There.
Is a mystery at the heart of our universe a.
Puzzle.
That so far no one has been able to solve it.
Can be weird welcome.
To the world.
If.
We can solve this mystery it will have profound consequences for.
All of us and.
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 have merely discovered.
I think discovered.
Invented.
It's both I have no idea.
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 Hanna Frey 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.
Human.
Dissipation.
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 rollercoaster.
This.
Ride wouldn't.
Be possible without physics and engineering and at the heart of all of that science.
It's.
Math master oh my god.
It's sobering to think how much we entrust our personal safety to matter.
Without even realizing it.
My rush of adrenaline relies.
On someone's.
Calculations.
Of kinetic energy momentum.
Tensor.
Strengths coefficients.
Of friction and much much more.
Do.
You make me do.
So.
Pretty bluntly the modern world wouldn't exist without mathematics he.
Is hiding behind almost.
Everything that's around us and subtly.
Imprinting almost everything.
That we now do and.
Yet it's.
Invisible it's intangible.
Where does mathematics come.
From where.
Des numbers live.
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.
Flower has.
Got eight petals if.
I take three away then.
It will be left with.
Just five I.
Don't.
Look a lot less pretty the.
Petals are gone but.
The number three still.
Exists.
Idea of three or any other number for that matter is still out there even.
If we destroy the physical object.
You can't say that about everything.
Pencils.
Had.
Never been invented then the idea of a pencil wouldn't exist.
The idea of numbers would still exist.
Every culture around the world we all agree on what the concept of Faunus is like and.
It doesn't matter whether it's called for cat fur fear.
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.
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 the 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.
Where.
The maths is invented.
Or discovered is.
Something we can't agree on.
Just too extraordinary to think that the.
Mathematical truths and everything is sort of product entirely of our conventions.
And the human mind and that's I don't think we're that inventive.
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 a 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 FEM and 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 only think one of the most beautiful is the nautilus shell so.
There's a little creature that.
Lives inside a and creates all these shapes and 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.
That one is coming out at.
Fourteen.
Point five.
And.
This one.
On.
The same axis is.
46.7.
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.
Ninety.
Nine point 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 looks like there's no connection between them at all but.
Looks can be deceptive because.
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 3.2.
- this number divided by this one gives.
3.25.
I think sorry I meant arithmetic isn't great I.
Think this number divided by this number then gives.
3.24.
Suddenly.
Same number starts to appear around about 3.2.
Ish 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 show I've.
Got it right to one decimal place.
Bad that.
Will 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 three point two times the width of the turn before and.
By repeating this very very simple mathematical rule it can create this beautifully.
Intricate spiraled.
Shell.
Clever.
Author lists.
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 may.
Seem random but.
They're all part of what's called the Fibonacci sequence.
Start with the numbers 1 & 1 and from that point do you keep adding up at the last two numbers so.
One on one is - 1.
+ 2 is 3.
2.
+ 3 is 5 and so on.
When.
Looking at the number of petals in a flower these.
Numbers from the Fibonacci sequence keep appearing.
That's just the start.
You look at the head of a sunflower you'll.
See the seeds are arranged in a spiraling pattern.
Count.
The number of spirals in one direction and you will often find a Fibonacci number.
Then.
If you count the spirals going in the opposite direction you'll.
Hit upon an adjacent.
Fibonacci number.
Do plants do this well.
It turns out that this is the best way for the flower to space out its seeds so they don't get damaged.
We.
Find these spirals so intriguing we've.
Worked hard to unlock their secrets.
We've.
Gotten very good at copying.
The patterns that we find in nature and using them to create things of great beauty like.
This majestic.
Stair.
Simple.
Glorious.
Mathematical.
Rules found.
Hidden in nature doesn't.
Seem to me like a coincidence.
These mathematical patterns once you spot them do feel discovered.
As if the maths is already out there I'm just waiting for you to find it.
Fascination for finding hidden mathematical patterns is nothing new.
Go back over 2,000.
Years to the time of the ancient Greeks and you will find the philosopher Pythagoras and.
His followers were.
Just as enthralled by the patterns they discovered.
Pythagorean's.
Were obsessed.
With numbers.
They were people who believed that numbers were a gift from God and part of their fascination might.
Have been thanks to their experiments.
With music.
Discovered patterns that linked the sound of beautiful music to the length of a vibrating string.
They believed was no accident but.
