How to Teach Maths

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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 four?

I'd be more worried about harvester.

Harvester?

Harvester on radio four?

That's very much a Radio 2 restaurant.

It's ridiculous.

Surf and turf, I don't think so.

They won't understand it, will they?

Do they even have Harvester?

Are we trying to work this out?

They do.

Thank you.

Good.

See, and 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 different.

Well, it will come as no surprise to anyone that Robin is not very good at mathematics.

Actually, that's not true.

I have this.

This will, 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 But also, I think it would have made biology a lot less intimidating if you realized that they were just using the physicist trick of using literal names for everything, but just in Latin.

Why is that the physics?

What do you mean, like the universe?

Well,

or supermassive black hole, or isn't there like a really very large telescope in Europe?

I swear you mean, yeah, the VLT, the very large telescope, yeah.

So, 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 forum and magnum, which is Latin for big hole.

I'm David Spiegelholter, I'm a statistician from the University of Cambridge.

I'm not a mathematician and I'm not a teacher.

I don't know why 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.

Thank you very much for joining us.

I'll muddle through it.

There's a 25% chance you'll be there.

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, you know, back in the Middle Ages sometime.

I'm Matt Parker.

I was once a secondary school math 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 Pasco, 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,

you know, geography, sort of if we map out where all the victims lived, where's that little round circle where where they probably lived?

English, how did they do it?

Yeah, I think pretty much biology, cutting up the cadavers.

I don't know.

You can 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 his 99.9997%

chance.

That it is?

That it is.

Right, okay.

And that was enough to get 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

he 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, it wasn't.

That's how they found it.

That's how 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 badge on?

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 genetic.

Might have gone from DNA.

Yeah, that was that got it.

But none of those are absolutely confirmatory.

Well, anyway, welcome to In Our Time.

And

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 program as well.

Very canny.

Now, Matt, define the 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, 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 learned 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,

that I realized what it was for and realised it all clicked into play.

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 really interesting.

It's the opposite.

It's 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 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 in, so I won't worry too much.

Not that we haven't all done some murders, but the...

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 who 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 math textbook and she insisted that every day I do one page of the math 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 difficult.

Suddenly, I wanted to do more and more and more.

And essentially, that is a tidal wave of success that I've been riding ever since.

I do think, though, I do think that I think of maths, it's like it's a bit of 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.

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, one nudge, maybe one day you sort of are a bit asleep in a lesson and you don't pay attention, and then the next lesson is much harder.

And then you start 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 stupid at it.

And 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 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, and 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, you know, because you seem to have always seen, 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 easy fix.

It's a self-filling 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 the 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 just give it a go 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 start and have just 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 math homework?

Yep, because really.

Oh, it's so useful.

See, this is what.

Sorry, one thing.

Angular momentum doesn't carry you forward, it takes you back to where you started.

I was assuming friction in my analogy.

So you spiraled in.

Yeah, yeah.

That is a lyric, by the way.

Angular momentum doesn't carry you forward, it takes you back.

But that is it, because what I find fascinating about maths, because I love doing my son's maths homework, and that's what 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 go, what is the system?

You 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 what I mean?

There are some.

I feel like you've paraphrased how helpful my advice is.

No, no, no.

And what I love is when you ring, you're obviously very engrossed in in the maths.

I imagine your son has long left.

Yeah.

25 years ago.

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 want it 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 managed 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 thought, I banged my head and I thought, yes, fine.

So I moved into statistics, which has been great.

But it makes me realize 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, okay, that's enough.

That's as much.

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.

Probably what you said, Hannah.

Because I enjoyed it and I used to do it.

So I got ahead and I just kept doing it.

But maths, I got a D at A level.

And I always found it difficult until 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 then they let me.

He came in with a band and then just never left.

So I ream worked.

I am going to become Professor Brian Cox.

Is that why they're called D Ream?

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 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 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, 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're 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 get 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 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, that is Sarah, that's what I was going to ask you about, you know, in terms of sometimes we are, 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, you know, for you, with things like mathematics, when you were at school, you know, how did you find it?

Well, that's why I found it really interesting how compassionate you've 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.

I think listening to your talk, I'm thinking about sort of sort of neural plasticity 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, Okay, I don't care.

I don't care what the answer is because

the click didn't happen, it never felt easy, and it 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?

Yeah, but that's in the murder circles, that's a good thing.

Lost count, bruv.

Yeah, I once saw an amazing play about maths, and I think this is what I would say about it.

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 you 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 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 it's 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

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 Western Europe.

I mean, it's like incredible how far we got in civilization without zero being really widely used.

There was a story once it was from canting boards, wasn't there, in Mesopotamia, I think.

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.

We all celebrate zero in different ways, is what I'm trying.

I was going to ask, I mean, you know, as Sarah was saying, 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 Erdős or Paul Erdos?

I never know how to, you know, 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 and with a carrier bag and a suitcase, I think, knock on the door and say, hello, is your mind open?

And then they'd 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 go off and just travel to the next house.

