[User] Please transcribe this text

[Assistant] You're like the Numberphile original, aren't you? You were in the first Numberphile video. Yeah, that's correct. You must've been in the most of anyone.


[User] Please transcribe this text

[Assistant] Yeah. Do you feel like in a warm attachment to the project?


[User] Please transcribe this text

[Assistant] There are multiple answers to why we write in Numberphile videos on brown paper as opposed to white paper or a white board or a black board. I did consider like buying slates and chalk but


[User] Please transcribe this text

[Assistant] The reason is, well, there are a few. One is it shows up better on film. Like it looks better filming the brown paper than white paper. I'm able to keep all the work afterwards. If it was on a whiteboard, it would all be erased and I want to be able to keep everything.


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[Assistant] As an object, but also as something I can refer back to. So I like that they're tangible objects. I like that it's like a physical object. It's unique and it's a bit gimmicky. You know, it's unique to the channel as opposed to the cliche of a whiteboard. It's a brand, isn't it? Yeah, it's like a brand.


[User] Please transcribe this text

[Assistant] And it's more kind of sort of physical and people interact with the paper and there's a big long shopping list of reasons, but.


[User] Please transcribe this text

[Assistant] Yeah. Yeah. Has it changed much from the start from your perspective for people who don't know, which is every single person except you and me, we've just been recording for the last couple of hours here in my office. Is it different like today than it was all those years ago?


[User] Please transcribe this text

[Assistant] No, no, no, that's what you like to do. Once you feel like you've got five you want to do, you'll jump on a train and come and visit me and we'll film together.


[User] Please transcribe this text

[Assistant] So James, I'd like to come back to Numberphile later, cause it is a big part of your life now making videos. So it's something we're obviously going to talk about, but before we get too lost in the weeds with the minutia of the videos, I want to find out a little bit more about you and your background. So where are you from?


[User] Please transcribe this text

[Assistant] Okay, so from nought to seventeen, what would you like? Would you like...


[User] Please transcribe this text

[Assistant] Math nerd boy right from the start, what were you into like as a real youngster?


[User] Please transcribe this text

[Assistant] So even as a youngster, cause like I imagine most kids get pretty obsessed with TV cause kids just love TV, don't they? But were you already at an early stage thinking a step ahead and like behind the lens, like how do they make that?


[User] Please transcribe this text

[Assistant] Do you remember which TV shows or movies or things like made the biggest impression of the many you watched probably?


[User] Please transcribe this text

[Assistant] Worse their ability? Were you better at maths than the other kids in the class? Or did you feel better?


[User] Please transcribe this text

[Assistant] And teachers weren't saying like it wasn't in your report card, James has an aptitude for this. Do you put that down to some kind of humility of yours or do you put that down to the education system or?


[User] Please transcribe this text

[Assistant] So those devices, those professor calculators for want of a better name, they look like a little man with a mustache and glasses, don't they? Like the way they're designed. Do you look at that now and feel warm feelings like you're a mentor?


[User] Please transcribe this text

[Assistant] What about like your family? Were they shoving math books in front of you or fostering that or were they just letting you get on with it?


[User] Please transcribe this text

[Assistant] Okay, so he's like, well that sounds very typical English, humble, mustn't grumble, do your bit.


[User] Please transcribe this text

[Assistant] Were there ever times where he would say to you then, don't do mathematics, James, you're not going to get like a good job out of that and do this? Or was he like, yeah, do what you want. I don't understand it, but do you do it?


[User] Please transcribe this text

[Assistant] So as you're getting a bit older in your teens, it must be becoming apparent now. Oh, actually I am pretty good at mathematics and you start thinking, okay, I'm not going to be a cameraman. I'm going to be a mathematician. When does that switch?


[User] Please transcribe this text

[Assistant] And that's all it took, it just took one teacher saying, you can do it, and you're, alright, they're now applying. I'm doing it, that's all it took.


[User] Please transcribe this text

[Assistant] English or mathematics. Okay. What score did you get? Although I don't understand how your level scores work.


[User] Please transcribe this text

[Assistant] But you were getting all the A's, so you had some choices. How come you ended up at...


[User] Please transcribe this text

[Assistant] So the step up from high school level mathematics to university level mathematics as an undergraduate, was that a big step or was that an easy transition?


[User] Please transcribe this text

[Assistant] And at university where you thought, yes, this was the right decision. Like, thank goodness I did mathematics.


[User] Please transcribe this text

[Assistant] At university, what were you like as like a person? What were you into? Were you in a rock band? Did you play cricket? Were you in the chess club? What were you like socially? How were you developing like as a person?


[User] Please transcribe this text

[Assistant] How many people in the Lancaster Juggling Club at peak? Is it like four or 400? 50 or so. Okay. Are you elected as president or you? Yeah. Right. No, it's not something that I see. You were called to public service for juggling.


[User] Please transcribe this text

[Assistant] So coming to the end of your Lancaster, your undergraduate degree, were you high in the class again? You were getting quite strong marks.


[User] Please transcribe this text

[Assistant] How did that affect you? Did it, you know, make you stronger or did it crush you for a while?


[User] Please transcribe this text

[Assistant] So this is towards the end of your degree. You're not going to be a spy or a code breaker by the looks of it. What do you do now? What's next?


[User] Please transcribe this text

[Assistant] What was it like being surrounded by all these other math geniuses? Like you said, for the first time you weren't necessarily the smartest guy in the room. Was that good for you or bad for you?


[User] Please transcribe this text

[Assistant] So you were telling me about the, the young James in Nottingham understanding that being a mathematician was a thing. It was possible.


[User] Please transcribe this text

[Assistant] Now you're doing a PhD, you're spending all your time with high level mathematicians doing high level mathematics. How was the reality of mathematics and mathematicians different from what the little boy imagined?


[User] Please transcribe this text

[Assistant] It does sound unfair to say to a young person, basically lock yourself in a room for three years and have an important original idea that hundreds of thousands of geniuses before you haven't had.


[User] Please transcribe this text

[Assistant] Became blurt. You did finish your PhD though. You became Dr. Grime. Yes. Now what do you do?


[User] Please transcribe this text

[Assistant] But sometimes, you know, when you and I are talking or making videos, you'll tell me about this extraordinary proof or a breakthrough or something amazing that a mathematician did. And I can tell from your enthusiasm that you're impressed by what they did and the impact they had and what a wonderful contribution they've made to mathematics.


[User] Please transcribe this text

[Assistant] Don't you ever wish you were that man or woman who'd done that rather than just being the person telling the story? The cheerleader.


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[Assistant] So how did you get from being a postdoc at a couple of different institutions to an outreach dude? What happened next?


[User] Please transcribe this text

[Assistant] At that point though, I'm assuming, you know, there's probably not- YouTube's not a big thing or anything like that. No, you're thinking you'll do it, you'll-


[User] Please transcribe this text

[Assistant] Apply to the BBC to present their next TV show.


[User] Please transcribe this text

[Assistant] What were you doing? Just putting like a camera on a tripod and standing in front of it and


[User] Please transcribe this text

[Assistant] Okay, so there was an ad for yogurt that had a singing banana. They named the tuck shop at your school singing banana. And then when you were sitting at a computer and had to come up with a handle, that's just what you pulled out of the air.


[User] Please transcribe this text

[Assistant] What was the job though, just to be like an outreach person, to go and give lectures or something, or go to schools?


[User] Please transcribe this text

[Assistant] So you went to the interview thinking, well I'm not going to get my hands on the Enigma, but...


[User] Please transcribe this text

[Assistant] That's the secret, James. It's always the interviews you think you bomb that you end up getting.


[User] Please transcribe this text

[Assistant] Brilliant, did you walk back and sign the papers? That's, I've never heard of someone hearing that quick.


[User] Please transcribe this text

[Assistant] Well let's explain that, because I guess a lot of people listening to this will just know you as the guy who's in lots of Numberphile videos. Explain to people this other job you have, your day job, your actual job, how you actually eat.


[User] Please transcribe this text

[Assistant] So what happens to people that go to a website today and book you and like, and you come out and...


[User] Please transcribe this text

[Assistant] No, I'll promote it for you. There'll be a link to James's website and the notes to this podcast. And if you know someone who wants to have a great talk about mathematics and the Enigma machine, you go, go ahead and click on that. Presumably you have to carry this machine all around the world.


[User] Please transcribe this text

[Assistant] What happens when you go through like customs at countries and you've got this Nazi code machine? I tell them it's a typewriter.


[User] Please transcribe this text

[Assistant] We're getting close to Numberphile again, clearly at this point. A lot of people probably want to know.


[User] Please transcribe this text

[Assistant] How you became involved in the project as a founding father.


[User] Please transcribe this text

[Assistant] Buckles on my hat. Yeah. Buckles on my shoes. I will be curious to hear how you tell this story because I've, I work on a few YouTube channels and I've been sitting in the audience before with some of my other collaborators, like on periodic videos. I was once sitting in an audience where, and Professor Poliakoff told the story of how he and I started making the periodic videos project.


