The Problem of Infinite Pi(e)

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Episode 4.

Now, this is one for you and not for me.

Because it's not, it's not really episode 4, it's episode 3.14.

It's a pie special.

I've just got to suck it up.

You know what, though?

I have a really good feeling about this, Adam.

I strongly suspect, Adam, that by the end of this recording, you, sir, will have had an epiphany.

It's a greedy pie question this week from Alex Walsham sent into curiouscases at bbc.co.uk.

Did you say greedy?

Greedy, it's actually four questions.

And I'm taking a back seat because you are going to like this.

This is pure math.

It is a delicious pie.

He writes, I have never truly understood pie.

Well, rest easy, my young Padawan.

We have a pie Jedi on the team.

Certainly do.

Question one, how did we discover pie?

Question two, how did we discover its use in measuring radius and circumference of circles?

Frankly, Alex, there is quite a lot of overlap there between questions one and two.

Question three, how do we know that pie goes on infinitely?

And question four, how do we know it never repeats?

There you go.

It's a pie special do you like?

You know what?

I actually think that we should dedicate some proper time to this.

I think we should do a 42-part special of Rutherford and Fry, although admittedly mainly fry.

It would be mostly fry, and that is fine by me.

But you know what pie is, though, don't you?

Yeah, I do.

Of course I do.

It's 3.1415 something something.

Okay tell me everything you know about pi.

Right.

So pi is the ratio between the circumference of a circle and the diameter.

Very good.

Anything else?

I know it's also an irrational number, which means that after the decimal point, the numbers go on forever and they never repeat.

Outstanding.

Anything else?

And we are done.

Next week on curious cases.

Not yet.

Not yet.

Not yet.

There's a lot more to say about Pi.

Because the thing is, is that it just, you find it everywhere.

It's not just in circles and in triangles.

You find it in rivers.

You find it in waves.

You find it in helicopters.

Anywhere in space where there's something moving or rotating, you'll find this really magical number.

Okay, I feel like this is the area we're going to explore over the next half an hour or so.

But first, as...

As is somewhat traditional on curious cases, give me some history because this is something we talk about all the time.

We learn about it in school, but where does it actually come from?

Yeah, so pie was first really looked at by the ancient Egyptians, and a bit later the ancient Babylonians.

And they figured out that the ratio between the diameter and the circle and the circumference of that circle is about three.

So essentially, they were the first to discover that pie is a constant for a circle, and it doesn't matter what size the circle is.

I also know that the ancient Egyptians, they made something which was a bit like a pie.

It was more like a sweet biscuit and it sort of had a honey filling with a chewy surrounds made from oats and wheat.

Are you gonna make pie jokes the whole way through?

I have very little to contribute otherwise.

Okay, well a little bit later in time, there was the ancient Greek mathematician Archimedes, and he came up with this incredibly clever method for how to work out the number pie using

polygons.

So what he would do is he imagined a shape like a hexagon, and then if you add in more sides so rather than six sides make it ten sides or make it twenty sides so that each each little straight bit gets shorter and shorter and shorter the more sides that you add the closer it is to a circle but those polygons have areas that are much easier to work out and the more sides you add the closer it gets to 3.14.

I see so a circle if you think of a circle as being a polygon with an infinite number of

sides.

Exactly right.

Nice.

I've got one.

Got another one.

Is it food-based?

The Romans, they had a pie called Plus Centre, and that's where the human placenta gets its name from because it's sometimes shaped like a big flat dessert pie.

I'm really glad you're here.

I mean, this week or every week?

All the time.

Yes, well, much as though I'm very happy to hear you drone on about pies all day.

Pie, not pies.

Pies all day.

We've got some other fine mathematical brains to help mostly me out.

Yeah, thank goodness we do.

Yeah, yeah, yeah.

We have Matt Parker, stand-up comedian, YouTuber, and best-selling maths author.