A window into God's worlds that had been gifted to the pythagorean's.
Mathematician.
And musician Ben sparks is fascinated.
By this age-old relationship.
Between music and maths.
Thank.
You for joining us on our with your beautiful cello there okay then you are you're.
Gonna have to explain this to me where.
Does the math come in in making this instrument sound nice the.
Wobbling is what's giving you the sound and if you make the string wobble you hear a sound so maybe you could.
Play your D string.
Oh sounds.
Lovely sounds lovely doesn't it and what they also notice is another no really related to that which is making if you.
Make it wobble twice as fast and to.
Do that you.
Can make the string half the length okay.
So you're putting your thing here why I guess pretty.
Much is that not hard way along okay.
What's.
Weird about these two noses they they sound kind of the same but they're definitely different and this is where the Greeks.
Notice they we call it an octave but if you play them together does it sound nice.
Delightfully.
Pleasant.
The octave the length of the vibrating string creates a relationship or ratio of two to one so.
That's if you chop it in half are there other fractions.
That make it sound nice well exactly what the Greeks were thinking is like what can we find other notes that sound.
Even nicer to get a more interesting together can you play us this is what they call a perfect fifth.
Happens when you play those two together there.
Very.
Pleasant the first we're about to launch into a jig yeah in a perfect fifth the ratio of the vibrating string is.
Three to two the.
High note is two thirds of the length of the low note.
Happens when you play a note that isn't one of these neat fractions when.
Notes aren't in these nice simple ratios we tend to notice that even if we're not aware of the mathematics right I.
Mean can you play a sort of really horrible harmony together maybe like a semitone apart.
The strings are not in a simple ratio the harmony sounds distinctly unpleasant.
Greeks were obsessed with having simple ratios describing the notes so they get nice harmonious noises how does this work for other.
Instruments I mean this is very clear you've got this this sort of string here but what about and I don't know.
Like the human voice right well every noisy over here is things wobbling somehow whether it's your vocal cords or.
A string or my vocal cords.
Really have you never used your vocal cords for a bit of music can we try oh I'm.
Such a fine singer please don't make me do this okay you got your earplugs in yeah.
Let's.
Try can you picture some note I mean there's something nice and low if you just do it to LA then now.
I've got a choice.
Just.
Like the cello it's the length of mine and Ben's vocal chords that's changing the pitch of these notes.
That was me singing a perfect fifth carats.
If I know love.
Know I think I can hear the neighborhood cats screeching so I think that's enough of that.
Patterns convinced the ancient Greeks that they'd been gifted a glimpse into this godly young why.
Else would these patterns exist.
Pythagoras.
And his followers were in little doubt the.
Maths was.
Just as real as the music was and it was even neater and more elegant than anything the human mind could conceive.
Were by no means the first people to use some form of maths there's.
Some evidence that marks found cut into bones from the Upper Paleolithic.
Era.
37,000.
Years ago we're tally marks used for counting.
It was the pythagorean's.
Who were the first to look for patterns.
Does feel to me as if maths is all around us and something we discover a fundamental.
Part of the world we live in and yet somehow very.
Strangely.
Separate from it.
Trying.
To make sense of this apparent paradox is.
At the heart of this battle about where maths really.
Lives.
Philosopher Plato is.
One of the most important.
Figures of the ancient Greek world but.
What he said about the origins of maths is still.
The basis for what many mathematicians.
Believe today.
He was fascinated by the geometric.
Shapes that could be produced by following the rules of mathematics.
Rules.
That he believed came from God.
I try and draw a circle really really carefully.
Takes.
Me back to my school days this.
Now.
Not doing bad.
That's.
Pretty good but if you look really closely.
Just not quite perfect to the circle but I'm not gonna beat myself up about this because even if I had access.
To the.
Most accurate computer in the world the.
Circle that it would draw still wouldn't be perfect.
Zoom.
In close enough and any physical circle will have bumps and imperfections that's because according to Plato flawless.
Circles don't exist in the real world he.
Believed the perfect circle lives in a divine world of perfect shapes a kind of mathematical.
Heaven where all of maths can be found but only if you're a true believer.
He was convinced that everything.
In the cosmos could be represented by five solid objects known as the platonic solids.
Say.
The earth was the rock solid cue.
Fire.
Was the very pointy tetrahedron.
And then.
With eight triangular.
Sides air was.
The octahedron.
While.
The icosahedron there.
Was twenty triangular sides represented water.