[User] Please transcribe this text

[Assistant] I mean, yeah, that's not, you're not far wrong there. That's, I mean, from my end, I was making a few different YouTube channels, periodic videos, Bible X ones you mentioned, 60 symbols and a few others. YouTube approached me and had grants available to start new channels. And they said to me, if you were going to start a new educational channel, what would you do?


[User] Please transcribe this text

[Assistant] And I said to them, Oh, I've got two ideas. I'd want to make an astronomy one, which became my deep sky videos channel.


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[Assistant] And I said I'd want to have a mathematics one. And my idea to do it was to do, was number file making about numbers. So it was less intimidating and not straight away math, math, math. And they agreed they were good ideas, but to my surprise, they funded both. So I had a grant and now I was like, Oh God, I've got to make these videos.


[User] Please transcribe this text

[Assistant] And that basically coincided with the time that you just happened to get in touch as a viewer and said, Hey, I like what you're doing. I'm interested.


[User] Please transcribe this text

[Assistant] This is what I'm doing. If you ever want to work together and I probably get a lot of messages like that still to this day and nine times out of 10.


[User] Please transcribe this text

[Assistant] I remember, I remember like, cause those stories about just arbitrary numbers that have interesting properties like still give me chill. Still sometimes now if we're filming you show me just some random fact about a number, I still get chills down my spine from that way more than all the others.


[User] Please transcribe this text

[Assistant] Some Numberphile videos, in fact lots of your Numberphile videos have become very, very popular, they've been watched millions and millions of times. That's like great, because that's always what we wanted to do.


[User] Please transcribe this text

[Assistant] But I guess that doesn't come without problems and negative sides as well. There's the notorious YouTube comments. There's the fear of getting things wrong on the internet, which is a fear that lives with everyone who makes things on the internet. How have you found coming to grips?


[User] Please transcribe this text

[Assistant] With that as you become better and better known and more and more people are watching and also the internet becomes a more crazy place. Do you read comments?


[User] Please transcribe this text

[Assistant] What are some of the nice things about doing it though? You keep doing it, so there must be some positives.


[User] Please transcribe this text

[Assistant] Do you meet people, you know, starting out at university who say that it hadn't made a difference?


[User] Please transcribe this text

[Assistant] Has it ever happened to you when you've been with your dad? No. That's the moment I wanna see.


[User] Please transcribe this text

[Assistant] When you give talks and things like that, and obviously I imagine you have question time at the end of a lot of your talks, what question do you think people ask of you the most?


[User] Please transcribe this text

[Assistant] I'm sure you'd prefer it, but my question is what question are you asked the most?


[User] Please transcribe this text

[Assistant] Let me ask you one then. Yeah. What's your favourite number for a video you've made? Nice question. You must get asked that a lot.


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[Assistant] Is there a topic or a video that you want to do on Numberphile that you haven't done yet for some reason because you're too intimidated by it or you can't quite get it right? Have you got your white whale?


[User] Please transcribe this text

[Assistant] Well then maybe I'll have to keep it a secret. One last thing. What's the next thing for you? Like, I hope you keep doing Lumberfar videos. I will keep begging you to do them and I'm so grateful that you do. But like, do you have like a next big step? Is there an end game? Do you want to present that BBC documentary? Do you want to?


[User] Please transcribe this text

[Assistant] Do something different in a new mode of communication. Do you want to go back into mathematics more and actually maybe prove something, create


[User] Please transcribe this text

[Assistant] To learn more about James, to watch his videos, all that sort of stuff. Maybe even book him to speak at your school or organization or club. Check out the links in the notes for this podcast. A good starting place is jamesgrime.com


[User] Please transcribe this text

[Assistant] Now thanks to James for joining us today and his ongoing dedication to Numberphile videos. For supporting this podcast, I'd also like to thank the Mathematical Sciences Research Institute in Berkeley, California.


[User] Please transcribe this text

[Assistant] And also in Berkeley, the audio engineering company, Maya Sound, which when they heard we were starting a podcast through their support behind us, we're really appreciative to them as well. We'll be back again soon with another episode, but from me, Brady Harren, it's bye for now.


[User] Please transcribe this text

[Assistant] I was born in Champaign, Illinois. Champaign? Yeah, spelled differently than the proper champagne.


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[Assistant] Yeah, but it's made in barns out of leftover corn.


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[Assistant] Yeah, no, I think I was normal. I mean, there's this phenomenon where the way you remember yourself has nothing to do with the way that other people remember you.


[User] Please transcribe this text

[Assistant] And so when I was small, I mean, I thought of myself as like quite outgoing and you know, like to have fun. But in reality, I think I was like a little nerd.


[User] Please transcribe this text

[Assistant] I really- you've pinned me down by asking the question that way?


[User] Please transcribe this text

[Assistant] I was back visiting 10 years after I graduated high school for a band reunion, so that's already partially answering your question.


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[Assistant] And I, at the time I think I had just gotten like my first post-PhD job, uhm, this like postdoc at MIT. And I went there and I was really expecting everyone to be like shocked that in the end what I had done was go get a PhD in mathematics and like do this super nerdy academic mathematician thing.


[User] Please transcribe this text

[Assistant] And then when I got there, everyone was like, oh yeah, yeah, we could tell when you were in school that that was the kind of thing you would end up doing. And I had thought like I would be, you know, a rock star or something.


[User] Please transcribe this text

[Assistant] No, not at all. Quite the opposite. Like, first of all, I didn't know that it was a job until I was probably in graduate school, I would say. Like, I didn't understand what research mathematics was and what that meant. And then the other thing is just, it wasn't kind of the group that I identified with as a kid. Uhm, I think I went to one meeting of math team when I was in my first year of high school.


[User] Please transcribe this text

[Assistant] When you're a 12 year old girl and you're kind of nerdy, social acceptance is like a really high priority.


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[Assistant] And so after my first meeting of math team, I was like, well, I think like I don't really want to belong to this group. I, you know,


[User] Please transcribe this text

[Assistant] I want to talk to different people and I want to sort of be more, um, be more sociable and be in, be in a different group. So it was a very sort of, first of all, very judgmental 12 year old girl, which is not super surprising, I suppose. But really it was like a conscious decision on my part that even though science and math was stuff that I was good at and I found fun.


[User] Please transcribe this text

[Assistant] Uhm, I'm sure I would have been better at it just from practicing and being surrounded at it, uhm, surrounded by it rather. But I'm not sure that that's like...


[User] Please transcribe this text

[Assistant] Something that would have changed my life for the positive in any way. I mean, we, we put a lot of pressure on sort of performance in school and that kind of thing. And, and it's a means to an end, not a thing in and of itself. And so, so in fact, I'm really happy with the way that I sort of circuitously came around to becoming a mathematician.


[User] Please transcribe this text

[Assistant] Oh, that's a good question. Okay, let's see. So when I was young, the two main things that I wanted to do, I think when I was really young, I wanted to be an astronaut, which is, you know, sciency, but I was in it for like the see the earth from the moon type of adventure.


[User] Please transcribe this text

[Assistant] The fear that any of my colleagues might hear such a thing, uh, will definitely prevent it.


[User] Please transcribe this text

[Assistant] So I was interested in like performance type things also in school and I did think about doing that. Uhm, I played the trumpet quite seriously in school and I thought about going into that. My uncle is a professional trumpet player.


[User] Please transcribe this text

[Assistant] Uhm, just a month ago or so I'm working on a piece because I might audition to join an orchestra.


[User] Please transcribe this text

[Assistant] Oh, so it was like late in university when I switched into maths. Alright. So I had started in biology. You said maths!


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[Assistant] I think I switch, it's basically like the maximum confusion level. I switch flexibly between math and maths. And z and zed, that's a big one for me. Because like I tried to give my students a break by learning to speak with zed instead of zed because I use it as a variable all the time when I teach.


[User] Please transcribe this text

[Assistant] That one, that one I use sell unless I'm consciously thinking about mobile. But mobile sounds weird to me because not only is it the different word for it, but it's pronounced differently than in an American accent. And so there's like the double hit of the change.


[User] Please transcribe this text

[Assistant] I was interested in genetics and the problem was, so I was in biology for like, I think a year.


[User] Please transcribe this text

[Assistant] And the problem was that there was a chem lab at 8am on Fridays. And like, I got to university and I realized that there was, you know, a lot of interesting things to learn in biology and chemistry and also a lot of interesting bars to go to.


[User] Please transcribe this text

[Assistant] I don't know how to answer that question because I think they're so closely related, right? Like there's kind of a feedback cycle of you're initially kind of not so good and then you lose interest and then it goes back and forth, you know, it gets worse and worse.


[User] Please transcribe this text

[Assistant] So hating lab work, I, I switched my major into psychology and I tried that for like one or two semesters. And the problem is, and I'm going to get in trouble with a lot of people here, they just make all that stuff up. Right? Like I, I was learning some like intros.