He's the author of the book Humble Pie

about maths mistakes.

And we have Dr.

Vicki Neal, who is a lecturer in maths at the University of Oxford and the author of Why Study Maths.

Vicki, have you got any favourite pie facts?

I've got lots of pie facts.

People didn't start using notation for pie till like the 1700s.

So pi wasn't called pi before the 1700s.

What do they call it?

Lots of different things.

Circle thing.

Yeah, like the ratio of something to something.

We use an ancient Greek letter, but it wasn't the ancient Greeks who called it pi.

Yeah, I don't think I knew that.

Any other good pie facts?

Yeah, so pi comes up in really surprising places.

So there's something called free analysis where pi comes up all the time.

So if you're listening to this as an MP3, the compression that's done to use that is based on free analysis, medical scanners.

Using Fourier analysis, pie is all over it.

Right.

When you say there's pie all over things,

you're not making it easy for me to be sensible in this discussion.

Matt, it's not a pie fight, but what are your favourite pie facts?

Ah, top pie favorite pie facts.

Coming in at number one, if you pick any two whole numbers at random and you check if they have any factors in common, the probability that they are co-prime is six divided by pi squared.

That is a good thing.

Is it?

Thank you.

Isn't that amazing?

For Hannah to be impressed with a maths for the square.

Yes.

I didn't know that.

I came straight out with the obscure bit of number theory, abstract maths, pi facts.

Now she's immediately impressed.

Yes.

I am immediately bewildered.

Can you just explain to me?

See, I know my audience, right?

Because mathematicians love pi, not because it's like the ratio of a circle's circumference to its diameter, although that is wonderful.

Mathematicians love pi because you'll think you'll be doing some totally unrelated mathematics and suddenly pi shows up out of nowhere.

Right?

And so I knew if I mentioned a thing about coprime numbers and factors, there shouldn't be pi.

Pi should not be there.

And suddenly the probability is 6 divided by pi squared.

And that just, that's what we love in mathematics, unexpected pi.

Right, right, okay.

And the one that I was particularly intrigued by, because I love the history of science and the history of mathematics, is this attempt in 1897 to force pi to be something that it isn't.

Oh, yes, this was in the States.

Yeah, was it Indiana?

Yeah.

They tried to legislate that pi should be 3.2.

It's a nice round number.

Exactly.

And in their defense, it would make maths a lot easier.

But I don't know why they decided that this was a matter for the law, but for some reason they did.

It was a unanimous vote that they were going to go 3.2.

And they got lucky that there happened to be a maths professor who was like in the upper house of the legislator and saw this was happening.

He was like, no, no.

There's not, nothing works like this.

That's not how pie works.

You can't just decide to make it 3.2 because that would make your lives easier.

And I've got the numbers here.

The voting numbers are in the House of Representatives.

They voted 67 to nil to

make pi 3.2.

That's what unifies the entire political spectrum.

Simplifying pi to something that it's not.

I don't get it.

If you were trying to approximate pi to one decimal place, you wouldn't even approximate it to 3.2.

No, it's a 3.1.

Nothing about this makes sense.

The thing is that you can actually just measure it.

I think that's why it's so mind-boggling.

Not if you're a 19th-century Indiana legislator.

Can Can I tell you my favourite way to work out pie?

Okay, so what you can do is you get a dartboard, a nice circular dartboard, and then you put it on a square surround that's exactly the right size, so it's very snugly fits inside it.

And then you get somebody who's really rubbish at darts,

like me, and somebody where their throwing is essentially random, and just get them to chuck like loads and loads and loads of darts at the dartboard.

And then because they're chucking randomly, some of them will be inside the circle and some of them will be outside the circle in the little corners of the square.

So you count up how many are inside, how many are outside, and that will tell you the ratio of the areas from which you can calculate pi.

And you don't even need a ruler.

And it comes out as 3.14.

I think you're tricking me.

This is a trick.

There are other ways that you can measure it.