Lance brittonic Sollers the dodecahedron this.
One was supposed to encapsulate the entire universe.
It's the whole universe sitting any more hands there it's kind of a neat idea.
There's.
Something special about the Platonic solids they're.
The only objects where every side is the same shape and there are only five try.
As you might you will never find another object with.
These unique mathematical.
Qualities.
All.
Of these shapes Plato believed existed.
In a world of perfect.
Shapes beyond.
The reach of us mere mortals a.
Place.
We call the Platonic.
World I know.
That these ideas might seem like they're a bit bonkers but.
There are actually quite a few people who believe them and those people come across as though they're sane.
Third favorite favorite mathematical.
Structure.
Octahedron.
AHA.
Platonic solids I presume.
A very heated I love dodecahedra I have a misspent youth making models.
Of polyhedra oh my goodness.
Are the Platonic solids Oh.
Guys.
Okay.
Very beautiful you.
Know at 67 mrs. Christmas can.
I keep these two please.
Platonic solids to me are a great example of how mathematics.
Is discovered.
Rather than invented when ancient Greeks discovered that this one existed they were free to invent the name of it they.
Called it the dodecahedron.
But the pure double key he drew himself it.
Was always out there to be discovered I have this kind of platonic view that there are triangles out there there are.
Numbers there are these circles that I'm seeking to understand so for me they feel like quite tangible things they're all part.
Of this mathematical landscape that I'm exploring.
Not everyone believes in this platonic world of mathematical.
Truths I think.
That the platonic world is in.
The human head it's a figment of imaginations.
I get that that there are people who really buy into this other realm of reality and.
Especially if your days and nights are spent thinking about and investigating and researching this.
Realm that doesn't mean that it's real.
Plato.
Would have strongly disagreed he.
Encouraged us to believe in this other world where.
All of maths could be found and.
Not to be fooled into thinking the world around us is all there is.
We perceive.
As reality he.
Cautioned is no.
More than shadows cast on the walls of a cave.
Had a very lively of.
Quite dark imagination.
To explain what he meant he came up with an analogy of a group of humans locked in a cave these.
People would have been imprisoned since childhood and they were shackled by their necks and their legs entrapped.
Staring.
A blank wall directly in front of them.
His mind's eye Plato pictured.
A fire burning.
High above the prisoners heads.
They have no idea it's.
Top of the wall is a path along.
Which all manner of people and objects are traveling.
The only thing the prisoners can see of them is the shadows they cast down.
The wall those.
Shadows are.
The prisoners reality.
According.
To Plato we.
Are no different to the prisoners in the cave who mistake the shadows for reality.
Plato is right what.
Does this mean for you and me is what.
We think of as reality and.
Maths just.
An illusion.
Are.
We living in Plato's cave and.
And just see see shadows it.
Is not impossible that.
That is the case you know we are maybe just all we're just some simulation.
Some world.
Of some more intelligent being this is all possible I mean if you think that there's some world.
Of mathematical objects it's different from ours it's not the physical world we live in but that doesn't make the physical world.
Any less real.
I don't think that there's anything to me in philosophy of maths that would force you to think that our world is.
An illusion of any kind our senses.
Evolved.
Really for one purpose survival.
Survival and the true nature of reality are two different subjects so the.
Fact that we have been able to survive by thinking about the world one way does not in any way say that.
That way of thinking about the world is truly what's happening out there.
Over.
2,000.
Years ago Plato took the geometry of shapes as evidence of God's influence.
Ideas.
That were limited to the senses and imagination.
Today.
Geometry.
Is at the cutting edge of science new.
Technologies have allowed us to look at the world beyond our senses and.
Once again it.
Seems the natural world really is written in the language of maths.
Is a model of a virus straight away you notice it's geometric shape.
Would have recognized this shape as one of the Platonic solids.
There's one person who understands geometry it's a mathematician.
Ride.
Into a rock is a professor of mathematics at the University.
Of York.
She's.
Trying to work out how viruses use maths to form their geometric shapes if.
You know that you.
Can find a way to stop them.
Why ridin and her colleagues have designed a computer simulation.
That puts the mathematician.
At the heart of the virus but.
We try to understand is how this.
Virus forms and.
Taught her to do that we will create the illusion of being inside of the virus in the position.
Where the genetic material normally is Ryden.
Has discovered that the virus harness is the power of maths to.
Build its shell in the quickest and most efficient.