And here was this incredible character.

I mean, 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 here 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 Eddish, 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, stab.

Drank, and that was, you know, and these characters that are, you know, 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 Erish's life and it's got mass 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, Edish was very much like that, but the reason we're 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 like everyone.

They enjoy the fact it's hard, but it's a real challenge to turn the handle.

And I love those stories, but I'm always mildly nervous

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

yeah, but isn't that the more exciting?

You know, you want the stories of the eccentrics and the strange to then go.

This is also an imaginative pursuit, David Shaikh.

Yeah, yeah, but I agree with Matt.

I think

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 it was also, you know, a real radical.

You should get in a lot of arguments.

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 is he?

21, 19?

Yeah, really young.

Really 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

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 overemphasizing the amount of stabbing and shooting.

Yeah.

And she started it to be a lot of fun.

And then he went into a car park and found the body.

So don't,

of course, actually one of the main stories I use in my teaching and inspiring people to be interested in statistics is about Harold 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 the data about when he used to kill his victims and when he could have been caught and all this kind of stuff.

Of course, so 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 is it 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, the 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 onto something.

Yeah.

I think this is going to revolutionize me.

I thought, you know, we did a really lurid show about flies and bats and fungus and we've done all these things this series.

This was the one that I thought would be nice and neat.

And now...

David,

why is it necessary for

many people to have a grounding in mathematics?

Because we've heard about the specifics of people doing research and so on.

But why would it be desirable for many more people to have those basic skills?

Well, yeah, at every level,

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, programs 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 a 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 this pandemic.

We've been bombarded with numbers and log scales and all that kind of stuff.

And you can just see people are being conned all the time by misuse of numbers.

We've done some research that 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, and when to spot that someone's trying to put one over on you, and they're 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, no, no, no, no, no, not a mention of that one at all, but

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, etc., etc.

I mean, Sarah, do you see that again?

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 are used in advertising or are made up, or you know, the small print is, we asked 13 people and 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

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 was looking into young men who'd had vaccinations, and then 100% 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 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 fast that the 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 is 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 said that they get loads 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 wanted to come back to infinity, the infinite monkey cage.

We thought infinity is one of those.

I was talking to Robin earlier, actually, and he said that

he feels if you talk about infinity in terms of the universe, so

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, infinity is a concept.

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 sounds.

Yeah, thinking of every single fraction, and then you make it a it in that way, because that was the first thing which I didn't get with Hilbert's Hotel, which I'm sure,

but when I started to think, okay, right, so 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, 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, but I've.

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 good.

Yeah, John Lloyd was furious.

He was in this theatre.

And when he found out there was, how could there be more than one kind of infinity, right?

And he was there with the astronomer royal, Martin Rees.

It was more of it, it was like a WCW wrestling match more than anything else, wasn't it?

I was quite surprised by Sir Martin Rees's 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 like gaps between these infinities, and there's

a lot going on with infinity was 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 that 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 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, so it depends on the stress and strain, I guess.

It's a Young's modulus joke for anyone 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 that's gotta I mean it's gotta 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 I staggering excitement at seventeen when I learnt 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, you have to invent an imaginary dimension that goes orthogonal to all the space we can see around us.

But yeah, and train stations.

Sorry, you've got the train stations.

Yeah, now 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.

And I felt then, 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, yeah, some of that real excitement.

They become tremendously useful

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, be 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, oh, that's turned out to be.

That's a really cool thing.

Supermassive telescope.

It is very interesting, though, that something that was,

you know,

well, the history, you said don't ask me about history, but the 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 it I suppose it leads us into questions about where mathematics comes from.

Is it invented?

Is it discovered?

Well, not back to that again.

David has dismissed my question completely, but Hannah feels it may be useful.

Okay.

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 traveling 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 you get to the same place.

And then all of a sudden, through 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 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

if we meet aliens,

mass 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 see, oh, have you discovered this yet?

Oh, we've discovered that.

It would still be the same discoveries in maths, whatever universe other intelligent life comes from.

And for me, that's why it's discovered.

There'll be different laws of physics.

Brian Greene, 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.

Sorry.

Matt, that's so interesting because we have a thing in comedy

where if 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?

Have you seen?

There was a cartoon someone put up the other day, which I 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,

what a

breadth piece of work that is.

Questions then?

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 1, in Planck units.

You can keep that afraid.

That's actually scary.

All right, I'm going to go for this because it's a challenge.

10.

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 a...

And then 12.

12 millions.

That's what I went for.

So there you go, Rose.

And do come and see this 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.

This one is boobs, but obviously 800B5, which is, I suppose, the first mass joke, the first calculator joke.

Thank you very much to our brilliant panel.

And they have been David Spiegelholter, Hannah Frye, Matt Parker, Sarah Pascoe.

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 be on Mars.

He'll be in a glass chamber that we place him in, which keeps him kind of moist and smooth and young.

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 Inns?

Do you know?

Easy, 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?

No, I know.

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.

Till now, nice again.

Hello, I'm Dr.

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