[User] Please transcribe this text

[Assistant] Yeah, that's right. Don't blame Brady. I was learning all this stuff in Psych 101 and Psych 201 and all of this neuropsychology stuff.


[User] Please transcribe this text

[Assistant] So uhm, so then I switched to something more valuable, which was Italian.


[User] Please transcribe this text

[Assistant] Oh, I really hate to tell you all of my justifications. This one is the worst. So I had to take some like language requirement at my university and I wanted to take Portuguese, but the class was full so I took Italian instead.


[User] Please transcribe this text

[Assistant] The professor was attractive, so I took more Italian classes.


[User] Please transcribe this text

[Assistant] So I'm in computer science and I have to take some introduction to proofs class in mathematics because it's one of the requirements for CS. Again, because of like scheduling randomness, I ended up in the honors section of the intro to proofs class.


[User] Please transcribe this text

[Assistant] And it was really fantastic and it was sort of like the first time when I had made, so this is a thing that I get to still experience and is a lot of the reason why I'm in this field still.


[User] Please transcribe this text

[Assistant] Which is I got to experience for the first time that transition from totally not understanding something, like being completely lost, someone explaining it to you, you know, possibly over and over again and still not having it get into your brain. And then suddenly one moment, you just get it. It just clicks. And then forever after you are able to understand it.


[User] Please transcribe this text

[Assistant] And so I had this phenomenon with a piece of mathematics in that course.


[User] Please transcribe this text

[Assistant] Yeah, it was, it was the Bolzano-Weierstrass theorem. So it's this theorem that says if you take a collection of points, say, let's say real numbers between 0 and 1, okay, if you have infinitely many of them,


[User] Please transcribe this text

[Assistant] I'm trying to think of a better way to describe it, that it's essentially saying that, uhm, if you have infinitely many points in like a closed box, that there has to be some point which is well approximated by them. Anyways, it's, it's just some like, little-


[User] Please transcribe this text

[Assistant] Well it depends on the infinite set of points you start with. Okay. Right, so if you think about the set of points like one and one half and one third and one quarter and one fifth and la la la, that's an infinite set of points that are between zero and one.


[User] Please transcribe this text

[Assistant] And they accumulate at the point zero. So the theorem itself is not telling you where the point is, it's just telling you that it exists. But for some examples you can figure out what it is.


[User] Please transcribe this text

[Assistant] What I was looking for was like, what's a degree that is sort of like minimal effort?


[User] Please transcribe this text

[Assistant] Outcome, and it was a very like, uh, cost benefit analysis way to look at, at university, which I think is pretty common actually, and, and not something that we talk about. We talk a lot, at least on the faculty level, we talk a lot about like, passion for subject and that kind of thing, and that's not really how a lot of students make their decisions, and I didn't either.


[User] Please transcribe this text

[Assistant] Because I just hadn't experienced it for the first few years.


[User] Please transcribe this text

[Assistant] Yeah, yeah, so the next term, instead of taking this like hodgepodge of coursework that I had been doing, I took four advanced math courses. Now I'm like self-conscious about math versus maths.


[User] Please transcribe this text

[Assistant] That's a great question. So they were not like, congratulations on being proactive.


[User] Please transcribe this text

[Assistant] I think they were not that worried because, uh, like one feature of my personality that has been sort of constant since I was quite young is a high level of independence.


[User] Please transcribe this text

[Assistant] And so I think, you know, they had some knowledge that whatever it ended up being, I would come through with some level of competence and independence and.


[User] Please transcribe this text

[Assistant] Well, some of the decisions have still been accidental. I think, for example, deciding to apply to graduate school, it seemed easier than applying to other jobs.


[User] Please transcribe this text

[Assistant] I think that if at any point I had stopped seeing like a practical future for myself that I probably would have switched.


[User] Please transcribe this text

[Assistant] Yeah, so I did keep the practicalities in mind still because I think like this is a really big motivator for me is that I want to have a nice life outside of work, which is funny given that you just asked me what I'm going to do over the weekend and I said I'm going to work.


[User] Please transcribe this text

[Assistant] But uhm, but no, in reality, like the flexibility of the job and that kind of things I view as compensating for the fact that it's not, you know, going to...


[User] Please transcribe this text

[Assistant] To the extent that I thought about it, it would be research mathematician. Yeah. Yeah. Because I already knew that I was really interested in this feature of academia, which is, um, like the level of independence that you have not having a boss telling you what to work on. I could already see was like a high priority for myself.


[User] Please transcribe this text

[Assistant] Uhm, because I had done this honours intro to proofs class, uhm, they moved me to the honours section of the maths undergraduate cohort.


[User] Please transcribe this text

[Assistant] And that was pretty small. Uhm, I think it was just two of us out of the 16 or 15 or something like that that were in the group of honors mathematicians.


[User] Please transcribe this text

[Assistant] The only like sort of negative thing at that level for me was just that


[User] Please transcribe this text

[Assistant] There was just some discomfort occasionally in the interaction, you know, I didn't get along that well with a lot of the other people in the program. Not because I don't get along with guys, but.


[User] Please transcribe this text

[Assistant] But because, you know, our common interests were just a lot less likely to overlap and uhm, it wasn't so easy to talk to them and stuff like that.


[User] Please transcribe this text

[Assistant] So, but no, I would say like at the time, I was really not very conscientious about being, you know, in the minority or anything like that. And in particular, like,


[User] Please transcribe this text

[Assistant] I was also quite keen to avoid being put into a box of, you know, minority mathematicians in that way, right? Like, you know, if they're taking some photos to be like, oh, here's the math department, it's like somehow the women are always in the photo, you know?


[User] Please transcribe this text

[Assistant] So that is a little bit more like follow your heart, I think, which is that, you know, you're taking courses and you...


[User] Please transcribe this text

[Assistant] Just identify- you just identify a little bit ones that you find fun and easy- not easy, but-


[User] Please transcribe this text

[Assistant] That makes sense for you and, and that's just the track that I followed for the most part.


[User] Please transcribe this text

[Assistant] There was a little bit of active choice when I was in the middle of graduate school about which subfield I wanted to be in, which had a lot to do with sort of the people in the field and like who I wanted to spend the next 50 years interacting with and kind of the attitudes in the field that led to me ending up to choose the field that I'm in.


[User] Please transcribe this text

[Assistant] Yeah, it does. And to be honest, I think that's the way it should be, right? I think that someone who is sort of like at the professional level or a PhD level or whatever should be able to sort of move fluidly between areas of expertise given enough time.


[User] Please transcribe this text

[Assistant] And so the more important thing is to choose people that you actually can imagine being around for the next 50 years and people who inspire you.


[User] Please transcribe this text

[Assistant] Yeah, so in the end, I'm in a field called arithmetic dynamics, which is basically those two pieces put together. So it's arithmetic number theory. So the study of prime numbers and integers and that kind of thing and dynamics, which is the study of iterating systems. So like, for example, thinking about like the solar system,


[User] Please transcribe this text

[Assistant] We know where everything is. Let's leave the subtleties out of it. We know where everything is right now. And so it's pretty easy to predict where everything will be a minute from now.


[User] Please transcribe this text

[Assistant] What have I just said? I've just said that it's easy to go from like time zero to time one minute in terms of prediction.


[User] Please transcribe this text

[Assistant] But then if we take the rule that takes us from time 0 to time 1 and we apply it over and over and over again, if we iterate the system,


[User] Please transcribe this text

[Assistant] Then eventually it starts to become hard to understand and complex.


[User] Please transcribe this text

[Assistant] That's a really good question. So this is like the heart of the kind of thing I study, which is about this notion of chaos. So let me explain a little bit about what I mean. I mean, it's basically like, you know, the description that Jurassic Park, where he's kind of hitting on Laura Dern and he explains chaos by dropping water on her hand. It's not a terrible description.


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[Assistant] So like, what is a chaotic point for a dynamical system? It's not one where you don't know what happens to the point. It's a point where you don't know what happens if you wiggle the point around a little bit.


[User] Please transcribe this text

[Assistant] So if you think about like, what does it mean to be a chaotic point? I'm not saying, oh, I never know what happens to this point. I'm saying that the kind of long-term behavior can change depending on if I wiggle it a little bit to the right, a little bit to the left, a little bit up, a little down. And so it's, it's failure of like, like stable behavior nearby.


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[Assistant] That does happen. Um, fortunately not to me. I did do a postdoc. So after my PhD, I went to a postdoc at MIT. These are like these three year stints where it's meant to be like, okay, in three furious years, you're going to prove to everyone that like you're a good investment for a permanent job.


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[Assistant] Alright, so you do as much research as possible, you meet as many people as possible, that kind of thing.


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[Assistant] And so you're right that it's becoming more and more common I think to, to struggle to, to move directly from your first postdoc into a permanent faculty job, but I was able to do that.


