There is a mystery at the heart of our universe,
a puzzle that so far no one has been able to solve.
It cannot do with welcome to all the world.
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 matt 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
invented? It's both. I have no idea. Uh
oh my god why does any of this matter well maths under pins
from computers and mobile phones to our understanding of human biology
and our place in the universe
My name is hannah fry
in this series
I will explore how the greatest think is in history have tried to explain the origins of maths extraordinary power
Yeah,
you ruined his equation
I'm going to look at how in ancient times
how in the 17th and 18th centuries
we invented new mathematical systems and use them to create the scientific and industrial revolutions
And i'll reveal how in the 20th and 21st centuries
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
Noise.
In this episode
I go back to the time of the ancient greeks to find out where our fascination with numbers started
La, you know I think I can hear the neighborhood cats screeching
and reveal why we're now looking for maths deep inside our brains.
Yeah,
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,
its mathematic. Oh My god,
Yeah, I
yeah
Oh Sure
noise
yeah
yeah.
It's sobering to think how much we entrust our personal safety to math.
Yeah,
without even realizing it,
my rush of adrenalin relies on someone's calculations of kinetic energy,
momentum, tensile strength, coefficients of friction, and much, much more.
But
what do you make me do?
Yeah,
yeah.
To put it bluntly
the modern world wouldn't exist without mathematics
and subtly influencing almost everything that we now do
And Yet.
it's invisible. It's intangible.
So where does mathematics come from?
Where do numbers live?
Yeah,
noise
yeah
yeah.
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
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.
Uh
in every culture around the world
we all agree on what the concept of fullness is like
And it doesn't matter whether it's called for cattle
a 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.
So here's the question I want to answer.
Uh
Is it invented or discovered
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
Asked whether maths is invented or discovered
it's just too extraordinary to think that
other mathematical truths and everything is just a product entirely of our conventions
In the human mind
I don't I think with that inventive
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 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 in swedish
My mother tongue
the description
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 its invented and all in our heads,
how far can our inventive brains take us?
Yeah,
I want to start with d 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
is the nautilus shell.
So there's a little creature that lives inside here 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
these chambers.
So that one is coming out at 14.5
recent,
yeah.
And this one on the same axis is
46.7.
And
yeah,
I'm measuring how wide the shell would have been
As the nautilus grew
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
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
very clear pattern starts to emerge
So here
if we do this number divided by this, we get 3
2 to this number divided by this one gives 3
five, I think. Sorry, I meant arithmetic isn't great.
Uh And this number divided by this number
then gives 3.24.
And suddenly
the same number starts to appear around about 3
2 isch
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
It she'll at a constant rate
So every time it does a Complete turn
around about 3
2 times the width of the turn before
And by repeating this very
it can create this beautifully intricate spiral shell,
clever and naughty lists.
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
Yeah.
Some have three petals, some five, some eight, some 13,
but rarely any of the numbers in between.
Yeah,
these numbers crop up time and time again.
They seem random,
but they're all part of what's called the fibonacci sequence
You start with the numbers one and one
and from that point
you keep adding up the last two numbers
one and two is three,
two and three is five, and so on.
When looking at the number of petals in a flower,
these numbers from the fibonacci sequence keep appearing.
But that's just the start.
If you look at the head of a sunflower
you'll see the seeds are arranged in a spiraling pattern
Yeah.
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.
Yeah.
Why 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 staircase.
Yeah,
simple glorious mathematical rules found hidden in nature
doesn't seem to me like a coincidence.
Yeah.
These mathematical patterns, once you spot them, do feel discovered.
It's as if the mass is already out there
just waiting for you to find it.
Yeah,
this fascination for finding hidden mathematical patterns is nothing new.
Go back over 2000 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
the
the pythagorean zwerdling obsessed with numbers
They were people who believe that numbers were a gift from gods
And part of their fascination might have been thanks to their experiments with music,
make noise, noise,
noise,
noise
noise.
The pythagorean discovered patterns that linked the sound of beautiful music to the length of a vibrating string
This they believed was no accident
but a window into god's world that had been gifted to the pythagorean zones
Mathematician and musician ben sparks is fascinated by this age old relationship between music
and maths.
Yeah
noise
and
no no no,
thank you for joining us
I know with your beautiful cello there
okay then you're uh you're gonna have to explain this to me
Where did the math come in in
Making this instrument sound nice
is
we're giving you the sound
And if you make the string
what will you hear a sound
So maybe you could play your d string
Ah Wow Sounds Lovely Sounds lovely
isn't it
And what they also notices, and other no really related to that, which is make if you make it wobble twice as fast
And to do that
you can make the string half the length
Ok So you're putting your thing here
uh pretty much. Is that halfway along? Okay,
Um What's weird about these two notes
They They sound kind of the same
but they're definitely different
And This is what the greeks notice
They We call it an octave
But if you pay them together
does it sound nice
Are delightfully pleasant?
