[User] Please transcribe this text

[Assistant] I think that's true for me, it doesn't mean the door wasn't there for me, I just didn't open it at uni. Some people got that, even alongside me, they were like, I just love this stuff, and they went into academic maths because they wanted to get more of it.


[User] Please transcribe this text

[Assistant] I didn't go through the door, maybe. Your metaphor is like, that door is there, and it's even there at school.


[User] Please transcribe this text

[Assistant] But maybe having the teacher point out, like, that, through that door lies playful, adventurous maths. And through this door is, you're gonna get an A, because you do what you're told.


[User] Please transcribe this text

[Assistant] And you can go both directions at once, but I didn't notice the tinkering aspect of it, the ask your own questions aspect of maths, until I trained as a teacher.


[User] Please transcribe this text

[Assistant] And I'm very glad I did because it gave me massive more motivation to do a difficult job of teaching and something which has lasted now, like sort of motivation just to play with bits of maths that interest me.


[User] Please transcribe this text

[Assistant] I mean, every story about anyone who's successful in some bits of their life will probably credit someone who inspires them, but there were teachers at school who taught me well.


[User] Please transcribe this text

[Assistant] Expert in combinatorics and knot theory and probability, but also, like, had been around, like, he knew Professor Tolkien, you know, the guy that wrote the book, the Lord of the Rings book, so at Merton College, which is where Tolkien was as a professor.


[User] Please transcribe this text

[Assistant] Dominic Welsh had been there briefly overlapping with him and, you know, things like that, uh,


[User] Please transcribe this text

[Assistant] We're just great. I feel lucky to have gone to places where that sort of thing happened. But he was also a great tutor and a very human tutor and


[User] Please transcribe this text

[Assistant] He bucks the trend, which was around me at Oxford, of this super academic pressure. Dominic was...


[User] Please transcribe this text

[Assistant] She, she wrote lots of stuff about maths education, but she was also a really good course tutor.


[User] Please transcribe this text

[Assistant] It kind of changed my world view that year. Maybe it dragged it more idealistically left-wing than it should have done, but yeaah, you've got to be dragged towards extremes in order to balance out, right?


[User] Please transcribe this text

[Assistant] No, he did engineering. Actually, he did an environmental engineering degree.


[User] Please transcribe this text

[Assistant] He was determined not to go to Oxford or Cambridge. Like, this is part of the reaction I talked about earlier.


[User] Please transcribe this text

[Assistant] If we saw each other doing things, we would diverge. I can't do that, that's what Tim does. Okay. I can't do that, that's what Ben does. So, and he was really resistant, a little bit like I was, to the idea of going somewhere with a prestigious name like Oxford or Cambridge. He didn't even apply, although almost certainly could have got some offers.


[User] Please transcribe this text

[Assistant] Also, maybe there's a theme here, uh, he didn't pay a lot of attention to his degree and did lots of music.


[User] Please transcribe this text

[Assistant] But his was playing guitar and singing on the open mic scene, had a little band going. I actually remember going across to Cardiff to do a gig with Tim. I think we caught ourselves, there were two other guys, we had a band called Short Straw.


[User] Please transcribe this text

[Assistant] On stage, I think it just looked a little bit like a farmer's hat. Right. And then combined, combined with short straw and like, everyone was like, these are a bunch of sort of dorset yokels trying to sing. So he did music stuff and ended up, uh,


[User] Please transcribe this text

[Assistant] Not for want of talent, but just want of appreciation.


[User] Please transcribe this text

[Assistant] That's what it was, yeah. Tim did engineering though, and as a result of not enjoying his course, decided not to do the fourth year, which is quite common on engineering degrees.


[User] Please transcribe this text

[Assistant] I think they were interested in keeping him in there because he was probably doing well, he just didn't really enjoy it. Anyway, he decided to carry on because they were going to pay him to do a PhD, a graduate study thing.


[User] Please transcribe this text

[Assistant] And, uh, mainly though, I think because he could stay on the open mic scene in Cardiff. So he stayed for another three years doing a PhD and I think hated it. But there was a conversation sort of 10 years later, uh, where he was finishing off his PhD. I'd gone back to study at Oxford again and we ended up talking on the phone and he said, oh, what are you, what are you studying today?


[User] Please transcribe this text

[Assistant] I was like, ah, I'm trying to figure out Navier-Stokes equations and how they sort of relate to fluid dynamics.


[User] Please transcribe this text

[Assistant] And he went quiet and then, uh, and it's like, you realize I'm re- I'm reading that exact page right now in my textbook as well. So we, we'd come full circle and that was one of those crazy twin moments of like, we're doing exactly the same thing. 10 years after diverging, we're back studying the same stuff.


[User] Please transcribe this text

[Assistant] He works as a music teacher and a web designer and a general freelance oddbody.


[User] Please transcribe this text

[Assistant] Is a dangerous thing. I didn't intend to go there. It was one of those things during the PGCE from about halfway through you start applying for jobs because you need a job and you know, there's only one way to practice doing the application things. And one of the first jobs I applied for, because it came up at the time, was a job at the school I used to go to.


[User] Please transcribe this text

[Assistant] And I thought, well that's a good way to practice it. And then I got off of the job and I was like, do I want it? And I think it's a sign of a decent school experience that I even considered going back there. And I did decide to go back there and I figured that...


[User] Please transcribe this text

[Assistant] Maybe that's a good place to learn my trade as a teacher in a place that has some familiarity without, you know, there's plenty to learn as a teacher. So I did two years there.


[User] Please transcribe this text

[Assistant] What is interesting, I think I had left it just long enough that there were no pupils who were there still while I was a pupil. I'd left, you know, one generation through the school, so that was good. But there were quite a few teachers that were the same.


[User] Please transcribe this text

[Assistant] And that was a mixture of good and weird as hell. I could do all sorts of teacher stories, but they're probably still functioning, so I should, uh, I should censor some of them.


[User] Please transcribe this text

[Assistant] Oh man, that was a crowd. My school particularly had a weird set up where if you wanted to see a teacher, you'd go and loiter near a little lobby near the staff room.


[User] Please transcribe this text

[Assistant] And there was these sort of holy steps, which only teachers could walk off and then you could see them turn left into the staff room and you never saw that. Now, you know, there was occasional after school concerts and things where we, you know, roam the schools and investigate all the places we weren't allowed to see during school. So I had been in there as a, as a sort of illicit visit as a, as a pupil. I mean, who doesn't do that?


[User] Please transcribe this text

[Assistant] I think it was like a, it was some Christmas concert and, uh, we were backstage, if you like, and everyone else was, you know, and you're waiting your turn to go on, but you've got time to kill. So we were wandering darkened corridors and managed to break into the teacher's corridor. I remember someone running down it in slight panic and running into the photocopier cause it was dark. This crunch. I don't know if it worked out that way.


[User] Please transcribe this text

[Assistant] Having to call teachers by their name instead of sir, or whatever. There's a few teachers where it was really hard to break that, even after years of being away.


[User] Please transcribe this text

[Assistant] And a few, and lots of teachers who became good friends, despite having taught me, they became colleagues and friends. So that's a good redemption process to go through to stop school just from being these teenage memories. I'm glad I didn't stay there much longer. I did two years there.


[User] Please transcribe this text

[Assistant] But that was enough, I think, to, uh, otherwise you can get institutionalised really easily. In schools more than many jobs, but particularly a school you were at as a kid, you get so used to that way of working.


[User] Please transcribe this text

[Assistant] I remember the headmaster, even when I got the job, saying, uhm, look, if you're still here in two years, I'm gonna be putting job applications in your pigeonhole. I don't think he was being nasty.


[User] Please transcribe this text

[Assistant] I think he realised that early career you should move on. And so I took that advice, but I think having done my PGCE and two years of teaching, I began to realise that I really loved maths.


[User] Please transcribe this text

[Assistant] More so than I had when I was doing my degree. That was the change, like you said. It happened after my degree.


[User] Please transcribe this text

[Assistant] So I decided to go back and study, if I could, while I still kind of recognized that I loved it. So I applied for a master's course back at Oxford, mathematical modeling and scientific computing, a very applied maths course. But crucially, like, you could apply for funding, right? So you could ask someone to pay you to go and study. I like the sound of that.


[User] Please transcribe this text

[Assistant] It was really hard. Actually, that was really interesting for me as a mathematician. I remembered what it felt like to do uni maths again. And after a break, you get really rusty. School maths is one thing, but university level maths. I was working alongside lots of recent graduates who'd just done their degree and carrying straight on and I was out of my depth.


[User] Please transcribe this text

[Assistant] I remember going into lectures and getting angry, just really boiling rage inside, and I think at the time I was thinking, these people can't teach, I know about teaching, I'm a teacher, and this lecture is just rolling on in a monotone.


[User] Please transcribe this text

[Assistant] Yes, although I don't think that was really what's going on. That's true.


[User] Please transcribe this text

[Assistant] University teachers aren't necessarily employed to be good teachers, they're employed to research and...


[User] Please transcribe this text

[Assistant] Teaching comes as a secondary. Some of them are amazing teachers and some of them are not. I don't think many people would disagree with that.


[User] Please transcribe this text

[Assistant] But I recognised eventually, after I came out of those lectures and calmed down a bit, that the anger is quite often a result of not understanding.