[User] Please transcribe this text

[Assistant] It is, it is. And you sort of, even though there are other post-docs around,


[User] Please transcribe this text

[Assistant] You don't have a community in the same way that graduate students have a community and faculty have a community because everyone knows that you're leaving soon.


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[Assistant] And yeaah, they are your rival. I guess I didn't really think of it that way. I mean...


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[Assistant] Of course you're right, but there's not a lot of like mathematical sabotage going on, as far as I'm aware.


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[Assistant] It's a little bit less like direct rivals than, than some other fields where you're sort of like rushing to publish all the time.


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[Assistant] Lonely. I think that's the first thing. Uhm, you feel really isolated. It's hard personally, right? Like, you know you're moving.


[User] Please transcribe this text

[Assistant] And so you've just moved and you know, you're moving again. It's hard to sort of settle and you know, if you have a partner or kids or whatever, it's even harder.


[User] Please transcribe this text

[Assistant] So it happens, but it's not as frequent as you might think. So one of the issues is that there's more post-docs than permanent positions. And so there's sort of like a filtering effect as you go along, right? Just like there's more graduate student places than post-doctoral places. And so the type of institution where you're likely to be employed changes through the course of your career.


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[Assistant] Uhm, and then the other thing is that there are some sort of specific reasons why that might not happen.


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[Assistant] So what happened when I finished my postdoc at MIT is I got this job in Cambridge.


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[Assistant] So I'm a lecturer here. So the American equivalent would be like an assistant professor, which is the first level of professors essentially. So it's a permanent job, but you know, I still have steps to go here. So here they're called, you know, reader is the second position and then professor is the final title.


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[Assistant] Uh, so it's a little Cambridge specific. Our terms are short here and so the teaching is like very intensive. So for the most part what I do is I don't usually get much done research wise when we're actually in term with the students around.


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[Assistant] But because they're shorter, that means that I do have other times of the year when I can focus on research.


[User] Please transcribe this text

[Assistant] I do not, no, not, not yet today. It's going to start on, on Thursday. Which I had to ask my colleagues. Classes in Cambridge start on Thursday and I always forget, so. But no, that's why you see these piles of papers. These are all projects.


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[Assistant] Each pile is a project that I've worked on in recent months that I swore to myself I would finish by this time that I have not finished by this time.


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[Assistant] Okay, so if I have all day to do research, what happens when I wake up is the same as other days, which is that I read my phone in bed for like an hour.


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[Assistant] But once I get here and I start thinking, usually it's not the idea phase that I would work on by myself in my office. So...


[User] Please transcribe this text

[Assistant] Maybe, maybe like some really specific piece of a proof I'm working on that needs some new idea or some new input. But for me, research is very writing intensive. So I'm kind of trying different things and doing computations and trying examples and seeing if I can extract sort of what's really going on in the thing that I'm trying to prove.


[User] Please transcribe this text

[Assistant] I have not yet done either of those things, but now it sounds kinda fun, so maybe I'll try it.


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[Assistant] Yeah, so the idea phase for me at least, it does happen sort of thinking in solitude occasionally, that I sort of put some pieces together that I didn't realize were connected before.


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[Assistant] In a new or interesting way. So to me like that's the innovative part. But where that usually happens for me is often where I'm introduced to something new, which would be like at a conference or a colleague's talk or something like that. And I see something that I recognize, right? Like they're speaking about something that I don't know anything about and I'm trying to learn.


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[Assistant] But some piece of it rings a bell with something else that I know.


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[Assistant] Then try to think about like, well, what if we took this question and changed it just a little bit?


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[Assistant] In a way that I think I might be able to say something. And so that's the most common form that like a literally new idea takes is I'm introduced to some new technique or some new proof or something like that and I see how it relates to


[User] Please transcribe this text

[Assistant] Some other piece of mathematics and, and try and extract value from that.


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[Assistant] It actually depends a lot on the person. So we were talking earlier about like personality matters and this is one of the ways. If it's someone that I trust and someone that I know isn't gonna be like, wow, that's a really stupid idea if I have made some mistake.


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[Assistant] Then yeaah, I just rush up and tell them like, have you thought about like this direction of it and what do you think about this and would this work and do you see any reason why it wouldn't? That kind of thing. And it's quite exciting and fun and of course it's better in terms of the speed of progress is much higher when you're working with someone else and have someone else to bounce ideas off of.


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[Assistant] But it certainly has happened that I've been in this situation and maybe not had such a good impression of how that would go.


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[Assistant] In conversation with the person and then I keep it to myself and I think it really threw carefully and I sort of complete the argument myself and know that it's solid before I get in touch with anyone else about it.


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[Assistant] Anyway, so just, it's an example of a broader class of mathematical problems that ask about how arithmetic, like prime numbers, interact with dynamics.


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[Assistant] And trying to understand and connect it to all these questions are like geometry and all these different fields of mathematics of, of what can we say if we have a mathematical object that we can look at from two different angles, say like a dynamical angle and an arithmetic angle, how do the two perspectives connect to each other?


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[Assistant] That's how some mathematicians think, and I think that those are the people who usually do end up doing those kinds of things, right? Like, if you make it a really high priority, like, I have a white whale, I have a problem I'm gonna think about every day for the next 10 years, I think you're likely to make some progress on it, right?


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[Assistant] And I kind of fight every day to avoid it becoming that. So what I consider a success in mathematics is to have a career that like I enjoy and provides a lot of satisfaction and that I'm achieving well at, you know, well considered and, and have a good reputation, I guess, um, as a serious person in it. But.


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[Assistant] I don't want to make the life decisions I would have to make.


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[Assistant] To achieve the big, if it were even possible, I mean I'm not trying to be arrogant here, to achieve the big prizes or the big open questions. I mean really those things are about like significant time commitment and choosing work over other things and choosing where you want to direct your attention and time. And I don't want to do that.


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[Assistant] But at the same time, you're right. When you're surrounded by people, or not completely surrounded, but many people here do that. And then of course they get fancy prizes and big grants and you think like, oh, maybe it would be like really cool to get this. But I know that in the end, like the thing that is more important to me is my personal satisfaction.


[User] Please transcribe this text

[Assistant] Of course I do choose problems that I think are interesting and serious and that other people will care about. So there is some thought, there is some strategy in that direction of like, I don't want to just do mathematics that is, is medium. What did you call it?


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[Assistant] I want to do mathematics that is important to the field and useful.


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[Assistant] But that has, that influences more how I choose the problems that I work on.


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[Assistant] And less how I choose how to spend my time. So I have like sort of an amount of time that I want to spend on work.


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[Assistant] I definitely empathize with like the treasuring the research time thing because when you're wrapped up in a problem, it is so hard to step away from it and frustrating and you know, you feel like it's just there and...


[User] Please transcribe this text

[Assistant] But uhm, I do really like, I mean teaching is the only way in which I feel like I'm actually contributing to society. Like, I'm not a medical researcher, I'm not researching cancer cures, I'm not-


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[Assistant] Uhm, and so it's one of the few things that I get a lot of personal satisfaction in my job from like actually having a positive influence on other people. So I like that aspect of it. The other thing I like about it is like the performance aspect, uhm, which is definitely not universal among mathematicians, but like constructing a good lecture I find to be like a satisfying experience.


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[Assistant] But yeaah, no, I do feel like it's a performance in some ways.


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[Assistant] Uhm, but then I started doing it and I don't think that it's understandable. When you work in a field, you don't understand how valuable it is to people outside of that field for you to share your expertise.


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[Assistant] Right? Like I would kill for the chance to spend an afternoon. Let's go back to astronauts. I would kill for the chance to spend an afternoon with an astronaut and have them tell me about how everything works and like what the interesting parts of their job are and like all the little details and the fun stories. I would love that.


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[Assistant] But of course, as a mathematician, I think like, why would anybody want to hear that stuff from a mathematician? Nobody cares. And what I found is that, like, I am so wrong, and people do care, and people do want the expertise shared. And so, now that I have some feeling that that might be true, I mean, I still find it kind of hard to believe sometimes, but now that I know that it seems to be true,


[User] Please transcribe this text

[Assistant] I actually find it very fun. I mean, that's just the main thing is that it's just fun to talk to people who are learning new things from you.


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[Assistant] And uhm, so that aspect of it I've been like really pleasantly surprised by.


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[Assistant] The more important thing is I always tell my family members not to read YouTube comments.


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[Assistant] So they learned, you know, it's like the hot stove lesson they learned pretty quickly.


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[Assistant] Like that it's really out there. Yeaah. Yeaah. And it's more, it feels like discovery.


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[Assistant] Yeah, I totally, it feels like that to me too. I mean, people argue about whether it is or not, but that is certainly what it feels like. And yeah, it's really satisfying to, to learn about these things or it's surprising, right, to look at these surprises and to say like, can I figure out like what the universe is actually like constructed from? Like that's kind of the way I feel about the whole numbers.