Way possible.
Armed.
With this knowledge she's.
Trying to find a way to stop the viruses such as hepatitis B.
And even.
The common cold from developing in the first place.
Once.
You understand how this mechanism works you.
Can turn tables on viruses and actually prevent that process.
That.
Is what makes this research so exciting.
You know the mathematics of how the virus forms.
Its shell you can work out the way to disrupt it no.
Shell no.
Virus no infection.
Mathematicians.
Like rydym are joining.
The front line in the fight against disease.
Far.
Beyond the realm of human senses it really does seem like the universe somehow.
Knows maths.
Really is amazing how often these patterns seem to crop up there in plants there in marine life there.
Even in viruses.
Really is an awful lot that we can explore.
And exploit using the mathematics that we have.
Does lend weight to the idea that there is some natural order.
Underpinning.
The world around us.
Far it does feel like the idea that maths is discovered is leading the charge but perhaps we've been looking for patterns.
In the wrong places if.
It's all in our heads then the brain feels like a good place to look is.
There evidence in there of maths being an invention of the human mind.
I've.
Got a real treat in store for me today I am heading over to UCL the University of Iowa cap where some.
Colleagues are going to scan my brain and.
See which bits of it are working whenever I do mathematics.
Neuroscientist.
Professor Fred dick is going to place me inside an fMRI scanner.
He'll.
Measure my brain activity by tracking where the blood flows when.
I'm answering questions ranging.
From language to maths.
My brain treats the mathematical.
Problems in the same way as any other problem then it suggests there's nothing special about maths.
The same as any other language a clue perhaps that.
It's an invention.
I'll have ten seconds to think about each question I don't need to answer out loud I just have to work out.
The answer in my head.
Hello how is that.
Well.
We didn't want you to relax in there really I've.
Answered all the questions to the best of my ability after a few hours of processing professor.
Sophie Scott has my results it's not my brain that's your brain let.
Me make sure I understand what I'm seeing it okay so this is like you've cut my brain in half yes and.
I've got the left hand side there yes and the right hand size is that so it's like you've chopped.
My head down the middle and then split.
It out exactly.
What you can see here Hannah is the pattern of activity in your brain and you're hearing the straightfoward language and here.
You can see in the left hemisphere very.
Classic language areas activated.
Bright yellow areas are where there's increased blood flow an indication.
That the neurons in the left hand side of my brain are working.
Harder.
This is a side of the brain that we know is linked to language.
Compare.
That to the right hand side of my brain where there's hardly any yellow areas which.
Means there's far less activity.
Taking place.
Can we see maths please Oh hold on.
Time when I'm thinking about maths.
There are yellow areas in the right-hand side of my brain.
Is very different to the lack of activity seen when I was thinking about language.
Scans reveal there seems to be a place in our brains where.
Maths lives.
We're definitely able to say is this is not just the meanings of the words that you were reading we're not just.
Looking at you thinking about the meaning of words you're seeing something that does seem to be qualitatively.
Different for the maths maths is real this is real at least in my head.
At.
A what really.
Struck me about that conversation and safe it is then it's.
Doesn't matter whether you're doing two.
Plus two equals four or.
Whether you're answering these much higher level math questions.
The same bit of your brain that's doing the grunt work it's not the same thing that does words or language.
You're seeing these problems and you're.
Manipulating.
Them in your mind.
Research.
With similar experiments shows it's broadly the same for all of us in your.
Brain and mine there.
Is a specific place where we do maths.
But this doesn't prove that maths is something we discover it.
Could still be an invention just.
One that we learn at school.
To.
Get to the bottom of this question I need some volunteers who've never had a math lesson in their lives.
Dr.
Sam wass is an experimental psychologist.
At the University of East London helping.
Him with some experiments are six months old IRA and Leo who's just under a year.
Begin with each child is placed in a room where they're shown a series of images.
Sam.
Uses a battery of tests to analyze how they react to different situations.
First experiment.
Uses eye tracking technology.
To see how the baby follows the movement of a piggy puppet is that good so here we can see a feed.
Out of what the child is looking at and those two red dots are where the baby is looking.
We're presenting is a puppet that jumps up and then disappears and it jumps up and disappears two times in a row.
And then it stops we.
Present the same sequence again and again and as the baby watches it again and again they're looking times the amount of.
Attention that they're paying to the screen diminishes and that tells us that the Trotters to learn this sequence now.