Yeah.
In 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
where can we find other notes that sound even nicer
To get a more interesting together
Can you place this is what they call a perfect 5th
What happens when you play those two together? Then
Um Very pleasant fellow about to launch into a jig in a perfect 5th.
The ratio of the vibrating string is three to two.
The high note is 2/3 of the length of the low note.
What happens when you play a note? That isn't one of these neat fractions?
When notes on in these nice
simple ratios
we tend to notice it
Even if we're not aware of the mathematics
right
I mean did you place a really horrible harmony together, maybe like a semitone apart
When the strings are not in a simple ratio
The harmony sounds distinctly unpleasant
The greeks were obsessed with having simple ratios
describing the notes
so they get nice harmonious noises
How does this work for other intimate
I mean this is very clear
You've got this this this sort of string here
But what about
um I don't know
like the human voice
right
What every noise you ever hear
Things wobbling somehow
uh or a string or my vocal cord really have you never use your vocal cords for a bit of music
Can we try? I I I'm such financing and please don't make me do this
Ok Legal your in flags in.
Let's try
Can You Can you picture us
And no
I mean there's something nice and low
If you just do it to la then now got a chance to go back
Uh
uh
love just like the cello
it's the length of mine and ben's vocal chords that's changing the pitch of these notes
So that was me singing a perfect 5th is jerry Sophia. No la la
or you know I think I can hear the neighborhood cats screeching
So I think that's enough of that
Uh
these patterns convince the ancient greeks that they've been gifted a glimpse into this godly loan
Why else would these patterns exist
through?
Pythagoras and his followers were in little doubt
The maths was just as real as the music was
and it was even nita and more elegant than anything the human mind could conceive of
The pythagorean were by no means the first people to use some form of maths
There's some evidence that marx found cut into bones from the upper paleolithic era 37000 years ago,
with tally marks used for counting.
But it was the pythagorean who were the first to look for patterns.
It 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 months really lives.
Yeah,
the 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.
And 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,
it's just not quite perfect 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
Yeah.
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 true believer.
Yeah,
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 q
a fire was the very pointy tetrahedron.
And then with eight triangular sides aired was the octahedron.
While the icosahedron is 20. Triangular sides represented water.
The last platonic solids
the dodecahedron
the whole universe sitting in your 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
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.
Oh My 3rd famous favorite mathematical structure, the office
hydrogen,
aha,
the platonic solids, I presume. Aha.
Is it a decahedron
I love to take each a I have a misspent youth making models of polyhedra
these are the platonic solids
Oh Guys.
Okay, very beautiful.
You Know At 67. This is Christmas.
Can I keep these two please?
These 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
it was always out there to be discovered
I had this kind of platonic view that that there are triangles out
there there are numbers
there are these circles that I'm 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
But 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
And Especially if your days and nights are spent thinking about and investigating 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
What we perceive as reality
he cautioned
is no more than shadows cast on the walls of a cave
Plato had a very lively,
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
on their legs
and trapped staring a blank wall directly in front of them.
Another level
of the
in his mind's eye
but they have no idea. It's there.
On Top of the wall is a path
along which all manner of people and objects are travelling.
But the only thing the prisoners can see of them is the shadows
They cast down the wall
Those shadows are the prisoners. Reality,
yeah,
according to plato,
we are no different to the prisoners in the cave who mistake the shadows for reality
If 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 play toes cave um 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 in some uh 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
real
Um So I don't think 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.
But 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 2000 years ago
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
This is a model of a virus
straightaway. You notice it's geometric shape.
Plato would have recognized this shape as one of the platonic solids.
If there's one person who understands geometry, it's a mathematician.
Ride in tomorrow 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.
That's why ride and 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 if we got to do that,
we have a 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 it
she'll in the quickest and most efficient way possible
Armed with this knowledge
she's trying to find a way to stop 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.
If 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.
Today
mathematicians like ryden are joining the frontline in the fight against disease
Yeah,
far beyond the realm of human senses
it really does seem like the universe somehow knows maths
It really is amazing how often these patterns seem to crop up
there in plants there in marine life. There even in viruses,
there really is an awful lot that we can explore and exploit using the mathematics that we have
It does lend weight to the idea that there is some natural order
underpinning the world around us.
So 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?
