The Infinite Monkey Cage - How to Teach Maths

Episode Date: September 3, 2022

Brian Cox and Robin Ince are joined by comedian Sara Pascoe and the very numerate Prof Hannah Fry, maths comedian Matt Parker and statistician Prof David Spiegelhalter for a unique maths class. Are some of us just innately bad at maths or can everyone get to grips with algebra and calculus? What do our panel wish they'd been taught at school, and what is the key to a life-long love of numbers? Get your calculators ready!Executive Producer: Alexandra Feachem

In our new podcast, Nature Answers, rural stories from a changing planet, we are traveling with you to Uganda and Ghana to meet the people on the front lines of climate change. We will share stories of how they are thriving using lessons learned from nature. And good news, it is working. Learn more by listening to Nature Answers wherever you get your podcasts. This is the first radio ad you can smell. The new Cinnabon pull apart only at Wendy's. It's ooey gooey and just five bucks with a small coffee all day long. Taxes extra at participating Wendy's until May 5th. Terms and conditions apply. BBC Sounds. Music, radio, podcasts. I'm Robin Ince. And I'm Brian Cox. And this is the Infinite Monkey Cage. Today we'll be exploring mathematics. If mathematics really is the language of the

universe, then why do so few of us speak it fluently? In fact, that may well be why so few people in England speak it fluently, because if it is a language, people can't be bothered to learn languages, you know that. When they say it's the language of the universe, then I would imagine if aliens ever arrived on Earth, it would just be someone in Wendover talking very loudly, I don't

understand what you're saying, but I do not want the anal probe, thank you. Would you like us to take you to our leader, or would you like to go to a harvester? Are you allowed to say anal probe on Radio 4? I'd be more worried about harvester. Harvester?

Harvester on Radio 4? That's very much a Radio 2 restaurant. Ridiculous. Surf and turf, I don't think so. They won't understand it, will they? Do they even have harvesters? Are we trying to work this out? They do. Thank you. Good. So this is a Radio 4 audience.

These aren't the Radio 4 audience. These are the people who don't like to pay West End prices to go to the theatre. Very difficult. Well, it will come as no surprise to anyone that Robin is not very good at mathematics. Actually, that is not true. I have...

I think it will surprise you, Hannah, as well, this. I actually do have an advanced O level, advanced maths O level, and I still have no idea how I got it because I know that I got every single question wrong, but I think that I did so much of showing of my working out that statistically some of it had to be right because there was just so much of it. Why is it that mathematics befuddles so many people and why does it seem that many

people are quite happy to admit I can't do maths. What do we need to do to change the way that mathematics is taught to make us all more mathematically literate? Today we're joined by a statistician, two mathematicians and an expert on sex, power and money. They are... I'm Hannah Fry, I am a professor at UCL and the thing I wish I'd been taught at school is Latin because for starters I would understand a lot more punchlines from posh people. But also, I think it would have made biology a lot less intimidating if you realised that they were just using

the physicist trick of using literal names for everything, but just in Latin. What do you mean, like, the universe? Well, or supermassive back hole? Or isn't there like a really very large telescope in Europe? I see what you mean, yeah, the the BLT, the very large telescope, yeah. So in biology, right, there's one day someone's there with a skull, a human skull,

and they find there's a great big hole at the bottom of the human skull where the spine goes through. They're like, right, what should we call it? We can't call it a big hole, that'd be ridiculous. So they call it the foramen magnum, which is Latin for big hole. I'm David Spiegelhalter. I'm a statistician from the University of Cambridge. I'm not a mathematician and I'm not a teacher. I don't know what I'm doing here at all, really.

To be honest, David, I have realised you're meant to be on next week. So thank you very much for joining us. I'll muddle through. There's a 25% chance you'll be good. And what I wish I'd learnt at school was actually probability theory, because it wasn't part of the math syllabus when I was doing the maths when I did it back in the Middle Ages sometime. I'm Matt Parker.

I was once a secondary school maths teacher, so I'm mildly qualified to be here. And now I'm some combination of maths author, YouTuber and performer. And at school, I wish I'd been taught eigenvectors. Thank you. I will not be taking any questions at this time. My name's

Sarah Pascoe. I'm a comedian. And at school, I wish I'd learned more. I wish I'd learned something. And I'm one of those people who now finds learning things incredibly pleasurable but didn't have that at school and I think that would have been different if they'd kind of I think you could have teach all of the subjects but make them about true crime and then it would have been fascinating like maths would be sort of how many victims

um you know uh geography sort of if we map out where all the victims lived, where's that little mound circle where they probably lived? English, how did they do it? Yeah, I think pretty much... Biology. Biology, cutting out the cadavers, I don't know yet. You could do probability and statistics. The great exercise you could do that was about Richard III. Right. And was it really Richard III?