Yes, and I mean, some of them are more practically sensible than others, but you know, so if I'm allowed to go and climb across the studio,

I have here two billiard balls

and a convenient BBC cabinet.

So if I roll one of these at this beautiful BBC cupboard, it makes a nice thud.

And for the purposes of this demonstration, I think this BBC cupboard is perfectly elastic, so it bounces, the ball bounces off perfectly.

So I've actually got two of these balls, and if I put them in a straight line, I'm going to roll the one further away from the cupboard, towards the cupboard, and it's going to hit the other ball on the way.

Cannon one onto the other, essentially.

Yeah, exactly.

Cannon, that's a good word.

So, the question is:

how many thuds do you hear?

Because there's two types of thud.

There's ball hitting ball thud, and there's ball hitting cupboard thud.

Cupboard turns out to be a lot noisier than ball, but okay, count how many clicks you hear.

There's a double bounce there, so one, two, three.

Yeah, three.

Three point one four?

Yeah, what does this have to do with pie?

Well, okay, so with two balls the same size, we've got three collisions.

What you have to imagine doing is making one of the balls much, much heavier than the other.

So, the one that's further away from the cupboard, the one that you roll first that does the cannoning, imagine that's a hundred times the weight of the other one, or a thousand, or a million times the weight.

And what you end up with is lots more ricocheting going on with the balls.

So, the outer ball hits the inner ball, which hits the cupboard, which then the inner ball hits the outer ball again, and it kind of bounces backwards and forwards, and you count, but what you find is that you get 314 clicks, or the number of clicks you get is kind of getting closer and closer to an approximation to pi or a multiple of an approximation to pi, which is just bizarre.

That sounds like witchcraft to me.

Bizarre.

This is exactly what Matt was saying earlier, though.

This is the reason why mathematicians absolutely love this number.

Because in completely random places, rolling billiard balls around to BBC cupboards, you do it in the right way and suddenly pi pops up out of absolutely nowhere.

Okay, and Matt, you've got a demonstration of how we can measure pie as well, but it involves us actually leaving the studio.

Yes we need more headroom.

Okay well let's you and I will do that and we'll leave these two to I don't know talk about numbers or whatever it is that we do.

Let's go.

Okay so we are in the stairwell of Old Broadcasting House

and at the top of the stairwell there is a Oh, there's an old microphone stand with a piece of string and a pie.

An actual chicken.

it looks like a chicken pie is it chicken and mushroom pie

Matt what are you doing you've got a tape measure yeah so we're going to suspend this a quarter of the length of acceleration due to gravity right so the acceleration due to gravity is 9.81 meters per second so we're going to set this to 2.45 meters and so this

is a pendulum or a pie endulum if you will and the equation for the period of time it takes a pendulum to swing has a pie in it.

But because this is the correct length, it will take exactly pi seconds to swing backwards and forwards.

Oh, I see.

I mean,

if we said this swinging.

But how far, though?

It doesn't matter.

It doesn't matter how heavy the pi is, doesn't matter how far it swings.

The only thing the period of a pendulum depends on is pi,

the length of the pendulum, and what acceleration due gravity is, how much gravity you've got.

So if this was on a different planet, it would take a different amount of time to swing.

But anywhere on Earth, the same length pendulum takes the same amount of time, and if it's a quarter gravity, it takes pi seconds.

So, here, so I propose we do 10 swings, yeah, and then divide by 10.

And then divide by 10.

When it passes my finger, you start timing.

Are you ready?

Got it, and we're off.

Go

nine.

Are you ready?

You ready?

And

ten.

You're not going to believe this.

That's, I mean, that, so divided by ten.

3.141.

So we got by precisely right.

Yeah, we got precisely right.

That's pretty cool.

I'm actually quite excited to show Hannah this.

Alright, let's go back to the studio.

Alright, we're back.

We're back, we're back, we're back, we're back.