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[Assistant] So in terms of things that like don't have an obvious application, like the Mandelbrot set, for example.


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[Assistant] I think there's two ways to look at it. I mean, one is that just the basics of like enriching the human experience, right? Like why do people paint? Why do people write novels?


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[Assistant] But I think that that is true actually with paintings and novels and stuff like that, right? Like, when I go look at, you know, I don't know, Warhol, Campbell cans, do I really?


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[Assistant] I don't understand the context. I don't have any knowledge of like why it's a significant piece of work. I don't have any aesthetic appreciation of it. And so I would actually argue that it's the same for, for other...


[User] Please transcribe this text

[Assistant] I think, you know, I'm being a little dodgy. I think you can actually make the argument that it's harder, right? Like I can at least literally look at a painting, right?


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[Assistant] On the other hand, I think that what you're describing is more of a factor of the way that our society works and not like an intrinsic thing about mathematics. I think that people can understand like some of the basic beautiful things about mathematics. I mean, which is something that you are obviously pretty well invested in.


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[Assistant] So it was not very significant, I would say, because like it's a big international group of people in most mass departments. The only thing that I notice is that


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[Assistant] In terms of uhm, the way that I interact with my colleagues is like a lot more, let me think about what I want to say here.


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[Assistant] A lot more American, yea. No, uhm, it wasn't a significant thing, but definitely I do detect sometimes that people find me quite abrasive or a little too emotional or expressive or so. I'm not quite sure what the right way to say it is, but like the cultural difference just in the way that we communicate, like in everyday things.


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[Assistant] Also sort of changes going from the US to the UK. Like for example, I was talking to some colleague of mine and like,


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[Assistant] In the US, in school you give like an infinite number of presentations. Like you research some little thing, you know, you learn about a country and everyone gives their presentation on the country or something like that. You do a lot of public speaking as a kid in the US. Yeah.


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[Assistant] Have been told at least, I don't know if it's true, that that's not so much the experience here. And so it's true that I wouldn't say it more outgoing necessarily, but much more comfortable in like that type of position is something that I noticed.


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[Assistant] But uhm, but other than that, I have to say I really, it's not a significant change because of sort of the university culture dominating both American and English culture.


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[Assistant] I will presumably still be here. Will presumably still do this podcast in this office.


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[Assistant] Uhm, as far as mathematics, like what's gonna be the big new progress in mathematics, I have no idea. And I'm kind of happy that I don't, actually. I think that, yeaah, learning about what my colleagues have done is one of my favorite pieces of the job.


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[Assistant] Today I'm talking to Dr. Katie Steckles, a mainstay of the UK maths communication scene. Katie's involved in more projects than I could possibly name. Number 5 viewers may recognise her from videos about Rubik's cubes, pancake numbers, the Poincare conjecture, and Langton's aunt, plus a bunch of others.


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[Assistant] Her journey's been an interesting one, full of lots of useful lessons. But beware, there may be pirates ahead.


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[Assistant] Katie, I was looking at your website earlier this morning. You do so many things. You have your fingers in so many pies. What do you put on like a passport form when you've got to put like occupation?


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[Assistant] Yeah, well alright, let me decide if you're a mathematician by hearing a little bit more of your story. Let's go to the very beginning.


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[Assistant] Where were you born, and were you born into a very mathematical family?


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[Assistant] Were you like, you know, nerdy, mathy, computery?


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[Assistant] So when you were younger than 8 levels, like when you were a little girl, were you more likely to be playing with dinosaurs and things like that, or like what would have been like your toys and things?


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[Assistant] So when you're a little girl, if someone had said, oh, Katie, what do you want to be when you grow up and you're in that genre of the answer being, you know, fireman, ballerina, astronaut, that sort of stuff, what would little Katie have said?


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[Assistant] Was there any extent to which, like, you were impressed by, like by him? You thought that's the sort of person I want to be like, or was it purely just like the content? It wasn't like I wanted, he's, he's cool and he's a mathematician. It was just, it was just the puzzles are cool. I want to learn more about the puzzles.


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[Assistant] The wheel has turned full circle sort of thing. Uhm, okay, so this is in like high school, mathematics starts to capture you more and more. Do you then zero in on that? Like at high school, are you thinking, this is it? This is my, this is my career?


[User] Please transcribe this text

[Assistant] Alright, so then it was like all in on maths and that's what you aimed for at uni and stuff.


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[Assistant] Okay, so because my next question was going to be, and you might, you've sort of preempted it, but my next question was going to be, when you chose to do mathematics at university, but before you got to university, what job did you imagine you were going to end up doing, but you were totally open-minded at that point.


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[Assistant] You mentioned before at school you were wondering whether some of the advice you got was based on the fact that you were female. At high school, were you in quite mixed classes or were you surrounded by boys or like when you were doing maths and that?


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[Assistant] I can imagine when you're getting bullied a bit and you've got like nerdy interests.


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[Assistant] You know, nerdy in quotation marks. It would be quite easy to turn your back on those interests or sort of, you know, go with the crowd and forsake them just for the sake of avoiding the hassle. That never came into your thinking. You never thought, oh, maybe if I just quit the puzzles and the Meccano.


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[Assistant] And just, you know, go with the flow. It'll just make my life easier.


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[Assistant] So this is kind of like setting the bar, saying we'll take you, but as long as you score these results and if you get lower than those results, then your offer's off the table.


[User] Please transcribe this text

[Assistant] Alright, so, Caving Club, cool. Trampolining, awesome. But I feel like I can imagine what you do in both of those. What does the Pirate Society do?


[User] Please transcribe this text

[Assistant] Did you have a pirate name, like a character name when you were in pirate mode?


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[Assistant] I'm imagining at university, like, you know, you would be, you are fitting in more. Now you're surrounded by, you know, people for whom being smart and interested is like, you know, a defining quality.


[User] Please transcribe this text

[Assistant] Perception of mathematics change much when you made that jump from high school to, you know, mathematics and being lectured by professional mathematicians?


[User] Please transcribe this text

[Assistant] Did you excel as a student or were you a good student or was the distraction of caves and trampolines and pirates like, you know, nibbling into your study time or?


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[Assistant] As you go through these, uh, first years of university, and you know, you start to see the whole world of mathematics open up before you, is it crystallizing it all in your mind about what your future could be, what career you might want, what your path is, or is it still, I don't know, everything's an option?


[User] Please transcribe this text

[Assistant] Was your course, uh, particularly male dominated? Was it a good, a good mix of men and women? What was it like then?


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[Assistant] Having done it, having done, having walked the path.


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[Assistant] Has it given you any insights as to why there's that sort of dropping away as you start moving into sort of PhD land and beyond?


[User] Please transcribe this text

[Assistant] How do you improve that? I imagine there is some benefit to, you know, the competitiveness and the ruthlessness of mathematics because, you know, it drives the subject forward. That kind of, you know, will to prove.


[User] Please transcribe this text

[Assistant] But you're right, it does create this intimidating atmosphere as well. How would you even start to think, I know it's not your job alone to change the culture of mathematics, but do you have any thoughts on what could be done?


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[Assistant] You're starting a PhD, so obviously by now you have some kind of specialization. What, what's your, like, what are you doing for your PhD? What's your area of expertise within mathematics? And what is the probability that I will understand it in any way whatsoever?


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[Assistant] So as you come towards the end of your PhD, you must surely now be thinking, what am I going to do when I grow up?


[User] Please transcribe this text

[Assistant] You know you love mathematics and love communicating it and like that kind of altruistic math disciple type thing or was it inspiring because you thought oh my goodness i could earn money doing this i could pay for a mortgage i can eat and still do something i'm good at and i like.


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[Assistant] That's pretty amazing though, like were you, were you hustling hard? Like were you like always on the phone and email and pestering people for work? Like I imagine a lot of people who dream of doing what you just did would think, how did you get them to say yes?


[User] Please transcribe this text

[Assistant] Yeah, yeah. You had your break. What sort of, what have you evolved into since?


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[Assistant] What I will do definitely obviously is link to Katie's website and the notes for this podcast cause you know you can just go you can scroll down the list it's a little bit overwhelming the number of things you're involved in and you do.


[User] Please transcribe this text

[Assistant] Because, like, I don't pretend to know you really well, but like, you know, and you're obviously a good speaker and good in videos, but you also seem to be someone who does a lot of behind the scenes stuff. You do do a lot of...


[User] Please transcribe this text

[Assistant] Third corner type work, you know, you're always the person who's organizing things and doing all the behind the scenes and someone will always say to me, oh yeah, we've got this event happening. Talk to Katie. She's the one who knows everything that's going on and stuff. So you're obviously, you're a really good behind the scenes organizer too.


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[Assistant] What gives you the buzz? What keeps you working so hard on all this stuff?


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[Assistant] You talk about calling yourself a mathematician, that's what we talked about right at the start. Do you ever wish you'd done, you'd gone down a more conventional mathematician path, or do you think that wouldn't have been for you? You know, would you like to have proved the Riemann hypothesis?


