SCIENCE TODAY
You probably wondered why you had to do math
back in the classroom.
On top of it, you thought it was pure boredom.
Well, tonight we're going to try to interest you...
HOW I CAME TO HATE MATH
This is a math nerd.
- A what? - A math nerd.
Too much!
Facebook... What's his name?
Mark Zuckerberg.
In the film it's clear he's weird. He's autistic.
No way!
He just doesn't care about money!
He created Facebook because he's a pro at math,
but is that all he's got on the brain?
C minus...
C, F...
B minus.
Once bad at math always bad at math.
That's for sure!
It's fate.
It's destiny.
Too much value is placed on math.
Parents think it's all-important.
So when kids don't get it,
they think they're dumb.
They get frustrated, feel stuck,
and give up.
A mathematician, as considered by most,
has no imagination.
His thoughts parch the heart.
And he...
Following a line of thought developed in the 18th century,
he's not sensitive.
Take a round of cheese.
You examine its shape, its aroma, etc.
A mathematician is only interested in its shape.
He doesn't see the cheese,
just its circular shape, nothing else.
This extracting parts from reality
is what the mathematician is criticized for.
He doesn't live in the real world.
He's not only useless,
it's worse.
He literally kills reality. By carving it up,
he destroys the world.
Math is the science of death.
Mathematics is serious. It's exact.
It's scientific. It's explicit.
It's frightening.
People make light of it.
They say,
"I might be bad at math, but I'm still cool."
It's amazing how many claim they were last in math.
How could so many be last?
Mathematics is rigorous but also creative.
It's abstract but universal.
It's inegalitarian and democratic.
It's ancient yet always evolving.
It's solitary and collective at once.
It's difficult and super easy.
The words on the left are pretty grim.
Rigorous, abstract, inegalitarian,
ancient, solitary, difficult.
But then there's creative, universal, democratic,
constantly evolving, collective, super easy.
That's way more sexy!
It's still full of pins.
The Queen of Hearts.
It's missing the sleeves.
I love the creative aspect of sewing,
making shapes and playing with them.
It does require a lot of math.
Not that I do it for the math...
but you do have to deal with things like curvature.
For example, I sew for myself,
and I'm not shaped the same as my daughter.
It creates new geometric problems
and it's fun.
Professor of Mathematics
I was called Mr. Math as a kid.
It did go a bit to my head.
I drew graffiti on the walls of the bathroom at home.
Cubic equations and such.
Curious graffiti, for sure.
But they fascinated me. I couldn't solve them.
I asked my teacher to help me
and she never would.
But she did ask me to help her teach the others.
That's when I realized I understood it.
It was easy for me.
That's the way it was.
It was all there, clear as a bell.
But my classmates were lost.
They couldn't visualize objects. Nothing made sense.
They couldn't draw analogies. They had no points of reference.
So trying to come up with images
to explain, demonstrate, help them understand wasn't easy.
I never managed.
It did teach me a lot about life though.
I understood that all of it was hard.
The challenge of knowledge, the challenge of math
is being able to convey and share it.
What a musical entrance...
Not bad, huh?
Hi there!
Advanced Math Class
Like this? Usually a hat is worn...
There's an axis, an ellipse, which takes us back to the subject.
It has two symmetrical axes, a long and a short.
As a rule the long axis of the head
goes in this direction.
We need to remember that mathematics
isn't a single truth or a perfect object
that everyone will fathom or discover in the same manner.
It has a plural meaning.
Each person will interpret it differently.
Okay, 1+1 = 2.
But when you say, 1+1 = 2, what's essential?
The result, the addition, or the 1?
What do I have to do to get 2?
It's difficult to come up with good images,
several images,
so that everyone can relate.
A smile, a grimace.
A smile, and zero.
- Minus 1. - For me, it's zero.
From the top.
One...
one smile, and back at the start.
If we unfold it, it has to be zero...
Don't you see it here?
It's because if here
we continue on, we end up with another.
So it's the same thing above
except the corner is hiding it.
Down below it's there twice.
It counts as one.
And why?
Because what counts isn't necessarily
wthe corner.
You have to make the corners round.
The curve has to be smooth.
Let's start again. One,
two...
Math speaks deeply to who we are.
Words like axis, root, complex number,
imaginary number, negative,
division
also relate to our personal lives.
Okay, no problem.
Bye.
See you Friday.
Bell, you're a sweetie, but stop...
Educational Psychologist in Mathematics
Take a kid who's intelligent, clever,
too smart sometimes for his own good.
When he starts doing math
he suddenly becomes dumb.
It's so hard, it's utterly exhausting.
Then he closes his book and is suddenly full of pep.
It's because doing math demands enormous energy.
In one of his books, a French author wrote,
"I spent two hours not doing my math."
The time spent not doing math is exhausting.