They dug up in the Leicester car park. Who says it wasn't? I have said it wasn't, but I think it's probably... They worked out it's 99.9997% chance. That it is? That it is. Right, OK. And that was enough to get him buried. But I think that's a bit of true crime.

Yeah, it's fantastic. So what was the 0.3% of doubt? Well, because... This is just very unlikely you'll find it. It didn't have a sign around his neck saying this is richard iii wasn't there a big r in the car park no no that's how they found it they found him yeah to turn that around how were they 99.99 sure it was richard iii given that he didn't have a bad john and it was a long time ago yeah well they you know they started digging and it was a long time ago. Yeah, well, they started digging, and it was the first thing they found that morning, they found the skeleton.

And it had scoliosis, you know, curvature of the spine, and they did carbon dating, it was the right period, the right age. It had wounds after he died, and so on, but mainly it was the genetic line. Mitochondrial DNA, yeah. That got it. But none of those are absolutely confirmatory. Well, anyway, welcome to In Our Time.

This is our panel. I love the fact, David, that you started off by going, I'm not even entirely sure I'm here. And then you went, I'm going to make it even more difficult for them. I'm going to turn it into a history programme as well. Very canny. Now, Matt, define eigenvector. Right.

I will be taking that one question. So, you know when you've got a matrix and you're thinking, oh my goodness, I wonder if I could multiply this by a constant and a vector and get the same answer out the other side? That's your eigenvector. That's a great catchphrase, by the way.

That's your eigenvector. Matt, a great catchphrase, by the way. That's your eigenvector. Matt, what happens to your brain when you think that? About eigenvectors? Yeah. Well, what's great about eigenvectors is, like, you don't do it at school, but you've done all the background learning to be able to do it at school. And it's like missing that last capstone that will join together these unrelated bits of maths. And kind of the joy of maths is when it all clicks together.

And for me, when I learnt eigenvectors at university, I was like, I could have learnt this at school. And it would have made a lot of the other stuff I was learning make a lot more sense. I'm with Sarah, though, because I think that, for me, the stuff becomes most exciting when I know what it's for so I learned eigenvectors when I you know first year of my degree and whatever I was using them second year of my degree but I think it was only much later when I started working with like massive data sets and I realized

that it's kind of the direction in which there's most change right and only at that point when I was looking at sort of data on serial killers yeah that i realized what it was for and realized it all clicked into place so if you can't use it to kill someone i mean look you're not interested this show has gone very odd hasn't it it's the opposite is how to stop people killing by working out why they kill and where using maths i'm really interested how does it come into that that analysis okay so this is going to turn into a maths lecture maybe we should talk about this one later well do you know what i feel that rather than a lecturer on murder maths probably fits in

more with the genre we're meant to be working with so i wouldn't worry too much um not that we haven't all done some murders but the uh but But I want to start, actually, Hannah, with you, in terms of thinking about when did mathematics for you become not just a lesson at school, but something that really did inspire you? When did the fascination begin? I think it was a bit later than a lot of people are mathematicians. I think, certainly in primary school,

I wasn't, like, a natural mathematician. But then there was one summer where I have an Irish mother and she, like a lot of Irish mothers do, really was very keen on me doing a lot of homework. So there was one summer where she had a slightly warped idea of what a fun summer holiday might be. She bought a maths textbook and she insisted that every day I do one page of the maths textbook

and of course I hated it but the thing was is that when I went back to school then afterwards I had seen all of the examples before and I kind of understood stuff in a way that my classmates just didn't quite yet and then I think if you feel like you're good at something suddenly it becomes a lot more fun suddenly practicing wasn't so so difficult suddenly i wanted to do more and more and more essentially that is a tidal wave of success that i've been riding ever since um i do think though i do think that i think of maths it's like it's a bit of a an unstable equilibrium right i think you never meet an adult who is like i'm ambivalent about maths you know they're always i really hate it I really like it and I kind of think everyone must be born without a deep opinion about it one way or the other everyone

every child is like doesn't have an opinion one way or the other and I think all it takes is like one little nudge in one direction or the other for something to spiral so for me it was a positive spiral but I think for a lot of people it's you know oneudge, maybe one day you sort of a bit sleep in a lesson and you don't pay attention and then the next lesson is much harder and then you stop getting the answers right and you start feeling you're not good at it and over and over again, that gets reinforced

