why I don't do down votes.

I'm switching them off. Just being mean.

You mean to the philosophers. They will, you know, they have the power to cause things to exist, right?

They say, I think, therefore I am. So maybe they

48:33

also have the power to make you am not. Uh, right.

What was really going on, right, was this cubes thing. The computer just likes cube numbers.

It wants to charge you based on cube numbers divided by three. You ask it to add together two

48:49

and three and it says the number two and the number three. I love these.

And then it has I have to give you the number five. No, that cube is much larger.

Five is my favorite because five cubed is huge. I will charge you 30.

is 100 take away 4 take

49:05

away two cubes 825 take away 8 take away 27 divid by three yeah factor of three I think therefore I am

49:20

right interviews are tense otherwise cool but on the prime number one I've got 10 minutes oh I do need to go in a minute uh let's do the prime number one really quickly Any other questions? But I feel like we're I feel like we're exhausting the questions very quickly at the end.

Um I

49:39

this mini interview question in a way. Uh I did this in a video with New College semi-reently.

I guess this is something about me that I use everything multiple times. Sorry.

Um so suppose

49:55

P and Q are prime. uh given PQ and P -1 Q - one how could you find

50:13

the values of P and Q. This is based on a throwaway comment I saw towards the end of some number theory notes.

So, I mean, possibly someone's read lots of number theory notes or maybe they've thought a lot

50:28

about RSA, but they've thought quite a weird question about RSA because in RSA cryptography, um, this is something that you publish and this is something that you don't publish. Um, so if you publish both, then presumably somebody can work out P and Q.

Now, but the question here is how? Um, what on earth would you do?

50:46

Uh, obvious answer is factoriize both. Well, that's hard.

Um, if I could factoriize numbers, I would only need PQ, right? And then I would factoriize it and I would know the primes.

Um, so I'm not going to let you factoriize

51:01

both. Can we do something else that doesn't involve factorizing you count the factors or something then you know?

Oh no, that is five then over there, isn't it? I think that's what you're saying.

Maybe this is the number of things that are co-prime that whatever not relevant but true but not

51:16

relevant but the question uh from the interview will we have a good idea if we get in say if it goes well. Uh personal experience.

Uh no, you'll have no idea. Um I thought my interviews were terrible interviews.

I thought my interview singular was terrible. Um halfway through my

51:33

interview, I tried to simplify 5 ^ 4 / 6 ^ 4 by crossing out the fours to give 5 over 6. This was corrected because this is wrong.

In an exam, I would write that

51:48

I would never see it again and I would lose a lot of sleep. In the interview, they stopped me.

They corrected me and then I couldn't do the question. So, I did lose quite a lot of sleep, [laughter] but then I got in.

So, you know, I did

52:03

something else. I suppose we couldn't do that question.

So, we switched. Uh, find the difference.

Ah, the difference is interesting, right? So, the difference between these P minus P minus Q plus one.

difference. Oh, handwriting's gone.

I got to move

52:20

the pen to the right as you do the different letters. Uh, difference is P plus Q minus one.

Nice. I like it.

What? Now what?

So, we now know well, we know three things now. I suppose we know PQ.

We know still know P - 1 Q - 1. Now we know P plus Q minus one.

What else?

52:35

Almost there. Uh, have I dealt with an event?

How did I deal with rejection? That is slightly too personal.

I think I'm going to keep that one to myself. Uh

52:51

but the advice I would give you is that short term everything sucks. Um short term things are terrible.

Uh medium-term you find a different way. You find a different way to get towards the things that you want.

Uh and then long-term

53:10

almost entirely unaffected by the short term. Uh, in context here, that might mean interview doesn't go well, sucks, feels terrible for a long time.

Uh, maybe that means you don't go to Oxford, maybe it means you do go to Oxford, whatever. Medium term, presumably you're going to do math at university

53:25

somewhere. I think you'll have a good time because you've just watched two hours of maths content in a random assignment of things.

Um, I think you'll like the structured stuff a lot more. Um, long term, once you've got your maths degree, there's a lot of stuff you can do with that.

uh not necessarily

53:42

maths, but like loads of things where eventually it's not even going to matter which university you went to. Um I know at the moment it feels like it really does, but I'd say longterm it depends more on you than it does when you're university.

Uh it's not the old days anymore where you

53:59

just turn up to a job and say, "I got to Oxford as I imagine it happening in the old days." Um have more of an impression these days it's not like that. Uh right.

Simultaneous equations gives a quadratic. Yes, go for it.

What's blue

54:15

say? Uh P plus Q by subbing in.

Yeah, some quadratic stuff. We know P plus Q and we know P.

We know P plus Q and we know PQ. We can solve these.

In particular, we can write down a quadratic. So let's call this uh D+1.

This is the

54:31

difference. And I'm going to add one.

So going to call this D plus one. And we can write down let's call this A and B.

We can then go and solve this quadratic equation and we will get the roots P and

54:46

Q and then follow up was to do this with with um more numbers which is a bit of a silly way of changing it because if you change the number of numbers it's got nothing to do with RSA kind of doesn't really any anyway but yeah good right good fun yes once you get you can you

55:03

are at the top there developing the quadratic formula I think once you have P plus Q you can square and then subtract four times PQ. Uh, no, wait.

What am I doing? What did you say?

Uh, D minus one. Oh, was this P?

55:21

I think this is a minus sign with a circle over it. Yeah, it's a minus sign with a circle over it.

I'm really sorry. So, this would be D plus whatever we're calling the the constants.

Point is, you know, these coefficients in the quadratics.

55:37

I've done the algebra terribly there in a hurry, very excited. If I were being interviewed, my interviewer would now say, "What's D?