[User] Please transcribe this text

[Assistant] If you're used to understanding something or you want to understand something and someone's not making it clear,


[User] Please transcribe this text

[Assistant] It's a really normal reaction to get quite irate about it. And then there was this bombshell moment of realising that's how my students have felt over the last three years of teaching. If they don't get something, it's not a surprise that some of them


[User] Please transcribe this text

[Assistant] Uh, always stayed with me, I think. And every once in a while learning something difficult yourself and remembering the emotional reaction to it is pretty useful as a teacher and as a speaker and communicator.


[User] Please transcribe this text

[Assistant] And this was the third visit to Oxford, so I'd done my three year degree. I taught for a year, went back and did a PGCE at Oxford in fact, although it felt very different. Okay.


[User] Please transcribe this text

[Assistant] Sanctioned gap. And I hadn't had a gap year at any point in my life, so I decided to go travelling.


[User] Please transcribe this text

[Assistant] For the rest of that year, with a guitar, went off around the world. Yeah, I did literally did a round the world circuit carrying a little busking guitar with me.


[User] Please transcribe this text

[Assistant] Yeah, I didn't earn a lot of money. I didn't cover my costs. I offset my costs.


[User] Please transcribe this text

[Assistant] No, uhm, although the hat had become a bit of a thing, it was just one of those, like, it was a bit of extra, unnecessary baggage to carry on a round the world trip when, you know, baggage is at a premium. So I'd already decided to buy a small busking guitar.


[User] Please transcribe this text

[Assistant] That was carrying with me all the time and the hat couldn't fit. But metaphorically the hat was out on the street every time I stopped and put my guitar case down I was thinking it really should have been the hat.


[User] Please transcribe this text

[Assistant] Well I did kind of did an English speaking circuit, but, you know, so I started in San Francisco, worked up the West Coast to Vancouver, into Canada, New Zealand, for two months actually, spent a long time in New Zealand, a month in Australia, and then Singapore and South Africa, and then home.


[User] Please transcribe this text

[Assistant] Melbourne was pretty good as well. Melbourne's a good place to busking. I've still never been to Adelaide. One of these times if we overlap in Australia you have to show me around Adelaide.


[User] Please transcribe this text

[Assistant] Well, I dunno, I'm not, I'm not completely kidding. It did function. Like, it's, it becomes a topic of conversation rather than my job. Uhm, and I was a...


[User] Please transcribe this text

[Assistant] Possibly. I mean, busking my petitions don't have as easy a time as singing a crowded house song in Australia.


[User] Please transcribe this text

[Assistant] I used to do some online teaching and some teacher training on the side. And so occasionally I had, I think I did two sessions while I was traveling. I logged in from Australia or something.


[User] Please transcribe this text

[Assistant] To, to do an online session back in the UK. Keep my, keep my hand in.


[User] Please transcribe this text

[Assistant] I, I did about five months traveling. Yeah. Yeah. So I hadn't figured out what I wanted to do. I'd obviously done some teaching, I'd done some studying and I'd done some traveling. And it's like, what do I do when I have to sort of settle a bit?


[User] Please transcribe this text

[Assistant] I didn't really want to go back into full-time teaching because I'd started doing some other projects on the side.


[User] Please transcribe this text

[Assistant] Uh, that, that year I'd set myself up as a sole trader or declared myself as a self-employed person for, in order to take some jobs like tutoring. Um, and the occasional talk, which I'd started doing even while I was teaching still, someone said, Oh, can you come and.


[User] Please transcribe this text

[Assistant] The process of declaring myself as a self-employed sole trader in order to be have a sort of legitimate way to take those opportunities if they turned up was


[User] Please transcribe this text

[Assistant] So I spent the rest of that year tutoring, one-on-one GCSE A-level tutoring, and marking exams, which is extremely difficult and very sobering to realise that some human, some poor human has to mark every script that students write. And yea, that's a really good insight into how to teach people to pass exams.


[User] Please transcribe this text

[Assistant] In the end, the examiner's a human being who's bored out of their brain, and if you make life hard for them by writing illegibly or something, it ain't gonna help. Those sort of realizations only come when you mark the things.


[User] Please transcribe this text

[Assistant] Yeah, that was a curtain I hadn't seen behind even as a teacher. So you're preparing all these kids, and then, so I had this year of doing bits and pieces, and right, this is a good way to keep my hand in. And uhm, I remember I asked


[User] Please transcribe this text

[Assistant] Basic A-level maths, and they're like, fine, we've got enough markers for that, why don't you do, uh, some advanced statistics? I'm like, okay, yeah, whatever.


[User] Please transcribe this text

[Assistant] I then realised that I hadn't ever actually studied some of the things I was having to mark. So things like hypothesis tests, which are absolutely fundamentally brilliant and an important part of mathematics actually.


[User] Please transcribe this text

[Assistant] I'd never studied, despite having done an A level in maths and further maths and a degree in maths, I'd kinda dodged all those bits because I didn't enjoy it. And there's a stereotype about people not enjoying stats, I think that's wrong, it's desperately important, it can be frustrating, but I had to learn it from scratch before I could mark the thing.


[User] Please transcribe this text

[Assistant] So it was a mixture, I was kinda a bit blasé, and I don't think I was the most qualified to mark it, but I could learn it, and I knew I could learn it in time to be good enough to mark the thing.


[User] Please transcribe this text

[Assistant] And it was a serious responsibility. Marking exams is not fun and it is boring and you're on repeat and your brain's going to mush.


[User] Please transcribe this text

[Assistant] And all the time reminding yourself that someone's future depends on whether you put a one or a zero in that little box there. So it's a weird feeling. But it becomes, um, like a production line. So you've got to stay sane somehow. I'd be very careful about agreeing to do it, but I think all teachers should do it once, at least, just to see what it feels like.


[User] Please transcribe this text

[Assistant] So what happens now? That year of travelling with tutoring and examining made me realise that, you know, I like this slightly smorgasbord employment thing, but it wasn't very stable.


[User] Please transcribe this text

[Assistant] And so soon after I came back, I'm going off into story mode, but as long as you're happy with it.


[User] Please transcribe this text

[Assistant] I came back and I had long hair and a big ponytail and a big beard and...


[User] Please transcribe this text

[Assistant] I was used to sort of swanning around South Africa rather than England. This was probably now March.


[User] Please transcribe this text

[Assistant] Just cause that was fun. And one of the speakers got stuck in snow. There was a weird snowfall that year and he was coming from up north and he couldn't make it. So we had this hour long slot with a speaker and it was 10 minutes to go and he wasn't there and Joe was like, we need to put someone up on stage and


[User] Please transcribe this text

[Assistant] Bits and pieces. In fact, it was the stuff that I've done for you on Numberfather on the Mandelbrot set. It was an old version.


[User] Please transcribe this text

[Assistant] Very pleased is on the record because I love that bit of maths and I've been doing that for a long time and it's a nice story to tell people. But what happened is basically there's lots of kids who I'm entertaining, that's kind of what I'm doing it for. But there were also lots of maths teachers in the room.


[User] Please transcribe this text

[Assistant] Uh, who had, I dunno, jobs coming up. So at the end of that day, five job offers saying, oh, why don't you apply to come and work out of school? Because obviously I get announced on stage, oh, Ben's just back from travelling, was a maths teacher, and he's gonna tell you about this.


[User] Please transcribe this text

[Assistant] Yeah, I was rocking it. I remember there was basically a queue of people saying, would you, we've got a vacancy, come and talk. So I ended up talking to a few schools after that.


[User] Please transcribe this text

[Assistant] I felt really lucky, outrageously lucky to sort of land in the right place at the right time.


[User] Please transcribe this text

[Assistant] No, this was people saying, will you come and teach? Because maths teacher jobs are, everyone's desperate for maths teachers. So you're spotting an unemployed maths teacher who's not offensive or criminal, basically, is licensed to go and queue up and say, please apply for a job. And it's still, we've got a huge problem in the country of shortage of maths teachers.


[User] Please transcribe this text

[Assistant] So I think what happened is they spotted someone who clearly was qualified as a maths teacher


[User] Please transcribe this text

[Assistant] Posh private boarding school, which is not really my field of comfort, but they, I went, I applied for a job.


[User] Please transcribe this text

[Assistant] There, as a maths teacher, because they asked me to, I went and had a look around and thought, I don't really fit in here, certainly my hair doesn't fit in here.


[User] Please transcribe this text

[Assistant] At least that's what Deputy Head told me. He was like, you realise you're going to have to cut your hair if you were again. At the end of the day, I, I'd had five interviews with various staff and thought I was all very pretty and exclusive, but I don't really fit. And the last interview was with the Head and he said, it's obvious Ben that you don't want this job. Which is a bit of a face error. Like, why is it that obvious?


[User] Please transcribe this text

[Assistant] And he said, it's alright, we don't really want to give you that job, which is also a bit of a sobering start to an interview.


[User] Please transcribe this text

[Assistant] He said, what we'd like to do is recognise that you're doing lots of other stuff on the side.


[User] Please transcribe this text

[Assistant] Why don't we give you a half-time job, uh, as in a pastoral role, which you're clearly good at in the boarding school environment. We'll give you some teaching with it, but leave you plenty of time to explore your freelance options, speaking and tutoring.


[User] Please transcribe this text

[Assistant] As well. I hadn't really considered that as an option. I wasn't really sure how you go and ask a school for that sort of option.


[User] Please transcribe this text

[Assistant] But credit to the guy, he kind of spotted something which really made me interested. It's like, I can go back to teaching. They clearly want to talk.


[User] Please transcribe this text

[Assistant] There was a pretty good outcome for me. So I worked for five years in that school. Half time.