until you end up with like proper maths phobia. You're right that it's an emotional attachment to whether you feel good at it because no one ever says, yeah, I hate maths. I mean, I'm amazing at it, but I just don't enjoy it. It's always, I hate it because I felt ever says yeah I hate maths I mean I'm amazing at it but I just don't enjoy it like it's always I hate it because I felt stupid at it it's interesting what you say about practice because I think a lot of people think I can't do it there's a certain type of person that can do maths and most people can't and that's a very common refrain isn't it it's just not for me

it's not my kind of thing yeah and I think that's actually a really big cultural mistake that we make because it's not true if you go to other countries in the world it's not always the case if you go somewhere like singapore or south korea where they regularly top the tables for math performance actually they just have a really different attitude towards this stuff. So if I showed you a page of Japanese writing, right, unless you could speak Japanese, you wouldn't feel bad about not being able to immediately understand it. You would be like, well, obviously I don't understand it because I haven't learned Japanese. Whereas if I show you a page of maths, for some reason, we all think, oh, I must be stupid because I don't immediately understand it, when actually it's like, well, no, you just don't know it yet.

And in places like Singapore and in places like South Korea, they really have that attitude that it's like, of course I don't get it yet because I haven't learnt it yet. Matt, what about for you? When did maths go from being a... Because you seem to have always seemed, since I've known you, had such a joy about maths, but was there a transitional moment, a certain idea? It's actually very similar to have, have always seemed, since I've known you, had such a joy about maths. But was there a transitional moment, a certain idea? It's actually very similar to Hannah in that I had that bump early in life where my dad,

my dad was an accountant and he, when I was young, before I went to school, would give me maths to do as a treat. I didn't know any better, right? But it means that when I showed up at school, I'm like, all right, it's maths time. Here we go, right? And my first emotional opinion was I preferred addition to subtraction. And so I went through and changed

all the subtraction signs into plus signs. I'm like, oh, this is an easy fix. It's a self-fulfilling prophecy, almost. I like the fact, by the way, you phrased your theory about why people do or don't like maths as an unstable equilibrium. So the people who disagree with you don't understand what you've said.

But it's true. Once you get perturbed in one way or the other, that's people think, oh, I'm bad at maths, because once you get behind, it's very hard to catch up again. And I just, very lucky, had a rolling start. Obviously, still, everyone finds maths difficult. That's kind of the secret of mathematicians.

Maths people aren't people who find maths easy. they're the people who enjoy the fact it's difficult and and just give it a go and and don't mind the fact that they're going to have to wrestle with it until they learn it and so i just started again started with a rolling star and just uh that angular momentum has carried me on ever since and can i say by the way matt is one of my most you were in my top five most useful friends, right? I've got a friend who's a plumber. I've got a friend who's a doctor. If I ring you at four o'clock in the afternoon on a Sunday, what am I ringing you up about?

If I see your name on my phone and I haven't kept exact data, but to the nearest 10%, 40% of the time, it's a work thing, can you do a show? 60% can I help you with your son's maths homework? Yeah, it does. Oh, it's a work thing, can you do a show? 60%, can I help you with your son's maths homework? Yeah, he does. It's so useful. I just want to say one thing. Angular momentum doesn't carry

you forward. It takes you back to where you started. Oh, thank you. I was assuming friction in my analogy. So you spiralled in. That's a beautiful, that is a lyric, by the way. Angular momentum doesn't carry you forward, it takes you back. But that is...

What I find fascinating about maths, because I love doing my son's maths homework, and then I'll get frustrated, and I'll go, I can't work out the system, there'll be something algebraic. And I'll ring up Matt and I'll go, what is the system? And he'll go, no, there isn't a system, you just have to keep changing everything until it works and i find that fact well do you know i mean there are some you've paraphrased how helpful my advice is

and what i love is when you ring you're obviously very engrossed in the maths i imagine your son has long left yeah but 25 years ago. Yeah, exactly. But you're so frustrated that it's not making sense in the way it should. And I often feel like you're butting up against the beauty and the patterns in maths against the hoops for educational maths. So what your son has to do at school versus the logic and order you wanted to have. Yeah, no, that is very, very true. What about for you, David? When did you become interested in numbers?