And

I'm so excited about this.

Look, we did it.

When you were gone, I converted him into a maths enthusiast.

So we did the whole experiment.

You swing it back 10 times.

I timed it.

And look what number we got.

Hello!

Very good.

3.141.

I am genuinely...

I mean, the billiard balls were, I was, you know, it was good.

It was a bit of witchcraft.

That, that's really impressive.

Did it help that it was a pie?

It was an actual pie as well.

Chicken and mushroom, I'm told.

We'll be having that later.

I'm glad that you have had just a small insight into what it feels like to be an excited mathematician.

Well, you know my face, and you know when we do mathsy programmes, I look a bit bewildered and slightly bored, but look at me now.

Exactly.

The thing is though, Vicky, mathematicians don't just enjoy spotting pi, we actively make use for it too.

Can you tell us about why pi is a vastly superior way to measure angles than 360 degrees?

Yeah definitely.

Pi is definitely the right way to measure angles.

So we normally measure angles in degrees.

So if you imagine a hand on a clock sweeping out a full circle, it would turn 360 degrees.

And I guess the 360 comes from like the ancient Babylonians or something.

I mean 360 when you stop and think about it is a very strange choice.

Like why would there be 360 degrees in a whole turn rather than 100 degrees or 253 degrees or anything else?

It's like arbitrary.

It divides up quite nicely of course.

If you are cutting a pie up for your family into equal pieces with your protractor, which is I assume how you divide pie yourself,

then it's quite handy because 360 divides very nicely.

But if you went to a different planet and you asked the aliens how they were measuring angles on their planet, I don't think that they would be measuring with 360 degrees.

So, mathematicians, we say that there are two pi radians, different unit of measurement.

So, there's two pi radians in a whole turn.

So, if you imagine that hand on a clock sweeping around, it sweeps out two pi.

And I reckon if you went to another planet and you found the aliens, they would be measuring using pi.

Because that's a universal way of measuring circles rather than 360 degrees, which is completely arbitrary.

Exactly.

Pi is somehow some kind of fundamental kind of mathematical thing.

The fact that it's written as 3.whatever is just to do with our decimal number system.

But pi itself, that quantity pi, is some fundamental fact of maths and therefore the universe.

All right, you join us in the magical mystery tour of the number pi.

It's going to go on for a while, or at least as long as I can get away with before Adam shuts me down.

So far, we have discovered pi in some strange and unusual places.

We have measured pi with a pi, and every time it comes out to being 3.14.

Every single time it's quite magical.

Now, Vicki was just talking about space aliens and this being a universal number that aliens would recognize.

Finally, something I can actually relate to.

So earlier, I spoke to Mark Raymond, who's the chief engineer for mission operations and science at NASA's Jet Propulsion Lab, which is a pretty cool job.

Mark has led missions to explore remote parts of the solar system, like the dwarf planet Ceres out in the asteroid belt.

And it turns out, of course, navigating spacecraft through the solar system depends on Pi.

One of the missions that I really enjoyed working on was Dawn which launched in 2007 and Dawn explored the two most massive residents of the main asteroid belt between Mars and Jupiter Vesta and Ceres.

Pi is critical to knowing the trajectory and to calculating what direction to point the ion engine, when to use it, and what throttle level to use.

So without knowing the value of pi, we wouldn't be able to determine how to steer the spacecraft to reach these fantastically distant destinations.

Well, we use pi with 16 digits.

To illustrate why that level of accuracy is sufficient, let me give you the most extreme example.

Humankind's most distant spacecraft from Earth is Voyager 1.

It was launched in 1977.

So today

it's a little more than 23 billion kilometers away.

So let's imagine having a circle with a radius of that size.

And now suppose you want to calculate the circumference.

So if we use the value of pi where it's 16 digits, or in other words, rounded to the 15th decimal place, that gives a circumference of about 147 billion kilometers.