[User] Please transcribe this text

[Assistant] But then working half time in a boarding school is a bit of a joke. I lived there and for three of those years I lived in a boarding house and was as close to a father figure for some of those kids as they had during term time and that's worrying for all concerned. We're almost up to date so I did five years of that and


[User] Please transcribe this text

[Assistant] I had been working with the Advanced Maths Support Program, they used to be called the FMSP, they're now the AMSP.


[User] Please transcribe this text

[Assistant] They had employed me for a bit of my time while I was teaching down in Dorset and said, instead of paying you piecemeal for these talks, can we pay you a, second you a tiny bit from your job?


[User] Please transcribe this text

[Assistant] Originally they were set up to provide teaching, they were called the further maths support program because people who wanted to study further maths as an A level sometimes couldn't access it at their school. So originally, about 15 years ago, they were set up to provide some teaching for kids who couldn't access it at their school. Sometimes remote teaching online and sometimes


[User] Please transcribe this text

[Assistant] But also training teachers, that's a big part of it. And also doing enrichment to inspire people to make the choices later on. And that's the bit, those two bits of what I fell into doing some teacher training and some enrichment stuff.


[User] Please transcribe this text

[Assistant] Yeah, certainly if you can do that, I mean, you can try and do that. It sometimes doesn't work. It's important in any subject to remember.


[User] Please transcribe this text

[Assistant] Which is a very interesting observation right now when exams have just been cancelled in this country, and suddenly...


[User] Please transcribe this text

[Assistant] Everyone's noticing, you know, what is worth doing even if the exams are off.


[User] Please transcribe this text

[Assistant] And they're realising that studying maths in order to progress to the next stage, or because it's interesting, is a valid option. Or it's much more obviously a valid option again.


[User] Please transcribe this text

[Assistant] Yeah, they actually, they kind of bought my time out of the school, so I ended up being fully employed by the school, but this company paid for a chunk of that time. Okay. And what happened is that they were interested in connecting more with universities, that overlap from school to university is


[User] Please transcribe this text

[Assistant] So the AMSP said, we should have a connection with the university. And they approached Bath.


[User] Please transcribe this text

[Assistant] They had already had lots of connections with the university, but the university of Bath was also thinking, we need someone who knows about schools.


[User] Please transcribe this text

[Assistant] And so that little marriage was like, who could fit this role? And I was like, I'll do that. Put my hand up and...


[User] Please transcribe this text

[Assistant] So I moved from Dorset to Bath and stopped the teaching half of my job really, but kept the AMSP half of my job. So I ended up employed by the University of Bath, but the money comes from the AMSP.


[User] Please transcribe this text

[Assistant] And that's half a job and I go and do teach training enrichment for them. And that meant that the other half of my time is now completely unaccounted for. And so I'm freelance for the rest of my time. And that's kind of been the case for the last six years.


[User] Please transcribe this text

[Assistant] What's confusing is a lot of it ends up being very similar work to what I'm employed to do with the AMSP. So if a school approaches me, ah, can you come and do us a talk? I need to check whether...


[User] Please transcribe this text

[Assistant] That's part of my job with the AMSP, and if it's not for any reason or I've done my hours or whatever, then I could do that as a freelancer and invoice them.


[User] Please transcribe this text

[Assistant] That was a big shock actually, moving from a teaching world to having to charge people for your time is a strange shift.


[User] Please transcribe this text

[Assistant] No one teaches, I think, no one teaches to earn a lot of money. It's not super well paid, a decent wage, but it's not, it's not a very mercenary job. You do it for the love of it and it's hard work. Whereas suddenly having shifting to do the same sort of thing, but.


[User] Please transcribe this text

[Assistant] To give people a bill, that was a bit of a shock, so it takes a long time to get used to that way of working.


[User] Please transcribe this text

[Assistant] It is nice to reflect on it. I think everyone reflecting on their stories has...


[User] Please transcribe this text

[Assistant] Earlier on there's maybe realised that the parallels are interesting now because my brother is doing a very piecemeal job. He's doing sort of four or five different bits that he can flip between and some of them are freelance and some of them are employed.


[User] Please transcribe this text

[Assistant] And that's very similar to my, what do they call it, portfolio career. But what it gives us both is flexibility and we're clearly drawn to that.


[User] Please transcribe this text

[Assistant] Possibly we don't like being told what to do or at least having the option to revert to a situation where we're not told what to do. So I'm glad about that and I recognise that a twin brother who has the genetic experiment of doing the same thing as me or different things with the same starting point has ended up in a similar role. So maybe we're always going to go that way.


[User] Please transcribe this text

[Assistant] Which, uh, I'm using that phrase as an acronym sort of deliberately in my head with capital letters. And you know about this because we, there was a group of us who organized a sort of company. We're now a charity actually called Talking Maths in Public and we're running a sort of conference every couple of years for people who do this slightly weird niche job, which is stand up in front of people and.


[User] Please transcribe this text

[Assistant] Maybe I say it like it's a bad thing, but I, even when I'm doing music, I really enjoy, and all performers do I think, the enjoy, the feeling of doing something well.


[User] Please transcribe this text

[Assistant] And seeing other people having a good time because of it. That's very obvious in music if you get it right at a gig.


[User] Please transcribe this text

[Assistant] And you sing a song or something, and you just see people enjoying themselves. That's a huge...


[User] Please transcribe this text

[Assistant] Payback, which is why musicians do it not for a lot of money perhaps, but uhm, performing a mathematics talk can give me the same sort of rush.


[User] Please transcribe this text

[Assistant] Occasionally I will play music in a mathematics talk, but only if I can shoehorn it in.


[User] Please transcribe this text

[Assistant] I mean, the stereotype of maths being hard and sort of academic is something you can't ignore. So if you play into that too much and blind people with science, it's gonna absolutely not help you. So I guess my one


[User] Please transcribe this text

[Assistant] Obvious go to advice, which I have to tell myself regularly, is motivation. If you can find a way to motivate people to learn further, a lot of the work is done. And that might be showing them something surprising.


[User] Please transcribe this text

[Assistant] Showing them something interesting or pretty or cool or curious. And then you've got sort of the fuel which is necessary to go and study the detail.


[User] Please transcribe this text

[Assistant] Yeah, I don't think any human does anything without some sort of motivation, and it can be...


[User] Please transcribe this text

[Assistant] Do this because the carrot is dangled in front of you and you're like, I want that. So I guess nobody would like to think that people only do stuff because you threaten them to. It seems like an inefficient way of doing something. And if you can show them the carrot dangling and say, ah, that pretty picture, take the Mandelbrot set, like, look at that. What is that? And why does it happen? Is a lot of fuel for studying some difficult concepts.


[User] Please transcribe this text

[Assistant] People's tastes are different, right? And I think as a teacher particularly, that's in a classroom of people. You've got 30 kids and they all have different tastes and leanings. But if you don't show them a range of things, then the chance that some of them get turned on by that little image or something will be lost. I mean, I'm not claiming that everybody will get a massive rush out of everything I show everyone.


[User] Please transcribe this text

[Assistant] That's not done in order for them to study further. That's just imparting pleasure. But you don't impart the same pleasure to everyone all the time. I do think it's true though that nobody does anything without motivation. And whether you are concealing the motivation or haven't noticed it consciously, it's true whatever we do. Like, you know, you want to go and cook food, it's because you're hungry.


[User] Please transcribe this text

[Assistant] Partly. And so education's a bit like that. If you want to get through an idea to someone, you've got to show them even unconsciously a reason to do it.


[User] Please transcribe this text

[Assistant] The, uh, the stereotypes really kick in at that point. I mean, in any audience, you're gonna have people who pick you up on details, but maths teachers are the worst. The, the stereotype of us being pedants and like,


[User] Please transcribe this text

[Assistant] I spelled that wrong. Again, the apostrophe's in the wrong place. Even if it's not maths pedantry. So I think they're a frightening audience.


[User] Please transcribe this text

[Assistant] Right. And this is true of a lot of teachers. Teaching is hard. And so.


[User] Please transcribe this text

[Assistant] Well back to our carrot and stick metaphor, just survival as a teacher becomes your overriding motivation. And however much you love your subject, what's going to get you through the next period with the year nines on a Friday afternoon is more important because


[User] Please transcribe this text

[Assistant] Basically, it feels like your world's gonna end. So I, yeah, I mean, I remember feeling like that as a teacher, you start paying attention to maybe the bits of your subject, which should get you excited and you should be able to show people. And you start occasionally getting blinkered into, I just need to get through this and I need to find a decent assessment tool that helps me get through this and reduces the amount of blooming paperwork.


[User] Please transcribe this text

[Assistant] Mass teachers in general are harder when it's because they're doing a difficult job and it's, it's hard to get through the motivation sort of blinkers in the right context. If you can get through that, suddenly you can provide other motivation. And I know a lot of mass teachers who are


[User] Please transcribe this text

[Assistant] Insanely grateful that Numberphile exists, so fair play to you, because you're providing an easy, accessible way of seeing little nuggets of motivation that aren't exam-focused. And that's a really good thing.


[User] Please transcribe this text

[Assistant] Now, I feel a bit guilty that I'm not teaching in a classroom, but I, I feel like I...


[User] Please transcribe this text

[Assistant] Someone has to do, uh, these bits that are slightly outside the classroom.


[User] Please transcribe this text

[Assistant] And I'm really glad to be in this situation now. I don't know how long it will last, and freelance work is always a bit like, how long is this little niche gonna actually employ me?


[User] Please transcribe this text

[Assistant] But I feel like there are a lot of options and things will change, I have no doubt, in the future. Even during...