What's D plus one? What are you doing?" Um, and I would say, "Oh, yeah, this difference is D." And maybe I mean D minus one.

No, I really do mean plus one

55:53

to get the P plus Q up here. The D+ D plus one for sure.

People are going to do this now, aren't they? Whatever.

Right. Good.

I like doing these live. Occasionally we do like a pre-record where I interview a a student

56:09

or something or or a non student or like we do a sort of mock interview. Occasionally we've tried to do those at events.

I like doing these online on the internet. There's a lot of you and it's all in parallel.

People squaring that and subtracting 4

56:24

pq gives you p minus q ^2. Don't need a quadratic.

Yeah, make your own quadratic. and then you subtract that you get P minus Q and then you've got simultaneous equations to solve which will involve adding together those things and dividing by two there's the two in the quadratic formula right

56:40

downstairs you write down the quadratic formula right in some sense uh checklist for the interview we actually got selection criteria uh they're not very detailed but um uh we're looking for people who can let's see if I can memorize them no

56:56

let's Google them This is the interview prep. You've already had it.

I don't really have anything else. This is all I got.

Uh selection criteria for mathematical sciences admissions group. Uh we're

57:13

looking for stuff like this is really tiny writing, isn't it? Uh this is a bit of we haven't updated this in actually ages.

Uh except I fixed a thing about whatever. Um online interviews.

Uh we will look at what does this say we

57:30

will do aptitude technical skills capacity to absorb and use new ideas ability to think and work independently though we are going to help where needed perseverance and enthusiasm and we know that enthusiasm looks different in different people um but we've got

57:47

obvious things that we're looking for really uh I like it when people can do the question without um me doing the question for them I can check for that by asking I can't follow up to see if Okay, once we've done it together, can they do it without me? Bit like on course really.

Like in a tutorial, we do

58:03

it together and then I think, yeah, but can you now do it? So, I give the student one to do.

Uh, and uh I like it when people seem to understand what's going on a little bit as well. Um, that we're not just doing the calculations.

58:19

So here when we make a meal out doing the quadratics together then we might lose track of what we were trying to do which is maybe a thing about quadratic equations but maybe it's also a thing about just keeping track of what we're up to. Uh yeah yeah yeah it's kind of based on

58:35

RSA the question because PQ is a thing that you would calculate. You would keep your primes P and Q secret you would release the product.

Hope they can't factoriize it. hope there's no quantum computers.

Uh andor hope that the quantum computer is not very good at this. Uh good luck.

Um

58:52

you personally have to calculate P minus 1 * Q - 1 to do RSA. You have to keep that secret because if you release it then people will use just quadratic equations to work out your primes.

Not even any factorizing, not even any quadratic civ or any quantum computers,

59:09

just quadratic equation. Um, so don't do that.

Don't release that number. You get, you know, we got some RSA advice out of this in the end.

Also, don't do RSA yourself. Don't code it up yourself.

Knowing what RSA is is

59:25

all sorts of mistakes you might make while trying to code up RSA that other people have thought of. Uh, right.

Thanks. That was that was the Matt Live stream 2025.

Um, uh, if you got an interview, you are

59:40

part of the way. I would say halfway there on a log scale.

I'm sorry. You've done one thing, which was math emissions test.

Time for another thing. Halfway on a log scale.

That's such a stupid thing to end on. Right.

Good. That was my live stream.

59:56

Thank you, Cali, for gosh, two hours of whatever that was. Um, thank you everyone for joining in.

Um, if you've got an interview coming up, you'll find out uh relatively soon and uh wish you all the best of luck with that. If you're watching along because you're applying next year, then guess I might

00:11

see you next year in things like open days or online videos like this one. Uh if you're subscribed to the channel, you'll get uh notifications about what we're up to.

Uh this is our second channel, Oxford Mathematics Plus. Um we have a main channel called Oxford Mathematics without the plus uh which

00:28

does v videos of our current faculty and students and staff and people talking about maths and also has some recordings of actual lecture videos including these days we're uploading entire courses of lecture videos uh that you can watch along uh so you can see some content if

00:44

you like. Some of it's extraordinarily difficult um but that that's that's hasn't stopped us putting it on the on the web.

Uh we have a project in January which is called Oxford online maths club. Uh when we started this we thought

00:59

it was for year 13 students bridging them between you know math is done for them bridging them to university. It's also turned out to be quite popular with year 12 students and younger students.

Um, so if you know anyone who might be applying next year and they want to see

01:15

some supercurricular mathematics, so extra stuff that they might talk about, universal statement, a little bit like the kind of maths YouTube space, but we're doing live videos like this one. You could let them know that this channel exists and we're going to do Austin online maths club starting in

01:31

January. There's a dedicated website for that one.

A bit like we have the mat live website. If you put club on the end after the r slash uh or if you just search for online math club uh there's no need to register or join or sign up.

It's just another series of YouTube live streams with a slightly different color

01:48

scheme. Uh that's going to come uh that's going to come uh in January.

Uh we'll run that uh and maybe I'll see some of you there. Uh otherwise, as I said before, uh if it all goes well,

02:04

I'll see you in Oxford. Otherwise, uh I think you'll probably signed up to do maths somewhere.

Uh maybe I'll see you for master's study. Maybe not.

Uh I wish you all the best with all the maths that's going on. And as always, have a good evening.

Have a good weekend.

02:21

Right, we did it. There we go.

Uh yes, I think I now just switch it all off, don't I? Yeah.

Right. It's been fun.

See you around. Take care.

Uh, yes. Gosh, I pressed this one.

It

02:38

has been a couple of weeks. No, we're going to hold this for a moment.

Okay, boys.