But the question is, what is the error in the value of that circumference by our not using more digits of pi?

And it turns out that the error in the circumference is about six millimeters.

And so that says to me, 15 decimal points in pi is quite sufficient.

That is absolutely staggering.

To use a number to 15 decimal places and only be out by six millimeters across interstellar distances.

So, Matt, this, I suppose, is the answer to the question why legislation in Indiana trying to make pi 3.2

would not be a sensible way to proceed.

Yeah, it would be easier, but it would no longer match reality.

So, here's my challenge to you, and you have until the end of the programme to give me an answer to this.

How much would we have missed the moon by if we'd used 3.2 instead of 3.14 when we're in?

How much we missed the moon by?

His eyes widened in fear.

Here's a pen and paper.

Here's the thing, though,

with what Mark was talking about there.

You know, he was essentially saying that to 15 decimal places, it's sufficient.

You can do everything you reasonably need to do to do that.

And yet, Vicky, as a pure mathematician, you care, I mean, pure mathematicians care a lot about the fact that it goes on much further than 15 decimal places.

And, you know, even Adam knew that this was an irrational number.

Can you tell us a bit more about how do you define an irrational number?

So pi is an irrational number.

What does that mean?

It means you can't write it as one whole number divided by another.

So the rational numbers are the fractions.

They're the ratio of one whole number divided by another, like a half and a tenth and 315 millionths and so on.

I've just had a complete revelation.

That's why they're called irrational numbers because it's a ratio.

It's not because they're mad.

Yes.

Oh, you're all nodding at me in a really condescending way.

It does sound like very judgmental use of language that we call numbers rational and irrational.

And given that mathematicians cheerfully talk about imaginary numbers, you'd think we kind of were happy at giving value judgments.

But yeah, rational ratios.

I just witnessed an idiot discovering something.

I think one of his moment.

This reminds me distinctly of a conversation I once had with Adam where he said that he realised that

not all circles were the same

size, but they were all the same shape.

That's a really profound point.

Thank you, Vicki.

She just laughed and 10 years later is still laughing about the same thing.

I thought it was profound as well.

I think you're both right.

Yeah.

Oh, yeah.

There's one of those rare occasions.

But what does it...

Okay, so not being able to be written as a fraction is part of it.

But there's more to say than that.

Yeah, so pi is not only irrational, back to these value judgments and names we give numbers, it's also transcendental.

I mean, that sounds pretty good.

So transcendental means if you take pi and you're allowed to use any whole numbers you like and pi, and you can add, you can subtract, you can multiply and divide, you can't write down an equation involving pi and whole numbers that gives you zero.

So, what that means is it's quite hard to pin down what pi is.

So, the square root of two, for example, is irrational.

You can't write the square root of two as a fraction, but you can write down an equation that

square root of two satisfies, because if you square it and subtract two, you get zero.

So, root two is irrational, but if you like, not quite as out there.

Pi is really out there because it's transcendental.

And I guess that the way that most people would recognize that idea of an irrational number is that after the decimal point, the numbers go on forever and then they never settle into a repeating pattern.

Yeah, exactly.

So that never settling into the repeating pattern is that key thing.

So I guess if we take like a third, we can write that as 0.333 recurring.

So the decimal places kind of go on forever.

It doesn't stop, but there's a nice repeating pattern.

Or you might have a repeating block that's longer than a single digit, but pi never has that.

So, Alex, one of Alex's questions was: how do we know that it's irrational?

Yeah, and the answer is that we have to prove it, and that's probably slightly too fiddly for right now.

But lots of proofs of irrationality of pi, the square root of two, other things use a mathematical technique called proof by contradiction, where you say, well, imagine I can write it as a fraction, and then you kind of see what are the consequences of that.

And it turns out that, like, maths breaks.

So you can prove that pi is irrational.

And maths can never break at all.

Okay, but what about that?