[User] Please transcribe this text

[Assistant] I mean we're recording this in sort of lockdown state and so everyone's been stuck at home a lot longer, but I've as a result dug out an old midi piano and recording studio bit set up and I'm trying to like maybe resurrect a bit more music.


[User] Please transcribe this text

[Assistant] Which was a big part of my life for a long time and I haven't done a lot of recently. So.


[User] Please transcribe this text

[Assistant] I don't think I'm ever gonna make my way as a paying musician, or a paid musician, but there are lots of bits of things that I enjoy doing that I've had a chance recently to maybe tinker with again.


[User] Please transcribe this text

[Assistant] If you've ever, if anyone else listening has ever seen a Numberphile video from me, you realise that I spend a lot of my time tinkering on bits of software as well, like there's one called GeoGebra where you can make maths move, and I spend a lot of my time


[User] Please transcribe this text

[Assistant] Not personally, the AMSP, who I still work for, in a sort of floating role, is doing enrichment, particularly during lockdown, has had to change how it supports students, so I can see that might actually start happening again, maybe online, doing some tutoring to small groups and things, but right now, no, I'm not doing any tutoring, I don't have time to, uh, to make it happen.


[User] Please transcribe this text

[Assistant] Yeah, uh, we speak regularly, uh, he's got a five year old son called William.


[User] Please transcribe this text

[Assistant] Who, uh, I need to catch up with from time to time, but to be honest, one of the main things Tim and I do is every, every Sunday night we have, uh,


[User] Please transcribe this text

[Assistant] We, we both log on to Steam and play, play games together. We, we start with a sort of audio call, headset, and then.


[User] Please transcribe this text

[Assistant] I used to spend a lot of time playing XCOM, uh, which is sort of turn-based strategy thing, but when playing with other people, it's a really different thing.


[User] Please transcribe this text

[Assistant] I enjoy playing games on my own, but they're usually sort of...


[User] Please transcribe this text

[Assistant] It's much slower paced and people playing with me would be like seriously bored. So it's much more arcadey stuff when I'm joining with other people.


[User] Please transcribe this text

[Assistant] I mean, one of these days I need to record some music myself, but uhm, that, I think


[User] Please transcribe this text

[Assistant] Okay, I'll have a try. I'm not gonna promise anything. My, uh, my musical skills almost always ended up being I wanted to sing, which is always very difficult to do as a background thing. And so my guitar skills are basically background accompaniment and anything which is just guitar always makes me feel like I really, really should have actually, you know, learned to play this properly.


[User] Please transcribe this text

[Assistant] So I'm originally from Israel. I grew up in the desert. So it's a small town outside Be'er Sheva. Very hot, very dry. But there were some forests nearby, so it's this kind of very nice and pluralized kind of background.


[User] Please transcribe this text

[Assistant] This very intense dry hit, that's the main difference.


[User] Please transcribe this text

[Assistant] When I was like 6 or 7 I loved dinosaurs, you know, and then it moved to like fighter jets and birds and stuff like this. But my father tells a story and, you know.


[User] Please transcribe this text

[Assistant] It's not that reliable every time I get younger in the story that, you know, when I was like four or something, I already knew that if you have like one tile on the floor and you have half.


[User] Please transcribe this text

[Assistant] This kind of understanding of infinity. I always had like a little bit of math in this. My father, who's not a mathematician at all, you know, when I was six, we would sit and he would show me how to do long multiplication and long division and just give me numbers and I would play with it. So mostly I was encouraged to be curious.


[User] Please transcribe this text

[Assistant] I'm telling everybody in my family who would even listen. I get the idea of the poof, but I want you to tell me how you got from this sum to this closed number. How do you get her?


[User] Please transcribe this text

[Assistant] I don't know what pure math is, but I think that is what pure math is. And they all gave me the same stupid answer. Oh, you have to be able to do this in order to learn how to do that. I ended up dropping out of high school. I didn't have to learn all of that, but then again, also at the university they didn't teach me this. Hang on a second.


[User] Please transcribe this text

[Assistant] You know, it sort of ran its course and by the end of the 11th grade...


[User] Please transcribe this text

[Assistant] Just felt like there's nothing left for me though. Were you a good student? Like were you getting good marks or?


[User] Please transcribe this text

[Assistant] I was as a kid, but then I was sort of a rebellious teenager and I didn't care for this as much. So the things, if I liked the teacher, I would do well, but if the teacher annoyed me, I would just cut classes and never show up.


[User] Please transcribe this text

[Assistant] That's the GED, the equivalent diploma. You can do it yourself. You just have to register.


[User] Please transcribe this text

[Assistant] And you just go to the exam, and that's it. So, like, a few of the exams I already did in whatever school years I could do it, and the rest I just did on my own, with the exception of math that I postponed for a bit later, and I took like a preparation course, because you know, that's a bit harder to force yourself to sit down. But literature, you just need to read some poems, read some stories, think about them enough, and you know.


[User] Please transcribe this text

[Assistant] You can spit out whatever they want you to spit out, so. I didn't put a lot of effort and I got decent grades and that was all of it for me. I hated the idea of


[User] Please transcribe this text

[Assistant] Servers that you don't hear about, or, you know, language to communicate with printers, you know, which is pretty amazing, and, and nobody there understood it.


[User] Please transcribe this text

[Assistant] So I just had all the fun learning this stuff. And then by the end of it, I was like, okay, I'll go and study computer science and math. And then I found out that there's a degree that let you do both together.


[User] Please transcribe this text

[Assistant] But because I dropped out of school, I couldn't get in because my exam grades were like borderline and it's a relatively popular program so I couldn't go in.


[User] Please transcribe this text

[Assistant] People at the university said, oh, just, you know, join the pure math. And it's the same for freshman year, so you can, if your grades are good.


[User] Please transcribe this text

[Assistant] Like, over 70, just, you can switch, and that's fine. But after one semester, you know, studying some set theory and, and, you know, this kind of abstract stuff, I was like, nope, I'm gonna be a mathematician, you know, it's gonna be.


[User] Please transcribe this text

[Assistant] Yeaah, so, kind of. So, first of all, math already grabbed me as a kid.


[User] Please transcribe this text

[Assistant] The thing that the army gave me was, it reminded me that I enjoy learning stuff. That it's school that takes the fun out of learning. And that if you have a, you know, a place where you can just enjoy it,


[User] Please transcribe this text

[Assistant] Then you can just run with it. And of course that if you go to the university and you learn stuff and it's a lot of self-work, that's fantastic, so.


[User] Please transcribe this text

[Assistant] Purely positive, of course there's a lot of downsides to it, but you know, you have to cut your hair, you know, you have to wake up very early every day, you know. But yeaah, and there's people telling you what to do all the time, but at the end of the day I ended up in a rather small place.


[User] Please transcribe this text

[Assistant] And they really appreciated the fact that, you know, I had this capacity to do things. So they just, you know, said, okay, you know, just go and do those things, you know, whatever you want.


[User] Please transcribe this text

[Assistant] Yeah, it's definitely the basics of set theory. So, uh, my professor was later my advisor during my masters, uh, Uri Abraham, and he's a fantastic teacher, you know, through and through, but it was...


[User] Please transcribe this text

[Assistant] Just the, the, the fact that you could make sense of infinity that, you know, really sort of clicked in my head. I remember there was, I think, like week four, five, something like this. There was some homework question about something with infinity.


[User] Please transcribe this text

[Assistant] And, you know, that sort of just said, okay, you know what? I love this. I'm going to do that.


[User] Please transcribe this text

[Assistant] Even though it's completely possible to talk about these things with teenagers, but, you know, they just don't do it. Okay, I wasn't the best high school student anyway, so maybe that's why.


[User] Please transcribe this text

[Assistant] But not as much, I was always intrigued by it because you know, it's infinity, but you don't have the tools because until you do set theory, you have no tools to really grasp what is infinity. Do you regret dropping out of high school? Was it a mistake? Best decision I've made.


[User] Please transcribe this text

[Assistant] Really? Explain that, cause, cause, would you, but you wouldn't recommend it to other young people. Of course I do. Really?


[User] Please transcribe this text

[Assistant] The secretary said to me, oh, you know, there's this teenager, he's like 15, and he's been taking classes here, and the set theory course that you're teaching has no prerequisite, so he wanted to take it, maybe you can talk to him and explain what's going on. And I effectively told him, look, if you're at 15 taking university classes, just drop out of high school, you have nothing to do there. And the secretary said to me,


[User] Please transcribe this text

[Assistant] His mom will kill me! No, he didn't drop out. It's fine. But if you're smart, you have nothing to do in high school. At least.


[User] Please transcribe this text

[Assistant] In my experience, obviously other high schools might be better for you and that's great, but the high school I had and I could see my older sister. I remember this one little bit that was


[User] Please transcribe this text

[Assistant] Maybe influential in this whole thing. When she was 16 or 17, she was talking to a friend and she told her, look, you can find, you know, the, the, the challenge and the fun part in your studies, but I, you know, I just feel being forced into this kind of stuff that I don't wanna do.


[User] Please transcribe this text

[Assistant] And I don't like doing things I don't wanna do. And as a teenager, in particular, you don't have this, oh, okay, I'll just do this and then I can do other things.


[User] Please transcribe this text

[Assistant] I mean, yeaah, but again, if you're smart, you're gonna go to math anyway, and at least in Israel, if you wanna study pure math, and you have a pulse and an ID, you will get in.