Yeah,
i've got a real treat in store for me today
where some colleagues are going to scan my brain and see which bits of it are working
Ok Gotta hold on to the for one movie,
neuroscience hissed
Professor fred dick is going to place me inside an FM r I scanner
Just push a heel
measure my brain activity by tracking where the blood flows
if my brain treats the mathematical problems in the same way as any other problem,
then it suggests there's nothing special about maths
It's the same as any other language
A clue
perhaps, that it's an invention
I'll have 10 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
Okay
hannah, how is that
Well We didn't want you to relax in there
i've answered all the questions to the best of my ability.
After a few hours of processing. Professor sophie scott has my results.
Is that my brain? That's your brain.
Let me make sure I understand what I'm saying
Okay So this is like
the left hand side there
Yes And the right hand sides is
shocked my head down the middle and then
split it out. Exactly.
So what you can see here
hannah
is the pattern of activity in your brain
You're hearing straightforward language
And here you can see in the left hemisphere
very classic language areas activated
The 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
which means there's far less activity taking place.
So can we can we see um matt's, please oh hold on,
But this I look at that yeah and also down at the bottom there.
This time when I'm thinking about maths
there are yellow areas in the right hand side of my brain
This is very different to the lack of activity seen when I was thinking about language
These scans reveal there seems to be a place in our brains where maths lives
What we're definitely able to say is this is not just the meanings of the words that you were reading
but not just looking
You think about the the meaning of words
Maths. Is Real This is real, at least in my head.
Yeah,
table
really struck me about that conversation and safe it is there
that is the
yeah,
it doesn't matter whether you're doing
two plus two equals four,
or whether you're answering these much higher level math question.
It's the same bit of your brain that's doing the grunt work
language. You're seeing these problems on your
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 math 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 have never had a math lesson in their lives
Yeah,
nice to just put one of those and their very nice that work
Very nice
DR sam was is an experimental psychologist at the university of east London
to begin with
each child is placed in a room where they're shown a series of images
Sam uses a battery of test to analyze how they react
to different situations.
The
the
the 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 say feed out of what the child is looking at
And those two red dots are where the baby is looking
Oh,
um,
what 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
their looking times the amount of attention that they're paying to the screen diminishes
And that tells us that the child 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 tunis of it popping up twice in a row and the three ness of it popping up three times
And if it does
then that tells us the child understands the difference between two and three
These tests reveal that the child is surprised when the puppet appears more often,
when larger scale experiments were carried out by researchers in the US
the results suggested the infants do have a sense of quantity.
So 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 hard
Why
It might be an eight 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 math part of our brains to discover the world of mathematical truths
Uh
yeah,
the evidence for maths being discovered is compelling
We found patterns in nature
The latest technology has uncovered startling patterns on viruses and scans
Reveal is a part of our brains where maths lives
But 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 math that we take for granted?
What 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
yeah,
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 flick through
you can see the kind of things that euclid was considering
So here it says that you can draw a straight line between any two points
which seems blind in office
Uh And here it says that all right angles are the same.
Now
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
He 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
Well
this was really the first time that someone had written down formal proofs for mathematical 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
is why this book is so important.
It's the reason why euclid elements is still relevant today.
Every page within it is as true now as it ever was.
And From that point of view
one that's 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 truth might feel decidedly shaky
Yeah,
oh no oh yes love saying well don't get counting wavy n
one thing we know about languages is that they never stand still
They constantly evolving to meet the challenges of a changing world
47
Yeah,
49.
We're an,
let's go find out the tricky one.
For centuries
the language of mass was thought to be fixed and unchangeable
That is, until something was found to be missing. It is did number zero.
What exactly is? Zero
as ever, means nothing.
If you've got zero flowers, you've got no flowers.
And if you got zero
sup 60 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 7th 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.
If you think about it for long enough,
zero is actually quite a strange concept.
It's almost as though the absence of anything
becomes something.
Is it just a number or an idea?
And How can something with no value have quite so much power?
It's not exactly clear who first thought of zero
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 suspicion,
the west already had a numerical system
Roman numerals
They did the job, but we're a bit unwieldy
For example, the number 1958 is written as m c m l v iii.
And No matter where you place
say
the letter c it will always represent the number 100
It was good for its time,
but times change. And a better system was needed.
Zero was different
where you place zero could change the values of the numbers around it
Think of the difference between 11 and 101,
although the concept of zero might have been created elsewhere,
it was in India, the zero started to be accepted as a proper number.
Yeah,
this is a page from the indian back shyly manuscript 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.