Yeah, I know, I know that it is, it's, it's a number which keeps on going and doesn't repeat, and that's why it's an irrational number.

Is there, have we counted high enough?

Have we gone through enough of the digits to see that a pattern might emerge?

Where, you know, if we go to a billion or a trillion, might it repeat after that?

Yeah, that's a great question.

So, I don't actually know how many digits of pi we know offhand.

I mean, loads.

Ideas.

Oh, Matt knows.

Go.

I would say 50 trillion.

Oh, it's actually 62.8 trillion.

This is

cold news, man.

So it is like a pi fight list, genuinely.

I'm sorry, Vicky.

So, so the problem with the computer thing here is that, okay, so maybe we know 62.whatever trillion digits a pi.

Well, in theory, maybe it's a recurring decimal.

We say it has these repeating blocks, but it doesn't repeat till after that.

So maybe you have a repeating block of 62.8 trillion digits, and then that same block again and again and again forever.

I mean, you don't, because we can prove that you don't, but somehow that's why we need a mathematical proof that you don't.

The computer is never going to tell us that.

Is it actually actually useful to know pi to 62 trillion digits at all?

Does that tell us anything other than that it is an irrational number?

Well, it doesn't tell us that it is an irrational number.

Yes, I was listening to you.

Apart from that, is there a point where, I mean, we've had the NASA engineer saying that after 15 decimal points, it doesn't make a difference over interstellar distances.

But is there any utility in knowing it to a trillion or 60 trillion or whatever?

I'm not aware of anybody who needs to know 62.8 trillion digits of pi.

Maybe Matt does.

You can find your birthday in it?

You can't.

It's not just that you can find your birthday in it, because if you can change, if you can change numbers into text, into letters, there's various ways that you could do it.

Really easy, obvious ways: 0, 1 is A and so on.

You can say that actually there's an infinite string of letters in Pi.

And because it goes on forever and ever and ever, in theory, you should not just be able to find your birthday in it, but you should be able to find your name.

You should be able to find the complete.

What do you think?

Well, only if Pi is a normal number.

I mean, caveat, caveat.

Caveat, caveat.

Oh, I was with you until you said normal number.

If every block of digits is equally likely to come up, then the complete works of Shakespeare will be written in pi.

It's kind of like the infinite monkeys, infinite typewriters' type idea.

And it's an idea that Carl Sagan, the astrophysicist and science fiction author, wrote in his book Contacts, that the alien civilization hid their message and how to get to them, how to contact them in the digits of pi as well.

Well, I mean, if such aliens exist, or if not, as you know, I've mentioned, given that every possible string is within pi, given a couple of caveats, then it's in there.

It's just indistinguishable from all the other infinite number of strings.

Yeah, but you wouldn't know how to find it at all.

I mean, that's the problem with infinity, right?

Sure, it's quite big.

Just to end on, we've talked about some of these concepts and the utility and space travel and the amazingness of discovering pi in all these places.

You wouldn't necessarily see it.

But I want to take it to the next intellectual level, which is the philosophy of pi.

I'm calling it the philosophy pi.

It doesn't really work.

But

let's just go with that.

I spoke to Eleanor Knox, who's a philosopher of physics at King's College London, and she gave us a taste of why numbers like pi can seem so magical.

There's a puzzle in general about why maths applies to the world at all.

Why do these strange objects, these numbers like pi, how do those numbers sort of glom onto the world, kind of catch onto the world, represent it at all?

But there's an even perhaps bigger and deeper one that you get when you get certain kinds of uses of mathematics that seem what Eugene Wigner called unreasonably effective.

So Eugene Wigner started this very famous paper, The Unreasonable Effectiveness of Mathematics, by talking about,

this little sort of vignette where

a statistician mentions that they're using pi and his friend says, oh, you're pulling my leg.

And that's because pi crops up in the most fundamental distribution in all of statistics, which is the Gaussian or normal distribution.