[User] Please transcribe this text

[Assistant] It's it's own filter, you know, if you don't go through the first year, you're not gonna go with it. Okay.


[User] Please transcribe this text

[Assistant] Almost, yeaah. I mean, you know, you just do this basic course and it was basic to the point that is painful to me as a set theorist now to think about, oh, that was set theory, that was nothing, that was really like the most basic introduction.


[User] Please transcribe this text

[Assistant] You know, it was fine, it was aimed also for people in computer science and, you know, they don't need a lot more than that. So it was just this, but then you, you touch the infinity part and all of school, all through everything else, people always tell you like, oh, you know, you can't deal with infinity, it's infinity, it's not a number, it's not this.


[User] Please transcribe this text

[Assistant] And then you have this very good professor, and he tells you, well, you can, in fact, do that. And you know, it just clicked in my head, and it just, this kind of missing piece, you know, that you go like, yes, this is home.


[User] Please transcribe this text

[Assistant] I did enjoy other things so i had an incredible professor.


[User] Please transcribe this text

[Assistant] Who taught me linear algebra too. And you know, part of enjoying math, you play with the concept.


[User] Please transcribe this text

[Assistant] They always tell you, oh, you have to do the homework. You don't have to do homework. You have to think about the concepts. And homework is just, you know, a medium.


[User] Please transcribe this text

[Assistant] Through which you think about the stuff from class. But I would go to a pub and I would think like, oh, so there's this vector space and it's defined over a field. But what happens, you know, we don't really use all of it. Let's try to define this over the integers.


[User] Please transcribe this text

[Assistant] And I would give it all this kind of fun names and I would go to his office hours and say, I don't have questions about the course, but I came up with these things, you know. And he was an amazing professor.


[User] Please transcribe this text

[Assistant] Unfortunately, that was his first year at the university and the students just wore him down. I took a course with him every year and every year it was more advanced course.


[User] Please transcribe this text

[Assistant] And by the third year, I could see that he was completely worn down in the big courses that he was teaching. Whereas the smaller one, it was always fun. So he was also very influential and he was teaching representation theory.


[User] Please transcribe this text

[Assistant] P-adic analysis in my second year that I could, you know, join in, because I would have maybe gone to number theory instead, but they didn't have the course and there was set theory and I already liked that one, so I just went there and...


[User] Please transcribe this text

[Assistant] What is set theory? Well, set theory is the way to make sense of infinity from the modern perspective. So, you know, if you go back


[User] Please transcribe this text

[Assistant] All the way to Galileo. And even before that, people knew, okay, there's infinitely many natural numbers.


[User] Please transcribe this text

[Assistant] And there's the Galileo paradox that says, well, the same amount of natural numbers.


[User] Please transcribe this text

[Assistant] So 0, 1, 2, 3 and so on as the even number. So 0, 2, 4. And Galileo said, well, the reason this is happening is because infinity is divine and we shouldn't deal with infinity. And that sort of continued in this kind of fashion here and there. I'm sorry, Galileo used the squares and the one before him, Adam or something. I don't remember the name.


[User] Please transcribe this text

[Assistant] It's even older, the even thing and Galileo pointed out with the squares, there's a lot of history about this. So...


[User] Please transcribe this text

[Assistant] As, you know, enlightenment moved and rolled out and you moved from the renaissance to this, oh maybe the church doesn't know everything.


[User] Please transcribe this text

[Assistant] Suddenly people said maybe infinity is not divine, maybe it's something you can deal with. And that slowly progressed and you see a lot of this mathematics that is very modern.


[User] Please transcribe this text

[Assistant] Coming out in the 19th century. And one of those things was Cantor saying, hang on, let's just take all of the natural numbers as a completed object and just work with it.


[User] Please transcribe this text

[Assistant] And we get more things, and suddenly you have a theory of infinities. You know, and it's absolutely fascinating, and it opened the door to so much amazing mathematics that came afterwards. It really is just about making sense of infinities.


[User] Please transcribe this text

[Assistant] Why is it called set theory? You want to think about sets, which is essentially how you think of a collection of mathematical objects that is also a mathematical object.


[User] Please transcribe this text

[Assistant] So, you want to study the property of these so-called sets to see what they do and how they behave. And one of these axioms says that there is a completed infinite set of the natural numbers.


[User] Please transcribe this text

[Assistant] Yeah, you know, that's the, the, that's not the ultimate set, that's sort of buying the land for your ultimate house. Right. That's, that's the, the land upon you build your castle.


[User] Please transcribe this text

[Assistant] And, you know, in a very Monty Python-esque way, the first castle they tried to build collapsed into the swamp, and then the second castle collapsed into the swamp, and the third one burnt down and then collapsed into the swamp.


[User] Please transcribe this text

[Assistant] But then came Tormelo, and after him, you know, Frankil and Scolam and other people, and they built a castle, and that castle held.


[User] Please transcribe this text

[Assistant] So, really what you want is to understand the properties of sets, because if you can interpret every mathematical object as being a set, what you're really studying is the mathematical universe.


[User] Please transcribe this text

[Assistant] So you're not studying the sets, you're studying the mathematical universe as a whole, and you want to understand how the infinite parts of it play together.


[User] Please transcribe this text

[Assistant] N is a prime number that's fine, but now you want to study all the prime numbers as a set and ask, you know, things about that. Or if you want to move from just the natural numbers and you ask about, you know, sine and cosine and exponents and integrals and all these kind of things, you suddenly find yourself


[User] Please transcribe this text

[Assistant] Dealing a lot with sets. Oh, a function is continuous except in this small number of points. So what does it even mean, a small number of points?


[User] Please transcribe this text

[Assistant] Effectively what you're assuming is that there is one infinite set, namely the natural numbers, and that every set has a power set, which is the collection of all the subsets. So, you know, you have the natural numbers and the even and the primes and the non-primes and, you know, everything which is a prime times


[User] Please transcribe this text

[Assistant] A lot of information. And then you can take the power set of the power set and so on and so on. That's sort of where the true power comes to set theory from the power set axiom.


[User] Please transcribe this text

[Assistant] I was kind of lucky quote unquote that my first year there was a huge strike so homework were not mandatory for the whole year and second year and on they don't really grade homework so you don't, you just do it sporadically every now and then.


[User] Please transcribe this text

[Assistant] Because as I mentioned before, homework is not important. What's important is to engage with the material. And we were just like eight, seven, eight people doing pure math. So we were always together in almost all the courses. So we, you know, we had this very fun and engaging group to, to discuss these things. I never really had to do that.


[User] Please transcribe this text

[Assistant] And, you know, there's this thing that all of my teachers, all of them, without fail,


[User] Please transcribe this text

[Assistant] He told us the story, oh when I was a student, I would go home and re-prove all the theorems we saw in class so I can really understand them.


[User] Please transcribe this text

[Assistant] I'm not doing this. What's wrong? Am I going to be good or not? And then you find out that it's not about proving the theorems from class. It's not about solving the homework. It's about engaging with it. And if you have people who also enjoy math and you sit and overbeard your discussion is about, oh, this proof or that proof and why does this work? Then you end up, you know, knowing a lot more than you would otherwise.


[User] Please transcribe this text

[Assistant] So my father was, you know, originally a historian. He, he didn't get into academia very well because it's more cutthroat in his field and there was politics involved. But he knew academia. And when I was, not even, before I even started my first year, he told me, oh, you're going to do a PhD.


[User] Please transcribe this text

[Assistant] And I said, what are you talking about? Let me finish my first year. And he said, look, your older brother studied engineering. That's point A to point B. That's how you get from A to B. There's like three different ways and you use this for that and you know, this for this.


[User] Please transcribe this text

[Assistant] So, people in engineering, maybe they do a masters to, to specify on something, but you're going into natural sciences.


[User] Please transcribe this text

[Assistant] They just throw you into the ocean and they tell you, swim and find yourself an island.


[User] Please transcribe this text

[Assistant] So, by the end of my first year, I knew that I wanted to pursue this.


[User] Please transcribe this text

[Assistant] So for me there was no question. I originally hoped that my second year would be so busy that I can finish in two and a half.


[User] Please transcribe this text

[Assistant] Oh, definitely not. So when I was, especially as an undergraduate, I used to go hiking in the desert like every two months. You know, I would just grab a backpack and go overnight to this


[User] Please transcribe this text

[Assistant] And I would hitchhike, you know, back and forth all the time. And one time, I was talking to somebody and he said, Oh, what are you studying? I said, Oh, pure math. And he said, Oh, you know, that's great. I'm an engineer. I would hire a mediocre pure mathematician over a good engineer.


[User] Please transcribe this text

[Assistant] Any day of the week. Because pure math is not about this one thing that you research. It's about being able to make abstractions and solve problems and then applying them down. So you know, it gives you this massive


[User] Please transcribe this text

[Assistant] So, I see a lot of my friends that gave up on academia that went to finance or programming or whatever you want to do with your life. Not saying that a PhD in math is going to help you with everything.


[User] Please transcribe this text

[Assistant] Maybe not with cooking, but it still can do a lot for you.


[User] Please transcribe this text

[Assistant] Kind of stress free, and then very stressful, and then stress free again.


[User] Please transcribe this text

[Assistant] Yeah, yeah. When I was a PhD I still lived away from Jerusalem. I did my PhD in Jerusalem and I still lived in Be'er Sheva. And my advisor for my masters would go with me to Jerusalem for, you know, set theory classes that we had by my advisor.


[User] Please transcribe this text

[Assistant] And he's our advisor, you know, on Wednesdays usually, so he would pick me up and we would go and talk either about math or whatever, and one time he was also taking one of his friends to visit her mother in the hospital or whatever.


