Magic Numbers: Hannah Fry's Mysterious World of Maths

- There is a mystery at the heart of our universe.

A puzzle that, so far, no one has been able to solve.

I can't, it's too weird!

Welcome to my world! (laughs)

If we can solve this mystery,

it will have profound consequences

for all of us.

That mystery is why mathematical rules and patterns

seem to infiltrate pretty much everything

in the world around us.

Many people have, in fact, described maths

as the underlying language of the universe.

But how did it get there?

Even after thousands of years,

this question causes controversy.

We still can't agree on what maths actually is

or where it comes from.

Is it something that's invented like a language?

Or is it something that we've merely discovered?

I think discovered.

Invented.

It's both.

(laughs) I have no idea.

Oh my God!

Why does any of this matter?

Well, maths underpins just about everything

in our modern world, from computers and mobile phones

to our understanding of human biology

and our place in the universe.

My name is Hannah Fry, and I'm a mathematician.

In this series, I will explore

how the greatest thinkers in history

have tried to explain the origins

of maths' extraordinary power.

You ruined his equation!

I'm going to look at how, in ancient times,

our ancestors thought maths was a gift from the gods.

How, in the 17th and 18th centuries,

we invented new mathematical systems

and used them to create the scientific

and industrial revolutions.

And I'll reveal how, in the 20th and 21st centuries,

radical new theories are forcing us to question, once again,

everything we thought we knew about maths and the universe.

The unexpected should be expected

because why would reality down there

bear any resemblance to reality up here?

In this episode, I go back to the time

of the Ancient Greeks to find out

where our fascination with numbers started.

You know I think I can

hear the neighborhood cats screeching.

And reveal why we're now looking

for maths deep inside our brains.

Our world is full of maths, often in unusual places

like this roller-coaster.

The thrill and excitement of this ride wouldn't be possible

without physics and engineering.

And at the heart of all of that science (laughs)

is mathematics.

Oh, my God!

It's sobering to think how much

we entrust our personal safety to maths

without even realizing it.

My rush of adrenaline relies on someone's calculations

of kinetic energy, momentum, tensile strengths,

coefficients of friction, and much, much more.

Oh, my God!

What do you make me do? (laughs)

To put it bluntly, the modern world

wouldn't exist without mathematics.

It is hiding behind almost everything that's around us

and subtly influencing almost everything that we now do.

And, yet, it's invisible.

It's intangible.

So, where does mathematics comes from?

Where do numbers live?

It's a question that goes to the very heart of our world.

We often think about numbers as something tied to objects,

like the number of fingers on one hand

or the number of petals on a flower.

This flower has got eight petals.

If I take three away, then it will be left with just five.

And it will look a lot less pretty.

The petals are gone, but the number three still exists.

The idea of three, or any other number for that matter,

is still out there, even if we destroy the physical object.

But you can't say that about everything.

If pencils had never been invented,

then the idea of a pencil wouldn't exist.

But the idea of numbers would still exist.

In every culture around the world,

we all agree on what the concept of fourness is like.

And it doesn't matter whether it's called four,

or even what the symbol looks like.

With numbers, I can destroy the physical object,

burn it to a crisp, but I can't destroy the idea of numbers.

So, here's the question I want to answer,

is it invented or discovered?

Is there some magical parallel world somewhere

where all mathematics lives?

A place where you have fundamental truths

that help us to understand rules of science,

helping us put man on the moon

and to study the tiniest particles of the universe?

Or, is maths all in our minds?

Is it just a figment of our imagination and intellect?

Whether maths is invented or discovered

is something we can't agree on.

It's just too extraordinary to think that

the mathematical truths in everything

are a sort of product entirely

of our conventions in the human mind.

I don't think we're that inventive. (laughs)

- It sometimes feels like mathematics is discovered,

especially when the work is going really well and it feels

like the equations are driving you forwards.

But then you take a step back,

and you realize that it's the human brain

that's imposing these ideas,

these patterns, on the world and from that perspective,

it feels like mathematics is something that comes from us.

The number five is called

in Swedish, my mother tongue.

That part we invent, the baggage, the description,

the language of mathematics.

But the structure itself, like the number five and the fact

that it's two plus three, that's the part that we discover.

- There's virtually no part of our existence

that isn't touched by maths.

So, if it is discovered, part of the fabric of the universe,

how can we unlock its secrets?

And if it's invented and all in our heads,

how far can our inventive brains take us?

I want to start with the discovered camp, those who say,

"Maths is all around us.

"You just need to know where to look."

Of all of the structures that you get in nature,

I think one of the most beautiful is the nautilus shell.

There's a little creature that lives

inside here and creates all these shapes,

and it hops from one chamber to the next as it grows.

And this shell is just incredibly intricate,

and you might wonder how something so small

can create something quite so remarkable.

But, actually, there is a hidden pattern in here

that you can start to see when you measure these chambers.

So, that one is coming out at 14.5 millimeters.

And this one,

on the same axis, is

46.7.

I'm measuring how wide the shell

would have been as the nautilus grew.

I pick an angle and measure the inner chamber,

and then a second measurement to the outer rim.

99.5.

I do this three times for three different angles

until I have three sets of numbers.

When you look at them, I mean,

they look pretty random, right?

It looks like there's no connection between them at all.

But looks can be deceptive,

because if you take each of these pairs of numbers

and divide one by the other,

a very clear pattern starts to emerge.

So here, if we do this number divided by this,

we get 3.22.

This number divided by this one gives 3.25, I think.

Sorry, my mental arithmetic isn't great!

And this number divided by this number

then gives 3.24.

And suddenly, the same number starts to appear,

around about 3.2-ish.

It doesn't matter where on the shell you measure,

the ratio of the width of these chambers ends up

being pretty much constant throughout the shell.

I've got it right to one decimal place.

Not bad.

That'll be down to my measuring skills

rather than the nautilus.

What all of this means is that the nautilus

is growing its shell at a constant rate.

So every time it does a complete turn, it ends up sitting

in a chamber that is around about 3.2 times the width

of the turn before.

And by repeating this very, very simple mathematical rule,

it can create this beautifully intricate spiralled shell.

Clever old nautilus!

The nautilus isn't the only living thing

that has a mathematical pattern hidden inside it.

If you've ever counted the petals on a flower,

you might have noticed something unusual.

Some have three petals.

Some five.

Some eight.

Some 13.

But rarely any of the numbers in between.

These numbers crop up time and time again.

They seem random, but they're all part of what's called

the Fibonacci sequence.