Yeah, I think I used to collect car numbers when I was a kid. And also, I had the great benefit of growing up in pre-decimal currency. And so my mum used to test me on how much five half-crowns made on the way to school. I think listening to Matt and Hannah, I completely agree. I just manage to keep ahead all the time and do a lot of examples and enjoy doing them. And because of just keeping ahead, one step ahead,

I kind of always felt, yeah, this is all right, this is quite fun. Because the moment you slip behind, you're ill, you miss some time, I know that's when people then start finding it really difficult to catch up. I think, you know, not everyone can do all maths. And certainly for me, I like the pure maths, but then when I went to university, by the second year, it got too difficult for me, too abstract. I just couldn't... I banged my head and I thought, yes, fine,

so I moved into statistics, which has been great. But it makes me realise, sort of everyone, I think, has got a sort of ceiling for abstraction that they can willingly handle. But until you get there, I kind of think it's so sad when people get left behind. You know, everyone should try to get as far as they want and then say, OK, that's enough. That's enough. I don't want to go any further. Brian, how are your A-levels? No, I was bad at maths. I think I've said I like physics.

So I did well at physics obviously well you said hannah you know because i enjoyed it and i used to do it so so i got ahead and i just kept doing it so i got but maths i got a d at a level and i always found it difficult until i i share i absolutely agree with what you said i found it difficult until i went to university to do physics how did you get in and And then they let me in. I got in. He came in with a band and then just never left. It wasn't.

D-Ream were playing. Did you come in and say, I am going to become Professor Brian Cox? It's really... Is that why they're called D-Ream? Yeah. It's a really important point, actually, because I got in as a mature student, and as a mature student, as you probably know,

you can kind of... The entry requirements are much more flexible. And it does show you that... I strongly believe it, that judging people at the age of 18 on their results is... Well, I mean, it would... I wouldn't have done what I'd done if they'd just judged me on that.

And it was basically because I actually went to a New Order gig the night before the exam as well which had something to do with it but yeah but but I found just echoing what you said Hannah is that it's practice it was when I got to university I found that I had to practice it and then I found that I liked it I always think that when you have uh I don't know like Ian Wright or a really amazing footballer and then you hear their story about their natural talent and then they talk about when they were a child and Ian Wright I remember him once saying that he would get up basically at sunrise

and he would get a ball and he would go into the yard and he would play with that ball all the way and after the sun went down and then would go to bed and do the same the next day and same the next day and same the next day now of course Ian Wright is a naturally gifted footballer but when you get a young person how much of his talent was down to the fact that he practiced so much and how much

of it was just innate and i always think about mathematical ability it's like you there are some people who are naturally better at it than others, but I think it's that you achieve your potential via all the practice that you do. Well, Sarah, that's what I was going to ask you about, in terms of sometimes there is a myth, I think, that people have innate abilities, which is actually very often our alibi to say, oh, well, I don't have that innate ability,

so I can just pass that over. And I wonder, for you, with things like mathematics, when you were at school, how did you find it? Well, that's why I found it really interesting how compassionate you all said about people who, like, fell behind because they were sick or not concentrating. Because I think, actually, I was one of the people who was always there. And to use the Japanese analogy,

it's like people keep teaching you Japanese and you still can't speak Japanese. It's like every single day, someone who it makes really logical sense to, so much that it's easy for them, says it's like this and you're waiting for this click for it to make sense and it doesn't. And I think there is a limit.

Listening to your talk, I'm thinking about sort of neuroplasticity and actually how you use your brain changes what your brain can do. And if I'd known that, maybe I would have tried, but I think I was the kind of person who tried three times and then just went, OK, I don't care. I don't care what the answer is. Because the click didn't happen. It never felt easy.

And it never felt like it made sense. Even though I know intellectually it's the most sense. There's definitive answers. And that's why your inability to count means we still don't know how many people you have actually murdered even you've lost count on that haven't you but that's in the in murder circles that's a good thing you say i've lost count bruv yeah i once saw an amazing play about maths and i think this is what i would say about it was a story of the man who discovered zero and because it was all emotion and human i didn't think

oh i'm watching a play about maths i thought i was watching a play about human beings and so often when you do learn something and you see the beauty in it or hear people talking about something they understand even if you don't it is trying to find ways and maybe that is what has to happen at school with subjects where we do culturally go oh I'm allowed to say I'm bad at that thing and then just discount it that idea about the stories being really important so part of my job is trying to tell people stories about maths and I have a secret rule which is that I never use the word maths unless I can help it, because it's so tainted. It's so, like, it just brings up such awful memories for so many people that I think it's so much better, exactly as you're saying, Sarah,