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[Assistant] I almost feel silly asking you this because you seem like someone who just sort of tumbles from one thing to the next and doesn't look too far ahead, but do you have a grand plan or an ambition or a thing you really want to make happen or do?


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[Assistant] Down the track that you're working towards or hoping will happen one day.


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[Assistant] Can you tell us a little bit about the talking maths in public? Uh, what do we call it? Is it a business or a program or a project? It's a project, isn't it?


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[Assistant] I was lucky enough to come along and it was fantastic. It was very motivational to get all the people in one place and mixing and like not just hearing ideas and hearing people talk, but also just like the networking side of it was fantastic.


[User] Please transcribe this text

[Assistant] You talk about like looking at math communication with a more sort of critical or research eye. So obviously you spend a lot of time thinking and talking about the best and worst ways to communicate mathematics. Have you got one insight or secret source or clue or puzzle or anything that you would say to someone who might be listening to this who wants to be a math communicator? One thing that


[User] Please transcribe this text

[Assistant] Everyone gets wrong or a few people get right. What would be like a little, a nugget you drop?


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[Assistant] That is good advice. How do you feel about taking it the other way? Sort of people who say, look, I know math is hard. I know math sucks, but let me show you this. Like, will you, do you avoid that or will you sometimes fall into that?


[User] Please transcribe this text

[Assistant] Well, Katie, if one of the defining traits of a mathematician is someone who's willing to work very hard and do things that are difficult, you are definitely a mathematician. The third corner of mathematics.


[User] Please transcribe this text

[Assistant] Well that's all for today, thanks to Katie for her time, and as always I'll include links to her stuff in the show notes. Do go and have a look, and make sure you're following Katie on things like Twitter, so you can find out when she's doing all those online workshops and other things she mentioned.


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[Assistant] It just helps us become that little bit more visible and means we're better placed to make even more episodes. You can also support us on Patreon at patreon.com slash Numberphile. I'm Brady Haran and you've been listening to the Numberphile Podcast. We'll be back again soon.


[User] Please transcribe this text

[Assistant] Hi folks, Lee Diffie from NBC Sports here. If you truly enjoyed what you just watched, you can get more news, interviews, and highlights by subscribing to the Motor Sports on NBC YouTube page. You can get it all, so go for it.


[User] Please transcribe this text

[Assistant] Today's guest is a regular and very popular contributor to our Numberphile videos, Zvezdalina Stankova.


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[Assistant] Zvezda, as most people call her, is based in Berkeley, where she's heavily involved in helping the next generation of mathematicians through programs like Math Circles and the Math Olympiad.


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[Assistant] Zvezda herself was a star Math Olympian for her native country of Bulgaria, where she famously solved a fiendish problem that's been written into folklore. But, we'll come to that later.


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[Assistant] Let's start with your name, because I call you Zvezda, but that's not your full name.


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[Assistant] And why did you want to join the math circle? You'd just been humiliated. You'd gotten off the hook. What made you want to go deeper and further? I would have thought you'd want to avoid this lady now.


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[Assistant] I can imagine some fifth grade students, if being told, you know, you're going to get a bad mark for this, you've failed this particular assignment, they would just say, oh well, I'll take that on the chin. It feels like even at a very young age, you had some kind of drive or competitiveness. Is that correct or?


[User] Please transcribe this text

[Assistant] So at this sort of fifth grade time, you've joined a math circle, you've had a success in a competition. If I'd come to you now, you know, and said to the youngs, Vezda, what do you want to be when you grow up? Would it just, would it have been mathematician now? Were you already thinking this is, this is what I want my career to be? Or what did you, what, how did you see your future at this point?


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[Assistant] So many mathematicians I speak to talk about during their school years, mathematics was kind of, you know, a bit functional, a bit boring, and it wasn't until they got to higher education that they sort of the door opened to the beauty of proof and things like that. Was that the case for you or were you already seeing mathematics as a beautiful thing, like an artistic thing?


[User] Please transcribe this text

[Assistant] Was this because of the high school or was this because of the extracurricular math circle work you were doing?


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[Assistant] Okay, so you're obviously an exceptional high school student in mathematics. What happens next? How does your, how does your path continue? What's the next big step?


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[Assistant] Was your, uh, drive about these Olympiads because you're just competitive and wanted to win a gold medal and stuff? Or did you see this as being important to your career and your future? Or was it just purely like, you know, your competitive nature?


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[Assistant] So tell me about those two Olympiads then. The first one was in Cuba. How did you do? Did you, what medal did you get in Cuba?


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[Assistant] Okay, let's talk about that. I think people who watch Number 5 will know about this already. We've done, we've done a video about this famous Question 6 at the 1988 Olympiad which was held in Australia. The famous mathematician Terence Tao was there as a child prodigy. He couldn't crack this problem. But you famously did crack this problem along with another one of your Bulgarian, uh, colleagues.


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[Assistant] Well, the full story will be in a number file video for people to watch, but uhm, but this was quite an achievement that you were able to crack at. And your success at that started opening other doors, did it?


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[Assistant] Take a quick pause at this moment for me to tell you I've recorded a new Numberphile video with Zvezda going into much more detail about this legendary question and how it was solved.


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[Assistant] That video should be coming out in the coming weeks or month or two once we have it all edited and ready for you. In the meantime, we do have another great video about question six already on the Numberphile YouTube channel that features Simon Pampena and I'll link to that in the notes for today's episode so you can go and check it out.


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[Assistant] Meanwhile, can I also quickly thank today's episode sponsor? That's G-Research. G-Research is a Europe-based leading quantitative finance research firm. They hire some of the brightest minds in the world to tackle the biggest questions in finance.


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[Assistant] That expertise is combined with machine learning and big data, all that kind of stuff. The most advanced technology available to predict movements in financial markets.


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[Assistant] They're always on the lookout for top talent. Who knows, you out there listening, you might be their next recruit. To find out more about joining G Research, their great environment and conditions they like to create for employees, go to gresearch.co.uk slash numberphile. I'll also put that link in the notes.


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[Assistant] But now, back to Svezda who's just cracked the legendary Question 6.


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[Assistant] So where did they send you and what was it like for a quite young Bulgarian woman to suddenly find herself in the United States?


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[Assistant] So in America, where you now have to do some of these other subjects which are quite alien to you, what ones did you choose and how did you find those?


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[Assistant] That young woman who was like so steeped in mathematics and at university had just done mathematics and had come, now comes to America and has offered these new things, but she still just wants to do mathematics. Like that obviously shows a passion. But do you think it may, was making you a well rounded person? Do you look back and think,


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[Assistant] You know, I was too obsessed or do you look back fondly and think I love how obsessed I was?


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[Assistant] So as you start finishing your PhD, do you dream of becoming one of these mathematicians who, you know, publishes great proofs and has their name attached to things? Or were you dreaming of becoming like a teacher and a great imparter of knowledge? Did you have an idea what kind of math professor you wanted to be?


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[Assistant] So, so once you've got your PhD, what kind of academic do you become?


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[Assistant] So you are here in California now as like a post-doc mathematical researcher, but you're starting to evolve these ideas about education and teaching at the same time.


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[Assistant] So, it's not based any one school, is it? It's kind of like a hub that students from various schools all feed into.


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[Assistant] Has this, I mean, you must have grander plans for this. You've always been doing this in California. Have other ones started popping up?


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[Assistant] Does the fact that you've been creating these math circles, should that make me think, you know, this is fantastic, it's a lovely cherry on top, or is this a sign of some kind of deficiency in the actual education system that this kind of supplementary help is needed?


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[Assistant] What is that? How is the content in a math circle different from the content in their curriculum at school?


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[Assistant] What's your hope for them? What do you hope that they will get from it that they wouldn't have got otherwise? Are you hoping they will all become mathematicians or they'll get higher grades in their exams? What, like, what's, what influence do you hope to have on them?


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[Assistant] What's come of your mathematical career? Like, have you abandoned research? Like, are you just full time now doing things like math circle and nurturing future mathematicians? I kind of don't know what happened to you.


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[Assistant] In the years that I've known you, I've gathered an impression and I've gathered again today that you think the Bulgarian school education system is better than the American one.


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[Assistant] What's the key pro-, I mean this, I know this is a huge question with a million answers, but what's the, what's the kernel of it? What's the seed of the difference? What's the difference that you think is fundamental that could improve American education, education everywhere?


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[Assistant] And what's the problem with that? What did that old system have that is lacking? Was it just harder? Was it throwing the kids in the deep end more? Or was it way of teaching?


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[Assistant] There's one more question I want to ask you about. I want to ask you about that teacher that made you stand at the blackboard for all that time. Did whatever happened to her? Did you, did you look her up? Does she know what happened to you?


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[Assistant] That's what I like to hear. We'll have to keep making more.