[User] Please transcribe this text

[Assistant] She asks me, so did you have your crisis yet? And I was like, no, everything's going great. I'm not expecting a crisis. And they both left. I'm like, you'll see. And later that year, essentially everything I thought I had just completely collapsed. We found like a huge gap on the first stone that I laid and everything just


[User] Please transcribe this text

[Assistant] At the end, but that was the end of my third year, and I remember feeling that if that was my first year, I would have picked a different topic. Because in Israel you can do a PhD for up to seven years, you know, and even five years you still get funded.


[User] Please transcribe this text

[Assistant] So it's, you know, you take your time, just get good results. Because here in the UK, it's like you have three, four years.


[User] Please transcribe this text

[Assistant] You know, start from nothing, go all the way there, so you have no room for mistakes. But if you have five years, you, you really can do it. But after three years, you know, so you have to commit, you have to, you know, go through the fire and the gauntlet and, you know, come with it at the end.


[User] Please transcribe this text

[Assistant] Yeah, so, so I had this kind of definition for this kind of iteration of things, whatever.


[User] Please transcribe this text

[Assistant] And at the time, there was a visitor for like the whole semester from Vienna, and I knew that he kind of liked this kind of things, and you know, he agreed that once a week I sit for like, I sit him for an hour and showing all, everything, and he would just point out, okay, that looks fine, just, you know, prove it for yourself in detail, just so you know it works.


[User] Please transcribe this text

[Assistant] And there would always be like this kind of problems and I would come back like the next time, say, oh, you know, here's stuff. Same with my supervisor, you know, okay, it's fine, just, you know, make sure to check the details.


[User] Please transcribe this text

[Assistant] One of my colleagues and friends, we shared an office and shared the supervisor and we already wrote together one paper at that point.


[User] Please transcribe this text

[Assistant] You know, I showed him what I had. And then, you know, he said, no, I don't agree with this claim of yours. And I said, yeah, but that comes out of the very first thing that you obviously agreed with.


[User] Please transcribe this text

[Assistant] And he stopped and he thinks and he says, no, I actually disagree with that. And then together we came up with an example that had like less than 10 points kind of iteration. It was insanely simple, but so stupid. And that was just like, whoop, everything fell down.


[User] Please transcribe this text

[Assistant] It wasn't even a bad day, it was just oversight. Because I'm more of a big picture kind of idea, less, you know, nitty-gritty. So luckily at that point I had a lot of the big picture and I could just say, okay, what do I need to recover? I need this and that and, you know, you sort of build it back up.


[User] Please transcribe this text

[Assistant] So you have the shape of the tower, but all the inside collapse and you very quickly have to, you know...


[User] Please transcribe this text

[Assistant] Put in, you know, supports to, to keep it working. So I did that. It ended up overly complicated and over the years since then I've, you know, grown to say, okay, so you can do this and you can do that instead and so on and so on. So it was fine at the end, but yeah, at the time it was very, very intense.


[User] Please transcribe this text

[Assistant] Look, at the end of the day, you are who you are. And if you go and you jump, and you make this, you know, very far jumps, and you land, then that's who you are. And if you fall, you just disappear from academia because you fall too often. Not necessarily that you're being pushed out, you just give up because


[User] Please transcribe this text

[Assistant] Nobody wants to live their life just being wrong all the time.


[User] Please transcribe this text

[Assistant] So you just give up after a while, and that's absolutely fine. You just say, okay, you know what, I'm gonna take myself and find an industry job that pays three times as much. What I learned from this is more or less an about myself, that I'm usually wrong.


[User] Please transcribe this text

[Assistant] They just sort of throw it in the background and, you know, you meet someone and you sit for a beer and some conference and you ask them about this research or you tell stories like, you know, war experiences of this kind of thing.


[User] Please transcribe this text

[Assistant] Sometimes these things are public because, you know, you go on record and you say, oh, I think this, I think that, and then later you say, okay, I was wrong because of these things and, you know, there's some record to it.


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[Assistant] So I personally, I like to write this kind of experiences on my blog, you know, which is, you know, a place for me to sort of spit it out and say, Oh, look, it was so difficult and exhausting, but how much I ended up with. So at least in my case, it's.


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[Assistant] Not necessarily, it's sort of, you know, it's hidden. We then say, okay, so I was trying to prove this, and we tried that, and that didn't work because of this thing. So,


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[Assistant] You framed this as I learned the hard way that this approach is not gonna work because of this and that. So it's a positive thing. You actually proved something, but you proved it by first being wrong about it and then finding out why you were wrong.


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[Assistant] So, I didn't really wanna go to the US. I was hoping to stay around Europe.


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[Assistant] Yeah, so normally you're expected to do at least one or two post-docs abroad, and then maybe you come back to Israel. Not everybody do, but...


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[Assistant] At least if you're going to stay in academia, you usually go abroad and then you come back. If you're really, really good, they will even tell you you have a job waiting for you. Just go, enjoy a postdoc because it's, you know, a lot less stress. Enjoy your postdoc, come back, you know, we'll be fine.


[User] Please transcribe this text

[Assistant] I wasn't that good, I guess, although they did tell me, you know, oh, you and the other guy I mentioned from the mistake, you two have to have good postdocs so you can come back and continue the tradition of Seth theory in Jerusalem because, you know, it has two of, well, the most prominent Seth theorists. I heard from like two or three people, well, I hope that you do a good postdoc and come back.


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[Assistant] Shortly after I left, they gave a job to somebody who finished in Tel Aviv a few years earlier, and last year my friend started there as a tenure track, so they're fine.


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[Assistant] So, I didn't really know what I'm going to do. I applied to a few places, but, you know, there's this approach of, ooh, apply everywhere, and then one of the places will take you.


[User] Please transcribe this text

[Assistant] But it's not a fair approach if you do something very popular.


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[Assistant] Then fine, you know, somebody will take you. But if you do set theory, which is, you know, more specialized and not everywhere has big centers in set theory, then you're unlikely, if you just send applications to, I don't know, the University of Oxford, they're not gonna take you. They don't have set theory. So why would you even bother them?


[User] Please transcribe this text

[Assistant] So I tried to only apply to a few specific places, uh, in the US none of it panned out, uh, and then I ran into the person who'd become my supervisor in Vienna, who was there again, because he came often, and I said, hey, do you have some money for a postdoc? And he said,


[User] Please transcribe this text

[Assistant] Yeah, I should have, at least for a year, maybe a year and a half. Which is, you know, gives you some time. That's how I got my first job.


[User] Please transcribe this text

[Assistant] Well, before Vienna, I was applying to a Newton Fellowship.


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[Assistant] I've been to Cambridge for some conference, and I've met David Aspero, who works here at UEA, and we started working on a paper, I came to Norwich to work on this, you know, at some point afterwards, and as I was looking for a postdoc, I sent him an email, my advisor ran into him at a conference around the same week, and he said, oh, there's this thing called Newton Fellowship. So we applied.


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[Assistant] And everybody told me you're not gonna get it, but I got it, so that was lucky.


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[Assistant] Yeah, yeah, yeah. And so this is specifically a two year one, so it's not very big, but you have a decent travel money, so it's a nice postdoc.


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[Assistant] I applied to this, I was already, I talked to the guy from Vienna, to Martin, and he said, it's absolutely fine if you live early, no hard feelings, because you have to be upfront about these things.


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[Assistant] There's, you know, being a poster for someone.


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[Assistant] Now, they could also say, I don't need help on this project, just do good math, whatever you want, but it's still on the project. Okay. And there's fellowships that essentially say, okay, you write the project, here's a bunch of money,


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[Assistant] Go work on this project for the next however many years. Okay, so you're kind of, you're more your own boss? Yeah. Right. Yeah, so you have a host, it's somebody who's supposed to sort of oversee you and mentor you and all this stuff, but you know, you're kind of your own boss. Okay. Yeah.


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[Assistant] We had this project about something that's slightly different from my PhD work. Because everybody I met kept telling me, oh you have to do something different. Because if you just work on your PhD stuff then, you know, you don't show


[User] Please transcribe this text

[Assistant] Any kind of breadth of, of, you know, subject and knowledge and whatever. So I wrote something else and, and we got there. But...


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[Assistant] My real passion, whatever I did in my PhD, so every time I would sit alone in the office, I would go and work on that.


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[Assistant] You know, we worked a bit on our stuff, and I would work a lot on that stuff, and that was fun. But, you know, it's only two years, it's a bit stressful.


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[Assistant] Uh, at the end of the, they ask, oh, what would you do different? And I said, three years. That's, you know, because you have to start finding a job almost as soon as you start. That's really, that's crazy. Yeah. And then afterwards I just.


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[Assistant] A few other places. Then the university said, oh, there's this UKRI Future Leaders Fellowship thing. You know, you can try to apply for this. So...


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[Assistant] I started working and I got a lot of help here at the department and at the university level, they, they really helped me to, to make this into a really nice proposal. So you pass the, the internal sift gate and then, you know, you, you submit the application and you wait and you wait.


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[Assistant] I was giving a talk in Manchester and the morning after, I see my email.


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[Assistant] You know, you get back the reports, you know, the reviewer comments on the proposal, and you send it back. And then you wait, and you wait, and you wait. And they said that the announcements of who's invited for the interview are going to be on the first week of December. And it comes, and it goes, and your nerves are plucked.