to tell people a story and have, like, the beautiful ideas hidden in there, but they're the secondary thing, and never sort of point at them and say, hey, guys, look at the maths. Just let it kind of seep through a bit better by osmosis. And I just find that people just find it kind of seep through a bit better by osmosis and i just find that people just find it much more engaging if you do it that way and also there's a fascinating idea in that discovered zero did you think zero well it's kind of something that's yeah there

discovered it is interesting do we discover mathematics or do we invent it yeah i mean the idea of not having zero so if i remember rightly i think that shakespeare was roaming the streets of london before zero was commonplace in in western europe i mean it's like incredible how far we got in civilization without zero being really widely used there was a story it was from counting boards wasn't it in mesopotamia yeah and you would leave a counter there and then remove it and because it had sand on it it would leave an indentation that's one of the stories i once went to every platform zero at train stations in the uk in the same day that's we all celebrate

zero in different ways that's what i'm trying i was going to ask i mean you know as sarah was saying about the importance of stories. And that does seem to be the thing, that people don't connect. They see maths as, here is this symbolic language. And then I was thinking of people like, is it Paul Airdish or Paul Airdosh? I never know how to... I think there's a book called,

Is It Called The Man Who Thought Only Numbers? Something like that. And here was this fantastic, eccentric character. And he would literally turn up at people's houses with a carrier bag and a suitcase i think knock on the door say hello is your mind open and then they say oh yes come in come in and then he'd do this write a paper with the person until they were exhausted and then go all right okay there's nothing left of you so he'd go off and just

travel to the next house and here was this incredible character i mean i remember there's you know that great story that once a friend of his said just wait here i'm just going to pop out i thought he'll be safe he won't do anything he'll just stay in the room doing maths and he returned to his house opened the door and saw all over his kitchen it was blood and he was like oh my god what have i done i shouldn't have left him alone what have i done what have i done and then he noticed where the blood came from and he realized that it was actually from the fridge and so he walked up to the fridge and he opened the fridge and Paul Adish because he didn't really get round to learning any

other life skills, had decided he was thirsty, saw a carton of tomato juice, thought how do you open that? I imagine like this, stab, stab, stab, stab drank and that was and these characters, maths is filled with fascinating people but we don't find out about them

at school. I mean that's got something for everyone here. Is that a good advert for mathematics? That's exactly the point I was thinking, because, so, The Man Who Loved Only Numbers is a fantastic book because it talks about Erich's life, and it's got math puzzles, like, problems in it that you can work on, but the risk is perpetuating this kind of,

you need to just be this otherworldly detached being. And don't get me wrong, Edith was very much like that. But the reason we are so fascinated with him was he was so exceptional. Whereas the vast majority of jobbing mathematicians or people that work in tech or physics or engineering, right? They struggle with it it like everyone they enjoy the fact it's hard but it's it's a real challenge to turn the handle and i'm i love those stories but i'm always mildly nervous we're we're telling people this is what it is to be a mathematician and you need to descend from the sky with it as opposed to something you learn through um yeah but isn't that the more exciting you know you want the stories of the eccentrics and the strangers to then go, this is also an imaginative pursuit.

David's shaking his head vigorously. Yeah, but I agree with Matt. I think, you know, the bizarre, mad eccentrics, I don't think give a very good image for it. Although when I was at university, I was doing Galois theory, and I got inspired by the story of Galois, basically because he was this, you know, young genius, but he was also, you know, real radical, used to get in a lot of arguments, and he got inspired by the story of Galois basically because he was this young genius but he was also real radical, he used to get in a lot of arguments

and he got into a duel and he was a useless shot and so he knew he was going to die the next day and so he spent all the night filling notebook after notebook all his thoughts being written down and then went out and got himself killed the next day when he was, how old was he 21, 19? Yeah, really young

really young like that young, like that. And then, you know, people had to spend decades trying to decipher this stuff, and I spent a whole course doing Galois theory from this guy who got himself shot. So I find that quite an inspiring story. I like the guy who lives his whole life knocking on people's doors and having fun

and then stabbing tomorrow. It's not the guy who didn't really think ahead. Yeah, but in the end, though, for me, I don't think this is a good ad for what I call mathematical sciences or mathematical thinking. I'd much prefer stories about people who've gone out and solved real problems in the world. Those are the stories I like to have.