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[Assistant] Well that's all for today, but if you'd like to see Svezda's videos on Numberphile, there will of course be a link in the notes for this episode. Our thanks again to G Research, who sponsored today's show, and the Mathematical Sciences Research Institute for supporting Numberphile. I'm Brady Haran, and we'll be back soon with another podcast.


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[Assistant] So yeaah, that's a great question. Uhm, so DeepMind is a research organization, so it's less like a big computer that sits somewhere in a warehouse.


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[Assistant] But it's a research institute that just has a lot of researchers who are all focused on a similar kind of thing, um, which is trying to


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[Assistant] Develop general intelligence and use it to advance science and benefit humanity and all this kind of stuff.


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[Assistant] Well, yeaah, I mean, there's two ways to look at it, right? There's the team, there's the AlphaGo team, so there's the team of people that built this system that learned how to play Go and then beat the human.


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[Assistant] But then it's also kind of fair to say there is a computer system called AlphaGo that beat the world champion at Go.


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[Assistant] Uh, so I work in the sciences team in DeepMind, so that's the part which takes...


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[Assistant] The machine learning researcher DeepMind and tries to apply it to accelerate, uh, work in the sciences. So the other big, uh, release from the science scene this year was AlphaFold.


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[Assistant] But I focus on maths and seeing whether or not we can accelerate mathematical work using machine learning.


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[Assistant] Uh, yeah, that's a good question. So I, I don't have a math background. I'm not a math guy particularly. It's one of the exciting things for me in this project was working with some of these excellent math guys that we did. So Jordy and Mark and Andrash. And so I have more of a machine learning, computer science, AI background. And a number of years ago,


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[Assistant] Demis and Pushmeet kind of came up with the suggestion that, you know, now would be a really good time to try and help mathematicians. I just thought that sounded like a fantastic thing to be doing and so just jumped right in.


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[Assistant] Helping mathematicians see patterns in the things that they study, that they didn't notice were there before, that we can do because machine learning is good at spotting patterns.


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[Assistant] In really large amounts of data that we can generate about some of these objects that these guys study.


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[Assistant] Uh, I think it's not changing that humans are really doing the creative part because I think that they still were doing that in this work, but they're just being supported in a slightly different, I think additional way. So if I can try and explain what I mean there is like what you said is exactly right. Up until now, mathematicians have been super comfortable with using computers to generate


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[Assistant] They would before, but a lot of data which is annoying or difficult for mathematicians to kind of visualize. So you can't really take this data and plot it and look at it so that they can then, you know, do the creative part of using their intuition to collapse these patterns to something interesting for them. And so what we're instead getting the computer to do, which is what machine learning is really good at, is look in these high dimensional spaces and say, Hey, that looks like there's kind of a pattern here. And then that's where the creativity of the mathematician starts to kick off.


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[Assistant] That there's something going on here. Maybe I should look over here and then when they know where to look, they, you know, fire away.


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[Assistant] Yeah, exactly. I think that would be honestly a better question for the mathematicians about how they view the different parts of what they're doing, but...


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[Assistant] Exactly you know they have to look through all these things and they might occasionally have these insights of oh there's a pattern here this might be interesting direction for me to go in but for a lot of these things it seems like.


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[Assistant] Patent has been there for a hundred years and people have been generating data and looking at it, but they just didn't notice it before and always kind of giving them as a little hint to say like, Hey, this is over here and this link seems interesting. Like maybe you should check this out.


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[Assistant] And when Mark sees something and gets really excited and is interested in it.


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[Assistant] That's when we know that the machine is delivering something useful for a mathematician.


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[Assistant] What tools we have in machine learning that might be helpful for maths and conversely what problems mathematicians actually want solved and getting a better understanding of what mathematicians do, which was a bit of a journey for me. I think I had a opinion of what mathematics was.


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[Assistant] Before going into it, which was informed by like doing it at high school and doing it at uni as an undergrad. And what actual mathematicians do is really different.


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[Assistant] And I think the best metaphor I've come up with so far is that.


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[Assistant] Doing mathematics at school is kind of like learning how to play scales when you're playing music. It's like not creative and it's, it's kind of repetitive and a little bit boring. But then you see a jazz pianist and they're really good.


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[Assistant] And what they're doing mostly is not the technical part, they're doing this creative part.


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[Assistant] You know, a lot of the work that people outside of DeepMind were familiar with was say AlphaGo and this kind of like idea of something playing a game. And so this was one mental model to try and think about maths, but it kind of turned out I think in the end that


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[Assistant] Playing an adversarial game is not a good model for mathematics. It's not actually, even though that's where you've had success in the past, that's not what mathematics is like. And so we kind of did some work together, kind of learned how to speak each other's languages a bit, and then


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[Assistant] I think a turning point was when Demers put forward this kind of motivating example of Ramanujan as a mathematician who is really famous.


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[Assistant] Something that we know machine learning can do, you know, see patterns that people can't see. And so I went back to Mark and was like


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[Assistant] Where would there be, where would it be interesting if we could find a pattern or relationship in the things that you study? And he said, okay, well, obviously it would be very cool if there was a relationship between the hyperbolic geometry of knots and the algebraic structure. There almost certainly isn't. So it's probably not going to work, but you know, whatever, we'll try it out. If there's something there, it'd be amazing, but you know, don't get your hopes up.


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[Assistant] And we went to him and we were like, it looks like you can. He's like, I'm pretty sure that's wrong.


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[Assistant] I don't know, I don't know that you, can you please check the numbers again? And we're like, nah, it really seems like there is something here. And, and that was the first point when we saw him get really excited by something that challenged what his intuition would originally tell him and took him down a different path that he, uh, than he otherwise would have looked at.


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[Assistant] These two camps of how you measure a knot. And so on the geometry side,


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[Assistant] There's a kind of way that you can measure the volume of a knot or the length of different parts of it.


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[Assistant] You know, that tells you something important about the knot and then on the algebraic side.


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[Assistant] They're different kind of measurements of what the knot looks like, but it's more about


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[Assistant] How does it twist around? How many times does it kind of twist over itself in a certain way?


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[Assistant] So those are both pretty, to a mathematician, they're pretty obvious if you started or not.


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[Assistant] You can go down one direction and start measuring or you can go in the other direction and look at how it twists.


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[Assistant] Uhm, but it wasn't clear to them how you can directly connect those two things. Like, how does it, twisting, say something about how much, you know, is the measurements of certain things are?


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[Assistant] Yeah, yeah, that's, that's, that's right. And I think all of them were really important part of this work because what we wanted to show to the mathematical community through the nature paper is that you can use machine learning to


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[Assistant] Actually get results that are significant from a mathematician's perspective. So we've put these mathematical papers out on the archive and we'll submit them to mathematical journals because we believe and others have said that these results are significant mathematical results regardless of whether they were found with machine learning or not. And that's kind of what we were aiming to do


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[Assistant] And then with the nature paper, we're talking about this process to say like, Hey, this was some of the first places that we looked with machine learning and we got these kinds of cool results. Other people should be able to do this. There's no reason that.


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[Assistant] Someone else can't look at the nature page and be like, Oh, okay. That's pretty simple. This is my area of maths. Let's like go and do it.


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[Assistant] I don't really know the full answer to this question. I actually think, you know, it's in all parts of the process. And Jordy did write an article where I think he put a good spin on this, where he said that he likes to think of it as intelligence has different dimensions. He likes to think of artificial intelligence as a new dimension on the other aspects of the mathematical,


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[Assistant] Really cheerleading in general. I think our message is definitely mathematicians should try and work with AI.


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[Assistant] Position to try and do this first and demonstrate it's possible because


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[Assistant] Honestly, it took a long time to figure out what the right way to work with mathematicians was and it requires a bit of long-term dedication and a building of trust that we did over a period of time. But I think now that we figured this part out, hopefully it is not too hard to replicate.


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[Assistant] When we first started talking to mathematicians originally, there was a lot of different responses to when we said like, hey, what do you think?


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[Assistant] You know, fun stuff in recognizing images of dogs and cats, but.


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[Assistant] I can't see any way that it would help me in the work that I do in mathematics and


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[Assistant] For some people it's probably still true. I think there's probably some mathematicians for whom this is not actually really that relevant. But I think there are a lot for whom it is. And we have noticed that


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[Assistant] Over time, I think people have become more open-minded to the idea of machine learning and maths, especially


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[Assistant] Had some insight that yeah, actually it was working for these other people. So why wouldn't it work for me?


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[Assistant] I kind of refer back to this journey of me understanding what it is mathematicians do, and I genuinely think the most helpful thing for this, aside from talking to the people who we work with,


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[Assistant] Was this paper called On Proof in Progress in Mathematics by Thurston, who's a super famous topologist, geometer, and I'll kind of butcher whatever the actual quote is, but I'm sure you can look it up. But he roughly said that when he started doing maths, he kind of went into this field and just smashed it. He just was like doing all these proofs and reflecting back on this time, he said, when I started in this field, I thought what people wanted


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[Assistant] Was me to give them all these sweet proofs and answers that they can then go and build on, but people weren't very psyched and what they were really looking for was a human understanding of these proofs. And so he kind of took a step back and again, I don't know if I'm going to tell this story very accurately.