Instead of popping up twice as expected the.
Puppet appears.
Three times.
Does.
The child notice the difference between the tunas of it popping up twice in a row and the three nests of it.
Popping up three times and if it does then that tells us that the child understands the difference between two and three.
Tests reveal that the child is surprised when the puppet appears more often.
Larger scale experiments were carried out by researchers in the US the.
Results are did the infants do have a sense of quantity.
This research is really important because it's suggested that even infants as young as five months old can do the basics of.
Addition and subtraction they know the difference between one plus one equals two and one plus one equals one which is an.
Incorrect conclusion and that there was a really really strong.
Provocative.
Finding yeah this idea that the concept of mathematics and the basics of mathematics rules might be hardwired my DNA in our.
Genetic code this.
Research isn't conclusive.
But it does suggest we all come pre-programmed.
To do maths some.
Argue that we evolved this maths part of our brains to.
Discover the world of mathematical.
Truths.
Evidence for maths being discovered is compelling.
We found patterns in nature the.
Latest technology has uncovered startling.
Patterns in viruses and scans.
Reveal there's a part of our brains where maths lives.
This question is too important to leave the evidence here and move on if.
It is discovered if it lives in this other world.
Can.
We trust what it's telling us.
How.
Do we know that our idea of numbers is right how do we know someone isn't just gonna come along at some.
Point and say well actually you've.
Got that completely wrong and one plus one doesn't equal two after.
All how.
Do we know we.
Can rely on the maths that we take for granted.
You need to be sure of is your foundations.
If they're shaky then all of your carefully constructed ideas come crashing down and.
There was one mathematician who understood this only too well his.
Name was Euclid.
Around.
300.
BC in Alexandria he wrote one of the most famous and important.
Books of all time the.
Elements.
He.
Was trying to go right back to the beginning to find the smallest elements.
On which you can build the vast gigantic.
Structure of mathematics if you have a little flip through you can see the kind of things that you cleared was considering.
So here it says that you can draw a straight line between any two points which.
It's blindingly obvious and.
Here it says that all right angles are the same and.
These are quite simple concepts but I think that they really illustrate just how exhaustive.
Euclid.
Had to be to build the foundations for what was to come.
Took statements like these which mathematicians.
Assumed were true and put them to the test he then set out to prove a whole host of other theories based.
On these fundamental.
Building blocks.
Was really the first time that someone had written down formal.
Proofs for.
Assumptions now.
Mathematical proof isn't like scientific.
Proof or proof in a court of law there's.
No room for reasonable.
Doubt here instead.
If something is true mathematically.
Once then it is true forever and that is why this book is so important.
The reason why Euclid's elements is still relevant today.
Every.
Page within it is as true now as it ever was.
And from that point of view it really does feel like we're tapping into a world that already exists.
One that is just out there waiting to be discovered.
Unless.
Of course you throw a spanner in the works change.
The language of maths and invent.
A better way of doing things suddenly.
This rock-solid world of god-given truths might feel decidedly shaky.
One.
Thing we know about languages is that they never stand still they're.
Constantly evolving to meet the challenges of a changing world.
Forty-nine.
Wien.
Go for another tricky one for centuries.
Language of mass was thought to be fixed and unchangeable.
Is until.
Something was found to be missing.
Most.
Exactly is zero.
Zero.
Means nothing if you've got zero.
Flowers.
You've got no flowers and if.
You guys zero stop.
Or something you've got nothing so you can't really do anything with the zero I don't.
Really use it when I'm counting in numbers.
Before.
The seventh century neither did anyone else though.
People have always understood the concept of having nothing the.
Concept of zero is relatively.
New.
We had numbers and could count but zero didn't.
Exist.
You think about it for long enough zero.
Is actually quite a strange concept.
Almost as though the absence of anything.
Becomes.
Something.
It just a number or only dear and.
How can something with no value have quite so much power.
Not exactly clear who first thought of zero it might have originated in China or India what.
We do know is that zero arrived in Europe from the Middle East at about the same time as the Christian Crusades.
Against Islam when.
Ideas coming out of the Arab world were often met with suspicions.
West already had a numerical system Roman.
Numerals they did the job but.
Were a bit unwieldy.
For.
Example the number 1958.
Is written as mcm-l.
VIII.
No matter where you place say the letter C it will always represent the number 100.
Was good for its time but.
Times change and a better system was needed.