So when you map natural things like population statistics or if you went and measured all the lengths of leaves on a tree and things, you'll very often get

what we call a normal distribution.

It's one of the most natural distributions in statistics ever.

And that distribution is characterized in part by the number pi, which is extraordinary.

So those kinds of uses of pi, where you get all the way away from properties of circles and periodic motion, seem completely miraculous to many people.

And famously to Wigner, who is a very, very famous Nobel Prize-winning physicist.

It seemed completely mysterious that you might have this sort of magic number popping up, not just in the places you'd expect it, but all over the place.

So that does seem almost conspiratorial.

And I don't know if anyone has a really good response to that feeling of mystery that you get from these multiple uses of pi.

It's magic.

Honestly, she's grinning like a Cheshire cat

all the way through this programme.

You know, Galileo Galilei wrote about this and said that

if the universe

was written in a book, the language that it would be written in is mathematics.

And I think that there is...

If you have worked in this area, if you have explored what the world looks like and is shaped like and how it functions using this language, you are in no doubt of the unreasonable effectiveness of mathematics as a a way to describe it and how pie just popped up over and over and over again in unexpected places.

Fortunately, for people who aren't very good at maths, it's actually written in languages, mostly English, Latin, thrown in.

But we've almost run out of time, but I set Matt a maths problem, which was to ask him how far out from hitting the moon we'd be if we used 3.2 instead of 3.14, blah, blah, blah, to 15 decimal places.

And he does have an answer for you, Matt.

It's about 2%

of the moon.

That's pretty cheap.

A lot.

I mean you'd miss it by a few miles.

Yeah.

People would be very upset.

You'd have to fake it instead.

Thank you to our guests Matt Parker and Vicky Neal.

So Dr.

Runford, when it comes to the question of what on earth pi actually is, can we say case solved?

Why, yes, Professor Pi, yes we can.

Pi is the ratio between the diameter and the circumference of every circle.

It's an irrational number, which means that it can't be written as a fraction.

And the pattern of digits after the decimal point goes on forever without repeating.

It's so fundamental to mathematics that pie is essential to engineering at every level from MP3s to interstellar space.

And round pies have been consumed since the time of the engine Greeks.

And that's my joke.

You're not allowed that.

I actually really enjoyed that.

That was, there was, I mean, the revelation about the timing was genuine.

That was a genuine, couldn't quite believe we'd got it to two decimal places, which is all the timer actually does.

I've seen him do that in a room of like

3,000 school kids, and honestly, their jaws like dropped to the floor.

Mine did.

Mine absolutely did.

It's fascinating for a number of reasons, but it's also really interesting for me watching three mathematicians really enjoying themselves.

And also, you get a little bit

sort of almost mystical about the universality of it.

You know, the way it pops up in all these weird places that you didn't expect.

When you get mystical, I'm like, oh, this is interesting.

I never, the thing is, is that I've tried to explain this before, and it's just not something that you can really use words to describe.

It's something that you can only know about if you have tried to

understand the universe using mathematics because that you are left in absolutely no doubt that

you are on this voyage of a path that is not human-made.

I mean, I can't describe it in any better way.

I mean, that is truly fascinating because we know that of all the sciences, mathematics, if we're counting it as a science, is the one that has the highest proportion of religious people in it.

Do we?

We do.

We do worship pie.

And physics is next down the list, and weirdly, genetics and psychology and evolution are the least.

I'm curious about the cause and effect of that.

Is it that religious people like the sort of cleanness of of mathematics or is it that maths makes people religious

i i don't understand different causation and correlation all i know is that every mathematician that has ever tried to work on pie died

or will

or will die at some point sure correct

shall we move on from this pseudo-philosophical absolute nonsense you know that you know that um my twitter handle is like a little pun on pie all math and no trousers No.

You changed it?

No, not

my Twitter handle, not my Twitter bio.

What's your Twitter handle?

Fry R squared.