I feel like we're over-emphasising the amount of stabbing and shooting. She started it, to be honest. And then he went into a car park and found a body so don't no i know of course actually one of the main stories i use in my teaching and inspiring people to be interested in statistics is about how shipman's murders which i've done a lot of work on i was at the public inquiry and we worked out you know looking at data about when he used to kill his victims and when he could have been caught and all this kind of stuff, using statistical theory. So many people that he treated would have maybe died of natural causes, knowing the true amount of his victims is very, it is

statistics, they're guessing, because they have to compare it to so many other doctors. You have to do observed minus expected to get excess deaths, as same as we do with COVID. One of the stories that I use to talk to schools, building on those ideas of David, is trying to work out where serial killers come from using these mathematical techniques that are used by the police. So, you know, you're really genuinely on to something. Yeah. I mean, we do...

I think it's been a revelation. I thought, you know, we've done... We did a really lurid show about flies and bats and fungus. We've done all these things this series. This was the one i thought would be nice and neat and now david what why is it necessary for uh many people to have a grounding in mathematics because we've heard about the the specifics of people doing research and and and so on but why would it be desirable for many more people to have those basic skills? Well, at every level, but you know, the basic numeracy is required for everyone to function

in society. Otherwise you can be ripped off right, left and centre, and you are actually disempowered if you're not numerate. And so programmes like National Numeracy do a fantastic job in trying to encourage basic numeracy. But then we get above that, and the next stage is that we should be able to use maths to solve problems in real life and be able to do some basic operations maybe some little bit of spreadsheet work or something like that maybe look at some data and handle that and then the next stage where you can use it in professional purposes and then eventually you know some people might want to go on and be actual researchers so it's relevant at every level to everyone in society. So and not just to be clever and to do clever things, but just to function. Look at, you know, this pandemic, we've been

bombarded with numbers and log scales and all that kind of stuff. And you can just see people have been conned all the time by misuse of numbers. We've done some research and showed that the biggest predictor of being more immune to misinformation is numeracy. And actually improving people's numeracy might help them be less subject to all the nonsense that we see around them. So, I mean, my personal interest, as I said, is not particularly in mathematics. It's much more in terms of handling data, handling numbers in the news, in our lives, and how to make the best sense of them, how to interpret them, numbers in the news in our lives and how to make the best sense of them how to interpret them and when to spot that someone's trying to put one over on you and are using those numbers to manipulate your emotions either to make a number look big oh i'm not going to talk of course about 350 million

pounds on the side of the bus no no no no no no no not a mention of that one at all but um or to make it look reassuring and we've seen that oh god on twitter and everywhere it's being used all the time to either frighten people about covid or say oh it's all just flu and etc etc i mean sarah do you see that again again that because it's a kind of odd clash isn't it because in one way maths becomes in some people's minds so abstract it has no pragmatic use i think the psychology of everybody when we see numbers is fascinating and so often statistics aren't true or used in advertising or made up or you know the small print is we asked 13 people that kind of thing so but we trust numbers a lot actually we assume that numbers are much cleverer

than us people using numbers must know what they're talking about and actually covid was such an interesting example of that i was listening to a podcast which was about um it was a podcast just proving some of the things that had been said by joe rogan on his podcast about covid and one of the studies that was mentioned it was looking into young men who'd had vaccinations and then a hundred% of them had been admitted into hospital, which was extrapolated as evidence of how bad this heart defect was. And actually they spoke to the doctor whose study it was and whose paper it was. And the reason that 100% of them had gone to hospital is because he wanted to study what had happened to their hearts. None of them would have needed to go to hospital. They were actually all okay. It was very, very mild what happened. And all you had to do was read his paper. But the numbers of it

told a different story. And someone else can tell that story and seem to be backed up by this scientific evidence. So it is really fascinating. People are interesting in terms of, I guess, what they want to do and how effective it can be if you're backed up by numbers. I think Sarah's completely right there, because you trust that the people who have done the numbers know what they're talking about. And I think that when you put something into a mathematical form, if it's a graph or if it's a statistic,

or even if it's like the output of some kind of algorithm, I think it can take on this air of authority that makes it quite difficult to argue with. And I think that exactly as David says, that can then be used to manipulate you. And sometimes in terms of misinformation, particularly around, you know, COVID vaccine is a particularly prominent example,

but I think it's just everywhere. I think this stuff is really rife. So I remember a couple of years ago, I had a chat with someone who works for EPSRC, which is the kind of the body that gives out money to scientists to do their work. And they say that they get loads and loads of grant applications from people who are trying to use artificial intelligence to do something or other.