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[Assistant] It's like, refresh, refresh, all the time, refresh. Nothing. And you go like, okay, should I send them an email? Should I send them an email? And my head of school said, look, if they said the week, you have to give them the whole week. Monday morning, you can send them an email. The next Monday arrives and I said, there's like about 500 people probably applied. I don't need to send them an email. They know they're late.


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[Assistant] And a few hours later, you know, I get the email.


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[Assistant] And it says I've been invited to the interview and I, you know, immediately run and, and shout and, and very happy. You know, I start reaching out to people I know that have this to, to ask for tips, you know, okay, do practice interviews at least two and get a diverse panel for this kind of practice and so on and so on. And you work.


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[Assistant] And you, you know, workshop your, your seven minute presentation and they give you a list of optional questions and what people kept saying.


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[Assistant] And that was absolutely true, is that if you got to the interview, they want you to have the money.


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[Assistant] So the offer, and they slightly modified it in subsequent rounds, was a four year fellowship.


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[Assistant] And apparently they change it so that it's not guaranteed to have a permanent job, because some of the big universities don't like to, you know, hand out jobs like that, so they change the wordings. But for my round, it was still part of the deal. At worst, you're looking at maybe seven years of well-funded research. Extremely well-funded research, yeaah.


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[Assistant] And I ask for money to have two post-docs and conferences and a lot of travel. So, you know, very well-funded research center essentially for four to seven years.


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[Assistant] Almost, like the first two minutes you really feel like that, you know. You have to, you don't have to wear a suit, but you know, you kind of feel that you need to wear a suit. You know, I was talking here with-


[User] Please transcribe this text

[Assistant] I can't wear a suit with, you know, the hair just flowing to the side. Rock and roll hair, yeaah. So I talked with one of my colleagues here about this, wearing a suit, and he said, well, you don't have to wear a suit, but if you don't wear a suit, you're going to have to convince me you're a really good mathematician because you're not taking this seriously enough. Right.


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[Assistant] I don't know if I agree with this. I don't think everybody I spoke with would agree with this approach. But what do you have to lose? Just put on a suit.


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[Assistant] The first time I ever wore a suit was just a few months before that, you know, for a wedding that I went to. So...


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[Assistant] You know, it was a new experience and it wasn't that bad. So I figured, okay, why not? I even had a formal Friday, because I would normally just walk barefoot or just, you know, basic shirt and jeans, whatever, and I would just come with a suit every Friday.


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[Assistant] Yeah, so, you know, you go to the interview, I did this terrible mistake, so they tell you, you can come to a hotel, we can even reimburse you for this hotel, and I chose the same hotel as the interviews.


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[Assistant] Now that sounds smart because you say, well, I just come down and go to the interview, but it's super stressful because it's a lot of interview. So all of the hotel was the interviewers of the different panels. When I checked in, I went up in the elevator and this woman asked me, oh, are you here for the UK writing? I'm like, yeah. Oh, which panel are you sitting on?


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[Assistant] I was like, what? No, I'm interviewing. So it was very stressful, like after the interview I went for dinner with my colleague in Bristol and


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[Assistant] On the elevator, I meet one of my interviewers, and we talk a bit.


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[Assistant] He would only say that to me if I'm not getting it. Oh no. You know, it was extremely stressful. I would not recommend this.


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[Assistant] And I come back up, just to pick it up, and I say I'll just check my email, it's probably not there, it's probably gonna be another week, and exactly three seconds


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[Assistant] Fortunately we can't do that. But I can use the money for a big conference in three years when everything is hopefully back to normal.


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[Assistant] I'm teaching all through my masters and my PhD. I even, so normally you do like, TA work.


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[Assistant] And in Israel... The TA is teaching assistant? Teaching assistant, yeaah. And in Israel that means that you actually teach. So you do revisions of what was in the class and you solve things, but you also prove, you talk about the theory a little bit.


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[Assistant] So it's a lot more hands-on than what maybe happens here where they just sit in a room and people come and ask for help.


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[Assistant] You know, doing the homework. And so I've done a lot of teaching.


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[Assistant] And so I felt it's fine if I don't teach for the next couple of years.


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[Assistant] Now add to this the fact that, because of the army service in Israel, most of the students are older.


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[Assistant] They've seen the world, because nobody goes to university after the army service. They take a year, two years, they work, they travel, they sort of unwind from this very stressful experience. So they come to the university, they're already very much adults. It's not high school plus.


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[Assistant] So the level of students is incomparable to anywhere else in the world. Again, just about, you know, the maturity and stuff. I'm not saying that they're necessarily better than other students. It's just, you know, the starting point is a lot better.


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[Assistant] You know, the, why am I even teaching this? I'll give you this terrible example that I'm trying to, to...


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[Assistant] Make people upset about you have to write the exam before you start teaching the course you as the as the as the lecture.


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[Assistant] Now they say that this is, you know, to make sure that everything is fair for everybody.


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[Assistant] But how is that fair? I have seven years of teaching experience and no two years were alike. Because I would teach the same course like four years and then a different course for four years.


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[Assistant] So no two ears are alike. Every time students have something that they saw on another course that, you know, sort of primes them for a specific subtopic.


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[Assistant] You know, to be more interesting here or you put more focus there. If I have to write an exam before I even engage with the students,


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[Assistant] I covered my host a couple of times when he wasn't here and was like, oh, maybe you can cover one of my lectures in the Seth Theory course. And one time he said, you have to teach this proof, it's going to be in the exam. That is insane.


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[Assistant] That is crazy. The reason they do it, I was told, is that some 10 years ago or so there was a strike just before the exam period and the university ended up without exams.


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[Assistant] So now they want everybody to write the exam, and if you want to strike and not gate, then you do you.


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[Assistant] Okay, right. We just get somebody to read your solutions and grade the exams.


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[Assistant] The main focal point of SAS theory is adding axioms to your theory. So you have sort of the base theory for mathematics, and then you say, okay, what happens if we add these axioms that increase the, the, the, how strong is the theory? You can prove more.


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[Assistant] And you're free to choose different ones and do different work, but you want to ask how much can you prove with certain axioms.


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[Assistant] It's called large cardinal axiom. So if the basic one is kind of the set of all natural numbers is a set, that's, you know, it's called the axiom of infinity.


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[Assistant] So for some things we know it's necessary, but you can also ask how necessary, to what kind of fragment of the Axiom of Choice do you need to keep in order to prove a certain thing. And the Axiom of Choice lets you look at this large cardinal axioms.


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[Assistant] And say, oh, I have like three or four different ways to phrase this axiom and they're all equivalent, but this equivalence


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[Assistant] Is very much dependent on the axiom of choice. Now, some of these were studied extensively in the eighties. So you say, okay, I'm not assuming the axiom of choice, just this one way of phrasing it, but it's sort of the wrong way to think about this large cardinal axioms. And until a few years ago, there were no serious works on, let's look at the actual


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[Assistant] Large part of that, you know, of the cardinal. So I had some work about this with my friend from the PhD. We had this, obviously, I think that a fantastic paper.


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[Assistant] Where we break grounds and essentially create this whole new field. And what I want to do is sort of push that forward and see how far I can get with it.


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[Assistant] So, there's a problem that's open since 1902. When I was a master's student, I read about this. And I said to myself, what do you need to prove, you know...


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[Assistant] To, to solve this problem one way or another. That's essentially the thing that guides me to come up with new ideas.


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[Assistant] What's that called? It's called the partition principle, and the problem is whether or not it implies the action of choice. Okay. So, without getting technical, you can phrase the action of choice in a certain way, and then the partition principle says, okay, just, you know, remove this one tiny bit from the formulation, is it equivalent? We don't know.


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[Assistant] There's been some recent progress about this, some group of people from Brazil, none of which is a set theorist.


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[Assistant] Uh, develop this new thing called Flow, and they claim that, you know, they prove that, uh, it doesn't imply the action of choice. The first paper, uh, is available on archive. It had a lot of gaps.


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[Assistant] The second paper was released two months ago. I'm still reading through it. I just had some crazy two months so I had to put it aside. But I hope to get back to it last week. Right.


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[Assistant] People don't really know about that. In fact, a lot of people who teach set theory without knowing a lot about the action of choice would just assume that this is just the action of choice. And that's equivalent and that's it. And they're always surprised. Oh, you told me about this thing. Oh, really? It's not equivalent. Oh, it's open.


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[Assistant] But it is the oldest currently open problem, you know, in set theory. So, you know, I think it's...


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[Assistant] The very least interesting, right? And if you look at Fermat's last theorem, it's not a very important theorem, but on the journey to, you know, to get there, so much amazing new mathematics was developed. So even if this is not a very interesting problem, you know, on paper, I think that to get there, you will need to develop this very good tools and then you can apply them elsewhere.


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[Assistant] It's just at the end of how abstract you can be and still do pure math.


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[Assistant] You know, just in, in favor of completeness, there are other foundations of mathematics you can go to, and they're also sort of at the end, at the frontier, and there would be people who tell you, oh, don't study this because all math is going to be based on, you know, homotopy type theory in five years, you know. But that's not true.


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[Assistant] Today's guest is the London based school teacher, Bobby Seagull. Bobby's known to many people in the UK for a star turn on the quiz show, University Challenge.


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[Assistant] His initial moment in the spotlight has led to a part-time career in the media, fronting TV shows and becoming something of a mathematics cheerleader.


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[Assistant] But there's much more to Bobby's story, which includes all sorts of fascinating twists and turns.


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[Assistant] It's not uncommon when I do these podcasts for the person I'm interviewing to send me a few kind of little briefing notes and a few things to look at just to help with my research. You sent me six pages of bullet points totaling 2,392 words.