Was different where you place zero could change the values of the numbers around it think.
Of the difference between eleven and a hundred and one.
Although the concept of zero might have been created elsewhere it.
Was in India that zero started.
To be accepted as a proper number.
Is a page from the Indian back Shawnee manuscripts from around AD.
225.
Which.
Shows the dots above the characters representing.
Zero this.
Is the earliest.
Known use of the symbol zero that we know today.
Almost a thousand years Indian.
Mathematicians worked happily with zero while their Western counterparts piled.
On with the Roman numerals that was until Italian mathematician Fibonacci.
Recognized.
Its potential.
He'd been educated in North Africa so he'd seen this number system working firsthand.
Is a placeholder signifying.
The absence of a value a zero is also a number in its own right it allowed you to write down numbers.
And manipulate them much more quickly and easily than Roman numerals.
Realizing.
All this Fibonacci.
Champions.
The new number and brought it to the attention of Western Europe.
Wasn't something that we discovered.
It so much as something that was created as part of a new language to describe numbers.
And that's not to say isn't useful the.
Whole of modern technology is literally built on ones and zeros but.
Suddenly maths feels like something we've come up with something.
We've invented.
Needed a more user-friendly.
Numerical.
System so someone came up with the clever idea of zero not.
A gift from the gods but.
A smart way to make counting more convenient.
Is intriguing evidence that maths might be invented.
After all a product.
Of our intellect and imagination.
The idea of zero had been widely accepted mathematicians.
Could relax all conceivable numbers lay out on a single line with no holes and no gaps to speak of over here.
You have the positive numbers one sheep two donkeys.
The kind of stuff you find in real life and in.
The other direction all the negative numbers it's.
A bit trickier to imagine what negative one sheep looks like.
Number line stretches out in both directions all the way to infinity and zero.
Sits proudly in the middle everything.
Was well in numberland or was it this.
Is where it all starts to get a bit strange because.
There are some numbers that.
Are simply weird.
Are some fundamental.
Rules of maths that you learned at school two.
Times two equals four.
Three.
Times three equals nine a.
Positive.
Number multiplied.
By itself equals.
Another.
Positive number nothing.
Controversial so far.
Curiously.
A negative number multiplied by itself also gives a positive number.
Is that well.
This is not a math lecture so.
Let's just accept it as a fact and move on in.
Fact if you take any number and multiply it by itself square.
It then the answer is always going to be positive.
Plus two squared gives me plus four and.
Minus.
Two squared gives.
Me plus four what.
Do I have to square to get minus four but.
It's a question without an answer there.
Is no number that when multiplied by itself gives a negative answer that.
Is unless.
You invent your own meat.
I a number.
We simply made up.
Not.
Everyone was keying it became known as an imaginary number a deliberately chosen derogatory.
Term to.
Scoff at its existence.
Turns out AI is really.
Useful especially when it comes to simplifying problems with things like electricity or wireless technologies things that otherwise would seem impossible to.
Solve essentially.
If you're working with waves you will use I.
Imaginary.
Number broke all the rules it.
Didn't come from this world of ethereal numbers it wasn't god-given.
Was very definitely.
If you can have one imaginary.
Number why can't you have two or three or.
Infinitely.
Many of them why.
Can't you have negative imaginary numbers as well why can't in fact imaginary.
Numbers have their very own number line exactly.
The same as the real one just on a different axis.
Number line isn't a single line at all.
Numbers.
Two-dimensional.
Might think this all sounds are beached airy-fairy the.
Imaginary numbers that we just made up but.
If you've ever flown in an aircraft you've already trucks.
They're your life to these strange numbers.
Airports.
Air traffic controllers here rely on radar to keep everything moving safely.
And quickly.
You can busy definitely.
Need Raider so the busier the tower the busier the operation you need radar radar.
Works by sending out radio waves and examining that part of the signal that's reflected back the.
Complex equations.
That allow us to filter out the correct signal from other conflicting.
Frequencies is heavily.
Dependent on imaginary.
Numbers in.
This case separating.
Out moving objects like planes from flocks of birds or stationary.
Objects.
Numbers are a very.
Efficient.
Tool to be able to manipulate radio waves.
Numbers are fundamental develop eration imaginary.
Numbers allow us to track planes in real time without.
Them we never would have been able to use radar in our skies.
Did.
You know folks father nice try dad they just told you to text you a Papa.
I started this investigation going.
Back to the time of the ancient Greeks it.