And he told me that he had this trick that he uses to see if it's really that the AI is going to do it, or if it's kind of not. And what he does is he takes a sentence, and he takes away all of the technical sounding words and he replaces them with the word magic and if the sentence still makes grammatical sense then he knows that it's absolute nonsense i i wanted to come back to infinity the infinite monkey cage um we thought infinity is one of those i was talking to robin earlier actually and he said that um he feels if you talk about infinity in terms of the universe so it's a it's an infinite distance

in every direction it's very difficult to understand whereas if you talk about the infinity in terms of the number of numbers between naught and one then he finds it entirely comprehensible so so infinity is a concept it i think it's worth exploring because it's one of those things that's magical and baffling and the idea as you said that there's an infinite number of numbers between naught and one so if you're thinking of every single fraction and then you make it in that because that was the first thing which i didn't get with Hilbert's Hotel, which I'm sure many... But when I started to think, OK, right, there's different infinities.

So first of all, there's an infinity which is just all numbers. But then there's an infinity which is all prime numbers and that's still infinite, but that must be a smaller infinity. But it's still... And then I start to get a headache. Oh, yeah. And then the universe gets bigger and bigger and I'm all lost in it and screaming.

But I enjoy that screaming. So it's kind of... We had the biggest argument, didn't we? The biggest argument in the history of Monkey Cage, I think, was John Lloyd, wasn't it? He got very, very offended. Yeah, John Lloyd was furious. He was in this theatre and when he found out there was... How can there be more than one kind of infinity, right?

And he was there with the Astronomer Royal, Martin Rees. It was like a WCW wrestling match more than anything else, wasn't it? I was quite surprised by Sir Martin Rees' leotard. But apparently a gift originally from the Queen Mother. The idea of infinity

messing with your brain, actually the person who discovered that there is more than one type of infinity, and some infinities are bigger than others, and there's gaps between these infinities, and there's a lot going on with infinity. There's a guy called Cantor and he himself essentially couldn't handle these big ideas in his head.

And at one point, there were some diaries written. He believed that he had a chamber pot and he believed that as he stirred it, he was causing it to rain. I think the infinity didn't help. Another story Matt won't like. I'm just glad no-one got murdered. But actually, you say... Like, I love the notion of infinity,

and there are infinitely many different-sized infinities and all these things, and then you get all these logic puzzles where you've got a bucket, and you put an infinite number of balls into the bucket and then you take out every square one and all these weird counter-intuitive results and a lot of people would then say well what's the point how can i stab someone and i think sarah put it perfectly where was it the brain plus elasticity yeah yeah so it depends on the stress and strain i guess it's a young's modulus joke joke, if anyone's following along.

But the point of these things is if it's not something that's directly practical, maths is still teaching your brain how to think. And the fact that by doing ridiculous logic puzzles about infinitely many things, you're still training your brain to think in new creative ways. I mean, it's got to be a good thing. And so I love the fact that a lot of this is just the delight of improving your brain and learning how to think new ways. I'm just all coming back to me.

Staggering excitement at 17 when I learned about complex numbers. The square root of minus one. Now, where is the square root of minus one? You can't see it. So in order to play with the square root of minus one. Now where is the square root of minus one? You can't see it. So in order to play with the square root of minus one, you have to invent an imaginary dimension that goes orthogonal to all the space we can see around us.

But yeah, train stations. Sorry? Yeah, I always said that King's Cross goes from, the platforms go back to zero, and if they built another one, they have to go to minus one. And therefore, the underground platforms should have complex numbers as their numbers. Thank you! As their numbers.

Exactly. I felt like I'd been introduced, it's like the Illuminati or something, I was introduced to this inner sanctum of knowledge, and I was so excited by it, and still retain some of that real excitement. They become tremendously useful, fundamentally, some of that real excitement. They become tremendously useful. Oh, incredibly valuable. Fundamentally, in physics, for example, quantum mechanics is very hard to represent mathematically without complex numbers.

I think originally they were called imaginary numbers as, like, someone was trying to talk down the idea, being like, oh, yeah, you and your imaginary numbers. But that's great. It's like Big Bang Theory, isn't it? Or you and your Big Bang. Oh, bloody hell, that's turned out to like big bang theory isn't it or you and your big bang oh bloody i turned out to be that's a really massive telescope it is very interesting though that something that was uh you know i i well the history you said don't

ask you about history but the history of complex numbers so they weren't introduced to be useful as far as i understand but they're extremely useful and almost fundamental in describing the most fundamental physics, which is interesting, because it leaves... I suppose it leads us into questions about where mathematics comes from. Is it invented? Is it discovered? Oh, not back to that again. David has dismissed my question completely,

but Hannah feels it may be useful. OK. I think that if you have experience of doing advanced level mathematics, then you are under no illusions that you are on a voyage of discovery. So all of the things that you're doing in school, all of the letters and all of the, like, symbols and things, those are created, but they are describing something that you are absolutely sure is totally, totally real.