For almost a thousand years, indian mathematicians worked happily with zero
while their western counterparts ploughed on with the Roman numerals
That was until Italian mathematician fibonacci recognized its potential
Now he'd been educated in North Africa
so he'd seen this number system working
First hand
Zero is a placeholder, signifying the absence of a value
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 bought it to the attention of western europe
Yeah,
zero wasn't something that we discovered so much as something that was created as part of a new language to describe numbers
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
We needed a more user friendly numerical system
not a gift from the gods, but a smart way to make counting more convenient.
This is intriguing evidence that maths might be invented after all,
a product of our intellect and imagination.
Once 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
Yeah.
The number line stretches out in both directions all the way to infinity.
And zero sits proudly in the middle. Everything was well in number land,
or was it?
This is where it all starts to get a bit strange
because there are some numbers that are simply weird
There are some fundamental rules of mass 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
Why is that?
Well This is not a math lecture.
so let's just accept 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
If plus two squared gives me plus four
and minus two squared
gives me plus four.
What do I have to swear 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.
Meet I a number we simply made up,
not everyone was keen
It became known as an imaginary number
to scoff
and its existence.
It turns out I 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
this imaginary number broke all the rules
It didn't come from this world of serial numbers
god, given
it was very definitely invented. If you can have one imaginary number,
why can't you have to?
Or three or infinitely many of them?
Why can't you have negative imaginary numbers as well
Why can't
on a different axis.
The number line isn't a single line at all.
Numbers are two dimensional.
And The one that was left,
you might think this all sounds a bitch
airy fairy
imaginary numbers that we just made up
But if you've ever flown in an aircraft
to the winter night after being 320 and 48117239
judas shoddy behind the landing
at gatwick airports
Air traffic controllers here rely on radar to keep everything moving safely and quickly
Once you can busy definitely need radar.
So the bizarre that our busy and 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 for flocks of birds or stationary objects
uh efficient tool to be able to manipulate radio waves.
Imaginary numbers are fundamental to the operation
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 private extra dead
They just told you that actuate papa ahead of your papa
Easy to night fox for travel
Yeah,
when 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 to many mathematical patterns popping up all over the place
But if we can invent the rules, create new numbers and they work,
then perhaps i've got it wrong.
Maybe maths is invented, after all,
the concept of zero or negative numbers
or complex numbers or imaginary numbers
They cause 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 whole
there's something an invitation left there that should have a name
Zero kind of maybe came from that observation
The power of mathematics lies in the way it's language
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
There 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 dick heart
It was while in a restless sleep in 1619
and mathematics.
The first two could be better described as nightmares.
But the 3rd Dream The 3rd dream was intriguing.
Yeah.
As his eyes scanned the room
he saw books on the bedroom table at appeared and then disappeared
The opened one book of poems. And at random
course
the opening line of one which read what road shall I pursue in life
If
yeah,
then someone appeared out of thin air and recited another verse saying simply,
what is and is not
as with dreams, it's all about the interpretation you place upon them.
In descartes case, the effective these dreams was profound.
Mhm.
He was convinced that the dreams were pointing him in a single direction,
bringing together the whole of human knowledge by the means of reason.
He was nothing if not ambitious
ever in the field of mathematics.
As with so many brilliant ideas, it was deceptively simple.
Let's say that I'm meeting a friend for a coffee
Now I'm standing at the end of ns lee gardens
and they are somewhere over on gordon street
It's very easy for me to work out how to get there
in this case, three streets down and one along
it sounds like an incredibly simple idea.
But actually
it revolutionized mathematics.
Yeah.
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 stars.
It gets more interesting when you apply this idea to curves.
As this point moves around a circle, its coordinates changed.
And we can write down an equation that precisely and uniquely characterize as this circle
For 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.
What descartes and the other trail blazers like him
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 prefer 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.
It still feels like math belongs to a discovered world.
But after descartes,
it's a world that is increasingly devoid of a divine influence.
And we started this episode with just one question
Is mathematics invented or discovered
And based on the evidence so far
because it doesn't seem to me to be possible
could be the product of the human mind alone.
Yeah,
next time
I see how new mathematical systems allowed newton to create his laws of gravity
and even started describing the existence of things we didn't know
all more evidence of maths being a Discovery?
Now
infinity.
And it makes the question of where the mass is invented or discovered a lot more difficult to answer
What makes our world work
and how impacts our everyday life.
Just go to BBC dot co dot u k forward slash maths and follow the links to the open university
And Uh And hannah returns next Wednesday at nine.
In the meantime
she's with adam rutherford investigating everyday mysteries from pain thresholds
Today
tomorrow here on BBC for brian cox marvel ing at our place in the great scheme of things,
human universe, a date
noise.