Oh, I don't think I've ever noticed that in the 10 years would be what I've done.

Have you actually not noticed?

No, I just put a hang on.

Because it's like Pi R squared.

Yeah, I get that, but

that's why I called you Professor Pie

at the end.

There's actually a character in Viz called Professor Pie Face.

I don't care.

Yeah, I know you don't.

Should we do Curie of the Week?

Yeah, go on.

Fast and curious, occasionally spurious,

Now, this letter came into the inbox curious cases at bbc.co.uk, and it came from Isabel, aged 14.

Hannah.

Here we go.

Okay, I am writing to thank you for helping me out with some recent homework for my GCSE English Spoken Language assessment.

Our task was to create a presentation on something we would like to ban from the world.

I chose WASPs.

I

like her.

Then I remembered the episode The Sting in the Tale, so I decided to use it as reference material for my presentation and argument.

I have attached my presentation, and to cut a long story short, I achieved a distinction.

What?

Well done, Isabel.

Thank you again for your help.

I'm looking forward to hearing new episodes in the future.

Do I have veto over this?

Because we got the presentation.

This is in reference to the episode Sting in the Tail, which is what is the point of WASPs.

And I was very much Team Wasp and you were very much Team B.

And we had the amazing Serian Sumner on, who's written a book called Endless Forms and is the great WASP defender.

But let's have a look at what Isabel's presentation looks like.

It's called Why We Should Get Rid of Wasps.

First of all, the thing that hits me straight away is that she's gone for a very clean presentation style and I and I like it a lot.

She's got a crisp white background.

She's got images left and right of wasps actually looking pretty dashing.

Absolutely.

We've got what I think is a yellow jacket on the right with its very pinched waist, which I think is a feat of evolutionary engineering.

I think it's just emphasizing what a jerk it is.

What a stripey jerk, I believe we called them.

So, slide one, why I don't like wasps.

Oh, she's punchy, isn't she?

Wasps, full stop.

Don't look nice, ruin picnics, make summer horrible, eat your food.

I mean, what more do you want?

She says wasps are probably the most pointless insect in existence.

I mean, apart from the fact that they actually have a literal point on them, we spent the whole of that programme saying why they weren't pointless.

Hold on, next slide.

Professor Hannah Fry said every year around 10 people are killed by anaphylactic response to bee and wasp stings in the UK.

And around twice as many of these come from reactions to wasps as opposed to bees.

I mean, this is a slam dunk, as far as I'm concerned.

She cites, Isabel cites Serian Sumner on the programme who says that wasps are the evolutionary root of all bees and ants.

But Isabel's conclusion is: so, although they're very annoying, without them, we wouldn't have bees who pollinate plants for us.

The whole point of what Serian was saying is that wasps do more pollination than bees.

Look, let's go to the final slide.

To summarise, these 240 million-year-old insects are small, irritating, and hostile insects.

And then on the right-hand side, in a little splash, uh

splash speech bubble, she's just got killed them all, Professor Hannah Fry.

You know what?

Not only did you get a distinction from your teacher, you get a distinction from me and a Curie of the Wheat badge.

Well, you can have the Curie of the Wheat badge, you get an absolute fail from me.

Just because you're back at UCL as a lecturer now, Adam.

Anyway, join us next week for Curious Cases.

Send us in your questions, your coursework, and we'll grade them.

Anything else you want to send in?

Curiouscases at bbc.co.uk.

See you next week.

What makes you feel physically and mentally stronger?

The act of skating?

That's my zen.

That's my relaxation time.

That is the question I ask guests on my podcast to discover their secrets to health and happiness.

I see going to bed at the right time as an investment in tomorrow rather than a sacrifice for today.

We'll get inspiration from their achievements and find out how they take care of their physical and mental health.

I think it is really important for us to reflect on what have we missed, you know.

The new series of the Joe X podcast from BBC Radio 4.

Subscribe now on BBC Sounds.

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