And the best way I've heard this described is as though when you're playing around with those equations, it's like you're sort of travelling through a kind of thicket, right? It's going through forests and manipulating things, taking an equation, bending it, breaking it, going around one direction, going around the other direction, seeing if it gets to the same place. And then all of a sudden, through a a clearing you realize that you are in this beautifully manicured garden and everything is laid out absolutely perfectly and no one has been there before you and that is the closest i can possibly get to being able to describe the experience of of doing advanced level mathematics i've had that experience where I've discovered something and gone,

there is no way someone else has done this before me, right? I have found, oh, I've made this thing. And then I'll find out someone did it centuries, decades, whatever ago, because they've also stumbled across it. And you're right, the way we express it is different. But when you're saying very on, like when we met, if we meet aliens, maths will be the universal language. Even if we have different counting systems,

completely different chemistry, potentially different laws of physics, we'll still be like, hey, how about those prime numbers? And we'll say, oh, have you discovered this yet? Oh, we've discovered that, right? It'll still be the same discoveries in maths, whatever universe other intelligent life comes from. And for me, that's why it's discovered.

There won't be different laws of physics. Brian Green, wonderful writer, Brian Green, he said that every now and again he has a little nightmare where when the aliens arrive, they go, oh, we used to think mathematics was the language of the universe too. Go, oh, my God, no! Sorry, Sarah. Matt, that's so interesting, because we have a thing in comedy

where you think you've come up with a joke, and then you find out someone else has done that joke before, but we're not allowed to just carry on doing their joke. But you are allowed to do that with sums, are you? Thank you, mate. Have you seen it? There was a cartoon someone put up the other day which I thought was one of the cleverest cartoons I've ever seen. It's the number eight at a therapist saying,

I won't lie down or we'll be here forever. Which is, I mean, that... Oh! What an incredible piece of work that is. So wonderful. Questions there? So we always ask the audience a very, very difficult question. And as this is the end of this series,

we thought we'd ask probably the toughest one yet. What is the best number and why? What have you got there, Brian? So Lauren said four, because it's the smallest composite number, the smallest square prime number, and the day in June I was born. Ollie said 1.8 times 10 to 48

because that is the duration of Wonders of the Solar System, episode one, in plank units. You can keep that for a minute. That's actually scary. All right, I'm going to go for this because it's a challenge.

Ten... Hang on a minute. 10,000 million, million, million, million, million, million, million, million, million, million, million, million. So that's 10 to the 76. I was challenged to say 10 to the 76. So I think it's 10,000 and then... And then 12. 12 millions.

That's what I went for. So there you go, Rose. And do come and see the show. We're running at Blackpool end of the pier for the whole of August. Well, also, Rose says that would be very funny, which turned out not to be the case. So, this one is boobs, but obviously

800B5. Which is, I suppose, the first maths joke, the first calculator joke. Thank you very much to our brilliant panel, and they have been David Spiegelhalter, Hannah Fry, Matt Parker, Sarah Pascoe.

CHEERING This is the last episode of this series, so obviously next week we won't be here, we'll be on holiday. And, well, I'll be in Penzance, and Brian will be on Mars. But he won't really here, we'll be on holiday. And, well, I'll be in Penzance, and Brian will be on Mars. But he won't really be on Mars. He will be in a glass chamber that we place him in, which keeps him kind of moist and smooth and young,

and then we just have electrodes on his brain, and they simulate his belief that he's on Mars. So he's not actually going anywhere. Do you ever wonder what it's like working with Robin Ince? Easy. What happens in his mind? That he would sit here, the end of a Radio 4 series, another series, and come up with that?

You know what I mean? That's one of the reasons where, when I say we're going to be back at the end of the year, it might not be both of us. It will be something that sounds and looks like Brian Cox, but much like this version, which, as you know, is 5.0, we might have a Brian Cox 6.0, because, frankly, when I programmed his ego,

it's gone out of control. Thanks very much. Bye-bye. Bye. APPLAUSE Till now, and in my podcast, Just One Thing, I'm investigating some quick, simple, and surprising ways to improve your health and life. From a cup of coffee to increase fat burning. Maybe a nap to boost your productivity. Or how about a bit of dancing? To big up your brain power. So to benefit your brain and body in ways you might not expect,

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