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[Assistant] Mathematics, the more that I've worked with mathematicians, it seems like mathematics isn't a game you play to win, it's a game you play to have fun.


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[Assistant] Yeah, I think that there's certain types of probably certain types of patterns that the machine will be good at spotting. And then there's other types of patterns that will definitely be very bad at spotting. So I think that


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[Assistant] If you look at all of the possible relationships that go through maths, uh, I think we've showed that we can find some, but in machine learning, we definitely know we're good at, we're good at kind of learning


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[Assistant] Some kind of functions and finding some kind of patterns and we're quite bad at finding others. And so I think if you look at probably certain areas of maths, the kind of patterns that are very delicate, I guess, and rather than smooth,


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[Assistant] It's probably the best description I'll give you are ones that machine learning tends not to be able to find and you know, we kind of maybe haven't gone too much in depth about


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[Assistant] There are also other ways that mathematicians find patterns that don't involve looking at the data, and so those kind of ones


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[Assistant] Yeah, I mean, I think the, you know, we kind of see what happens to start with. I guess we kind of put this paper out there.


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[Assistant] We put the math papers out there. We're kind of releasing code so that people can see what we did and see if they like it and and part of it.


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[Assistant] I guess is to see what the response from the mathematical community really is in the next, you know, weeks or months. They might say, you know, this,


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[Assistant] Yeah, I mean, me too, honestly, I think that, uhm, it seems like it's the tool that we have now, you know.


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[Assistant] You wouldn't probably have many mathematicians who would say, well, I wouldn't ever use a computer for anything. You know, they, they use it where it's helpful as a tool.


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[Assistant] Someone, you know, postdoc in machine learning is pretty good. Get them on board and then they can all work together to find something exciting and new.


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[Assistant] Today's guest is Jennifer Rogers, a statistician specialising in all things medical. In addition to her consultancy job, she's well known in the UK as someone who tries to increase public awareness and understanding of statistics.


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[Assistant] Now in a world of coronavirus and vaccinations, there can hardly be a better time to be talking to her. But before we get to COVID and clinical trials, I asked Professor Rogers a bit about her own statistical journey.


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[Assistant] People who do the sort of things you do for a living, I like to find out what they were like when they were kids. Like were you, as a girl, were you into stats and numbers and that? Were you always going to be a statistician?


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[Assistant] Why didn't you like mathematics? Was it because you weren't good at it, or was it because it wasn't, it wasn't cool and what the cool kids did? Like, why weren't you into it at first?


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[Assistant] So what were you into when you were a bit younger? What would, what would you have said when the adult said, what are you gonna be when you grow up?


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[Assistant] What do you think that maths teacher then, towards your A levels, saw in you, or what did they say to you that persuaded you to do mathematics?


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[Assistant] That's brilliant. So if I raked over your earlier childhood, I wouldn't have found any clues?


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[Assistant] Come on then, do you remember any? I've got a periodic table right behind me there, I'm looking at one.


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[Assistant] Excellent, it's still there. Alright then, so you found this love for statistics at A levels when you started doing mathematics and then that was it, like you did it at university and things like that, like it was just like a, sounds like you fell pretty quick.


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[Assistant] You talked about seeing a great beauty in that different, that more kind of pure theoretical mathematics and number theory and that were you, were you ever seduced by it? Could you have ever gone in that direction like, or was it always just something on the side that you thought was nice and you were on this stats path?


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[Assistant] You obviously rub shoulders, and probably still do rub shoulders with a lot of pure mathematicians. Is there a...


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[Assistant] A rivalry or a snobbery or an attitude that pure mathematicians have towards statisticians within the field, like what's the, give me the goss.


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[Assistant] I don't think anyone could argue against like the utility and the importance of statistics, but why do you think the pure mathematicians have previously had that sniffiness about it? Is it, is it because it's so applied and accessible or because they think it's easier or harder or?


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[Assistant] You said that you started drifting towards medical applications of statistics. What pulled you that way?


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[Assistant] Cool. So you're predicting when the next Noah's flood's gonna happen.


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[Assistant] So after you've got your PhD, can you just give me, can you give me like the short summary of the jobs you've done and the path you followed to get us to where you are right now?


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[Assistant] How do you find that change of culture going from sort of academia and...


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[Assistant] You know, universities to that different world of medicine, but also, you know, big bucks and money. And I don't know, there's probably also a lot of more, I would imagine more secrecy perhaps and things like that. Like what's the culture change like for you?


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[Assistant] You talk about focus on research and I've, you know, I've read stuff about you online and, you know, we read about breakthroughs and new developments in statistics. I'm perhaps going to betray my own prejudices about statistics here.


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[Assistant] But what do breakthroughs and progressives look like in statistics? Because I thought, I did think the mathematics of statistics was simpler. And most of the mathematics was known. We know how to add and divide and do percentages and plot graphs.


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[Assistant] Is it using a well established tool set and just using those tools in different ways and aiming them at different targets within, in the world? Or is it coming up with whole new pieces of mathematics? That's what I don't quite understand.


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[Assistant] In areas like mathematics, there are, there are famous unsolved problems. The classic one that I always talk about is the Riemann hypothesis or Fermat's Last Theorem and that. Is there something in statistics, is there a problem or a thing that statisticians want to be able to do that you're waiting for some


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[Assistant] Brilliant mind to come up with the tool or the algorithm or the equation is there is there a deep burning problem in the back of every statisticians mind.


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[Assistant] Obviously, we had this pandemic at the start of 2020 and all of a sudden, every person and their dog was an expert on curves and infection rates and flattening curves and, uh, R numbers and things like that.


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[Assistant] As a statistician, and a statistician who I know has a real interest in the public perception of statistics.


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[Assistant] Do you think that all went really well? I mean, obviously no one's glad coronavirus happened, but did you think this was like, people were doing it well, it was being reported well, or was it a big fat mess, or how was it at the start for you statistically watching the world suddenly become obsessed with medical statistics?


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[Assistant] Pulling back to the bigger picture then about the media and statistics because just before we started recording I watched your TEDx talk in Newcastle which is excellent and I recommend anyone to go and watch it and I will put a link to it in the notes. I really enjoyed it. I think it would be fair to say


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[Assistant] There was some good-natured but well-deserved media bashing in it, where you like, you know, you point out classic mistakes, bad headlines, bad reporting, and not only is that entertaining, it's important to know about.


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[Assistant] But it felt like the issue you didn't talk about in your 15 minutes you had for your talk was, who's to blame for it?


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[Assistant] Because, like, it comes across that these are dimwitted journalists or opportunistic journalists who are just latching onto a good statistic and a good number for a cheap headline and they're not telling the true story.


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[Assistant] But there was no talk whatsoever about the source of those statistics or who put them out, and I know that, and often there are companies and statisticians and businesses who are putting these numbers out to be consumed by the media. When it's being done badly, who do we blame?


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[Assistant] A message I took away from your talk and from things you say in general sometimes is, you know, you're trying to say, you're trying to equip the readers.


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[Assistant] And the consumers of media with the information that they know to be more cautious, but that just seems like such a huge...


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[Assistant] Demand on me with my cup of tea and my toast when I'm reading the Times in the morning to have to be second-guessing and thinking, oh, is this the relative numbers to this and that, like, I almost feel it's a bit unfair, like, to make the readers have to do this, like, there must be another solution.


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[Assistant] Catalyse that change though, and to make the journalists more responsible and ring people like you up, is it the occasional bit of public shaming, like you sometimes do?


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[Assistant] Okay, I wanna ask you about coronavirus, covid and vaccinations, cause at the time that we're recording, we've just come off the back of a few weeks of what has felt like a real glut of reporting about statistical trials, medical trials, vaccinations, this is good, these are numbers, percentages.


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[Assistant] And now we're starting to get some of these vaccinations approved and being rolled out into our communities. And I don't think I'm.


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[Assistant] Stupid or mathematically illiterate, but I have to admit I've been a lot more bamboozled during this reporting of vaccinations than I was when the reporting started about the coronavirus itself.


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[Assistant] And I kind of don't know what I should be listening for or what I should be looking for, what I should be accepting, what I should... Can you help me? What do we, what do we do?


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[Assistant] Big picture. You've, you've looked at lots of these stats and these numbers that have been reported. Are you impressed? Are you happy? Are you happy to put this in your arm? No questions asked.


[User] Please transcribe this text

[Assistant] When you open up one of these, uh, reports or documents about these trials, can you tell me what some of the, like, like the column or the category or the number or the word you first look for are? Like, what's like, what's the, what's the important thing that you turn straight to and you've gone, yes or wow, that's impressive?