Did seem like maths.
Could only be discovered there were too many coincidences too.
Many mathematical.
Patterns popping up all over the place but.
If we can invent the rules creates.
New numbers and they work then.
Perhaps I've got it wrong maybe.
Maths is invented after all.
Concept of zero or negative numbers or complex numbers or imaginary numbers they.
Caused great consternation to.
The cultures that first invented or encountered.
Them there are some conjectures that zero.
Came because someone.
Constructing notice that as you dig a piece of earth out to make a hole there's.
Something an indication that there that should have a name zero.
Kind of maybe came from that observation.
Power of mathematics lies in the way its language and symbols have allowed us to manipulate the.
World but.
This was a world that followed the rules of God and the church by.
The 17th century a new breed of intellectual.
Was emerging not afraid to challenge authority.
Was one man who dared to question all of the philosophical and scientific assumptions that had gone before this.
Was someone who was trying to promote a new way of thinking using.
Reason.
Experimentation.
And observation this.
Was the young Frenchman called Rene Descartes.
Was while in a restless sleep in 1619.
That Descartes experienced a series of dreams that would change his life and.
First two could be better described as nightmares.
The third dream the third dream was intriguing.
As.
His.
Eyes scanned the room he saw books on the bedroom table it appeared.
And then disappeared.
Opened one book of poems and at random cost the opening line of one which read what.
Road shall I kiss you in life.
Someone appeared out of thin air and recited another verse saying simply what.
Is and is.
Dreams it's all about the interpretation you place upon them in.
Descartes case the effect of these dreams was profound.
Was convinced that the dreams were pointing him in a single direction bringing.
Together the whole of human knowledge by.
The means of reason.
Was nothing if not ambitious.
But his genius led to perhaps one of the greatest advances.
Ever in the field of mathematics as.
With so many brilliant ideas it was deceptively.
Say that I'm meeting a friend for a coffee now I'm standing at the end of ensley gardens and they are somewhere.
Over on Gordon Street it's.
Very easy for me to work out how to get there all I need to do is go on a map and.
Check the route in.
This case three streets down and one alone.
Sinan's like an incredibly simple idea.
Actually.
Revolutionized.
He showed that a pair of numbers can uniquely determine.
The position of a point in space it.
Sounds trivial but this was just the start it.
Gets more interesting when.
You apply this idea to curves.
As this point moves around a circle its coordinates.
Change and.
We can write down an equation that precisely.
And uniquely.
Characterizes.
This circle.
The first time shapes.
Could be described by a formula.
By.
Uniting the language of numbers and equations.
And symbols with shapes Descartes.
Was able to expand the horizons of mathematics.
Thus laying the foundations for the modern scientific.
World.
Descartes and the other trailblazers.
Like him do was.
To question accepted.
Wisdom at the time they.
Thought differently and the result was that they delivered monumental.
Breakthroughs for our understanding of the universe.
Descartes.
Lived in a time when many philosophers backed up their arguments with appeals to God but.
Descartes preferred to place his trust in the power of human logic and maths he.
Believed all ideas should have their foundations.
In experience.
And reason.
Rather.
Than.
Tradition and authority.
Still feels like maths belongs to a discovered world but.
After Descartes it's a world that is increasingly devoid.
Of a divine influence.
We started this episode with just one question is mathematics.
Invented or discovered and.
Based on the evidence so far I'm leaning quite heavily towards discovered because it doesn't seem to me to be possible there's.
Something so all-encompassing.
Could.
Be the product of the human mind alone.
Next.
Time I see how new mathematical.
Systems allowed Newton to create his laws of gravity and.
Started describing the existence of things we didn't know whether.
More evidence our maths being a discovery.
This could be a coincidence but.
I'm forced to think again when I confront one of the strangest mathematical concepts there is infinity.
It makes the question of where the math is invented or discovered a.
Lot more difficult to answer what.
Makes our world work the way that it does explore.
More about the magic and mystery of mathematics and how it impacts our everyday life just go to BBC code at UK.
Forward slash maths and follow the links to the Open University.
And Hannah.
Returns next Wednesday at 9:00 in the meantime she's with Adam Rutherford investigating.
Everyday mysteries from pain thresholds.
To deja vu the curious cases of Rutherford and Frey on iPlayer Radio.
Tomorrow.
Here on BBC four Brian Cox marveling at our place in the great scheme of things human.
Universe a date.