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[Assistant] I found it fascinating though reading all about you, and like, we can't possibly cover all these points you've got here, but...


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[Assistant] So, let's first deal with the elephant in the room, or the seagull in the room, and that is your surname, which I just thought, oh, it's an unusual surname, you know, people have unusual surnames, but reading your notes, there is quite a story behind it, the surname seagull.


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[Assistant] Hey, I was born in Glenelg, which is a palindrome.


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[Assistant] Oh wow. One last question about the seagull issue then.


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[Assistant] How do you feel about seagulls themselves now when you go to the sea side and you see them? Do you have a warmth and an affection towards them or a resentment towards them? Because seagulls are very polarizing animals.


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[Assistant] So tell me a little bit about childhood. I get the impression you four boys were pretty clever lads.


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[Assistant] Bobby, do you think your dad was being really strategic and thinking, if I do this, the boys are going to be, are going to grow up, you know, smart and interested and curious, or was that just him that he just wanted to go to the library with the boys and read books?


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[Assistant] Bobby, what did your father do? What was his, how did he earn money himself?


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[Assistant] Now, from the, uh, the tomb you sent me of notes, uh, that I was, that I was reading earlier, obviously there were four brothers, you're the second oldest. I got the impression it's your older brother, Davey, that you were particularly close to and sort of intertwines with your life more than the others perhaps.


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[Assistant] So what was that like? Having an older brother who obviously, you know, it sounded like he would have needed also a lot of, you know, care and stuff like that. Did that, did, did having a brother in that situation affect your life very much, do you think?


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[Assistant] What were you like? Obviously it sounds like you were incredibly bright and, you know, curious and, you know, being, uh, encouraged by your father. What were you wanting to do? What were your ambitions? What did you want to be when you grew up?


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[Assistant] Now, what kind of school were you going to at this point? Were you going to like, uh, you know, a challenging school if you were living in a part of London that, you know, wasn't flush with cash?


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[Assistant] Pull yourself up by the bootstraps sort of philosophy. Yeaah. I would say that. Having said that...


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[Assistant] I read that you ended up going to the poshest of all posh schools. How did this happen?


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[Assistant] Listeners from outside the UK, you can just give a, just a like a quick executive summary of what Eaton is, because they may have, Eaton may be a name they've heard of, but they might not realise this is kind of, you know, this is the super posh school where all the royal family goes and, uh, yeaah, like you say, almost all the prime ministers come from there and,


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[Assistant] You have to wear fancy uniforms and suits and outfits and things, don't you? Sort of paint the picture of Eden for us.


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[Assistant] Bobby, what did your parents think when you got in? I mean, you've already given away the ending, you did get the scholarship. Sorry, that was a bad story. What did your parents think when that offer came through? That must've, like, for someone in East Ham? Oh, yes, astonishing. I remember, I remember the day I


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[Assistant] Right, this is uh, this is cricket terminology. Cricket, oh yeah sorry, yeah cricket, cricket. So uh, so, how did you feel about that Bobby? You seem to me like someone who doesn't get very affected by that, or did it affect you being like, you know, surrounded by a whole boarding house of white boys?


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[Assistant] How did you perform academically? Were you still, like, you know, kicking goals?


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[Assistant] Bobby, why do you think you were so good at history then? What was it about you that gave you an aptitude for that?


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[Assistant] Just a quick break to thank Brilliant for sponsoring this episode.


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[Assistant] Brilliant's a hugely impressive online collection of interactive courses covering all sorts of topics from probability to calculus, from neural networks to cryptocurrency. All the courses are meticulously designed by people who really love learning.


[User] Please transcribe this text

[Assistant] I've met some of the brilliant people. They're all so passionate about education, about making us smarter. You can really tell when you look through their courses. To check it all out, go to brilliant.org slash number file. Using the slash number file will let them know you came from here.


[User] Please transcribe this text

[Assistant] And give you 20% off a premium subscription if you decide to sign up. By the way, you can also give a brilliant subscription as a gift to someone else, which I think is a really clever present. That's brilliant.org slash numberphile. Seriously, folks, check it out. It's not only smart and clever, it's really good fun.


[User] Please transcribe this text

[Assistant] Now Bobby, in this mighty tome you sent me about the not so brief history of Bobby, I think my favourite-


[User] Please transcribe this text

[Assistant] Sentence or the one that stuck out to me that I really want to hear about is how you ended up choosing where to go to university to start with. It seems like an interesting story to me. Tell me about how you decided where you would go to university.


[User] Please transcribe this text

[Assistant] Now he's doing maths at Trinity at Cambridge, like, which is like, top gun for mathematics.


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[Assistant] Like you kind of thought you needed to have a bit of distance from him.


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[Assistant] Now, so you're at Oxford, and it sounds like this is the first time that suddenly things change a bit.


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[Assistant] So for people listening outside the UK, a first is like the top mark you'll get on your degree.


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[Assistant] You're a university dropout. That's what I am. That's what it is. So the thinking here, Bobby, is going to Royal Holloway is because you want, you need a reboot, basically. You need a fresh start, otherwise you feel like you're not gonna get where you need to be.


[User] Please transcribe this text

[Assistant] I can imagine like it's a bit of a dent to your ego at this stage, cause obviously, you know, you've been, you've been having so many victories in life. Did you spin that to your family and friends as, oh, you know, just Oxford's not for me and I, and I want to be a change of surroundings or were you honest and were you saying, look,


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[Assistant] I've muttered up, I blew it, I took my eye off the ball and this is the only way I can fix it? Or how were you spinning it at the time as opposed to how you tell it now?


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[Assistant] For people who don't know, because obviously University Challenge is a real institution in the UK, but I know a lot of Americans and people around the world are listening. This is a quiz show in the United Kingdom where


[User] Please transcribe this text

[Assistant] Universities send in teams of four students to do sort of general knowledge quizzes against each other, a series of rounds and knockout competitions. And then there's a big final with two universities go head to head. And it's quite well known for the questions being,


[User] Please transcribe this text

[Assistant] Difficult, very specialized and things like that. And Bobby, you ended up on this show and became a bit of a cult hero. Can you tell me how that happened?


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[Assistant] Anna Preparer. I've got the document in front of me to prove that.


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[Assistant] Bobby, I just want to jump around a bit in the timeline again because it's something I want to understand a bit better.


[User] Please transcribe this text

[Assistant] You obviously, you know, did put, well you put more than a toe in the water when it came to sort of banking and accountancy and that sort of, that world of finance. Obviously, you know, there's money to be made there.


[User] Please transcribe this text

[Assistant] I never think of people who get into teaching as making a lot of money.


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[Assistant] What changed? What made you say when you were in with all the banking and the finance? Say, I'm gonna turn my back on this, I'm gonna go and convert to become a teacher. Why? What happened?


[User] Please transcribe this text

[Assistant] Bobby is that? I mean that's, you know, who am I to criticize that? What fantastic things to be doing. But you were saying that you kind of turned your back on finance and the money and various careers because you wanted that sort of granular one on one.


[User] Please transcribe this text

[Assistant] Moments, those human moments, and it feels like you've drifted away from that again now, now you're all big picture and policy and that sort of thing, like how are you balancing those two desires?


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[Assistant] Bobby, you mentioned your research. I know you have some thoughts in general on just public perception of mathematics. How are you feeling about that these days?


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[Assistant] You identify a problem, right, and it's easy, you know, everyone has heard, oh, I hate maths, I hated it at school, the TV presenters you talk about, joking about how they hated maths.


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[Assistant] And it does have this huge stigma attached to it. No one could deny that. A stigma that other areas don't have attached to it. But why?


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[Assistant] Why did maths get it? Why, why don't people say, oh god I hated reading at school?


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[Assistant] Oh god, I've never liked words. You never hear that? You absolutely do not. Why did numeracy get it and not literacy?


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[Assistant] Bobby, does it matter if people don't like mathematics though? Like as long as the people who need to send the probes to Mars or build the bridges or my accountant, as long as they know how to do mathematics, why does it matter if the person walking the street hates mathematics if they don't need to do it?


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[Assistant] Well that's all for today, our thanks to Bobby for his time and for those extensive preparation notes. For more information and links, check out all the details in the description for this episode.


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[Assistant] Also thanks to Brilliant for sponsoring this episode. Remember brilliant.org slash Numberphile. And also thanks to the Mathematical Sciences Research Institute in Berkeley, California for its important support of Numberphile.


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[Assistant] I'm Brady Harren. We'll be back with another podcast sometime pretty soon. In the meantime, it can never hurt to rate and subscribe the podcast and all the usual places. That helps inform all those invisible algorithms that decide the fate of podcasts and videos like ours.


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[Assistant] Did lots of maths as part of that, but very much maths as an engineer rather than maths as maths. So I think the conversations when I was growing up, maths was part of the conversation, but it wasn't.


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[Assistant] I think I was lucky in the teachers that I had who were always very supportive. I enjoyed...


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[Assistant] Showing me where maths could go beyond what we were doing at school. So I guess the work at school was inevitably very focused on the school curriculum and GCSEs and A levels and so on and


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[Assistant] I grappled with it, it wasn't that I found it all easy, I sort out.


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[Assistant] Demanding and the workload is intense, but I guess I was sort of up for that challenge.


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[Assistant] A bit of time doing admin for them and sorting out some spreadsheets and I spent a bit of time packing teddy bears in cardboard boxes, which is cool, just not very mathematical.