The anxiety of opening your book and not understanding anything.
Feeling that you never will.
Not knowing where to start. The test.
It's terrorizing and completely draining.
Math is risky business.
You try to understand, knowing you might fail.
At first, you struggle at it for hours.
Getting it wrong has its reward.
It's the beginning of an idea. You're reasoning.
It's a real adventure, the adventure of math.
The adventure is what comes.
The real work is turning what comes
into something interesting, alive, enriching,
whether it's right or wrong.
So am I a humanoid?
Am I a scientist?
A biologist?
Did I live in New York?
In the 21st century?
Am I Marie Curie?
Not the 20th.
Just one loop on the...
You can do A-C-B like this.
A, C then back to B.
No, it's not B-¹.
That's a C.
This is C-¹, and it goes here.
That's what I did.
- There? - It doesn't work.
In math, you have nothing to lean on.
When you study literature
you have a novel.
The teacher vanishes behind "The Red and the Black."
In math, theorems are difficult to grasp. They're evanescent.
Your math teacher is the incarnation
of mathematics.
I see lots of kids in grade school
who try to add. 3+2...
I watch them finger counting.
They try not to show it. They aren't supposed to.
It's really too bad.
They should use their hands and bodies as support,
even right through high school.
An inflection point is like a toboggan.
A toboggan at first goes increasingly faster.
It gets steeper. It continues the descent,
but towards a much gentler slope.
The moment it stops accelerating
and starts to slow down
is what we call the inflection point.
Then there's a definition based on the second derivative.
But if your body remembers the sensation of riding a toboggan,
the second derivative is easy as Pi.
Each mathematical notion
can be related to a physical experience.
- Goin' well? - Yeah.
The beauty of mathematics lies in those sweet moments
when I suddenly get it.
Now I have the words.
You more or less always understood.
But the road was just so tortuous, you ran out of breath.
It's like climbing a steep mountain face
only to realize how close you are to your starting point.
It's the moment you discover there was a straight path.
Now you can express it. You can convey it.
You can explain it so others understand.
It's an awesome moment.
The beauty of math is that moment
when the words used to describe it flow naturally.
26th International Congress of Mathematicians
When you get the phone call, you go...
You hang up and suddenly wonder if it wasn't a hoax.
The email confirmation comes,
but doubt remains.
Slowly you get other confirmations.
You're told to keep it quiet.
If someone mentions the Fields Medal, you play dumb.
They wish you luck, you thank them.
You can't say anything.
I had a course to prepare. It'll be of a hundred pages.
So I got to writing
but the sources were lacking.
I had to rework this, rewrite that.
Articles needed reworking. I ended up rewriting everything.
It's the book that's in command.
If the chapter doesn't sing,
if that little voice says "no," you rework it.
Over and over again.
After years, days and nights of work
it's there. It's finally done.
I worked on this thing
sometimes morning and night.
The first time I sat down to reread it,
make corrections and polish it up,
I took advantage of my vacation.
My family left on a trip and I stayed home.
I went to the marketplace,
bought a bunch of vegetables,
and made a big pot of soup.
I ate it for a full week.
Not to mention bread. Bread is absolutely vital.
I read all day.
I'd get up in the morning, read and revise
until I went to bed.
I did that for a week.
To achieve good results that's what is necessary.
In the history of mathematics
there's one award that stands apart.
Jean-Pierre Bourguignon, Institute of Advanced Scientific Studies (IHES)
It celebrates youth.
Recipients of the Fields Medal must be under 40.
The prize money isn't large,
characteristic of how mathematicians operate.
And in the field of study
it's the most prestigious award.
Mathematics is too often reduced to calculations.
Even if they play an important role,
mathematics is the largest manufacturer of concepts in the world.
In the 20th century the field of mathematics exploded.
In 1900, research mathematicians
numbered around 150 in the world.
Today there are 80,000!
And they each produce about one theorem a year.
It's just full of overflowing, abundant activity.
It's essential to bring attention to this movement.
Inaugural Address
Mathematician/Funder of Renaissance Technologies
Julia Robinson Mathematics Festival
It's often ideological.
Those involved often have biased opinions,
which are hard to change.
When we teach kids
we shouldn't have biased opinions or preconceived ideas.
It's surprising when you think
how little our brains have evolved over the millenniums.
Take a child...
What he learns at the beginning of his experience
isn't necessarily technology-dependant.
We should already have found better,
the best methods for teaching how to read and count.
Yet no one can agree. That isn't normal.
Yes, things are changing in high school curriculum.
We have to adapt to advances in science and technology.
But for kids, we should've found
the miracle method on which everyone agrees.
2 plus 2 still equals 4.
We have to be able to educate children
who, in some twenty years, will become active citizens.
We need to anticipate what life will be like for them.
We live in a changing world. A world of progress.
A world that is often violent and cruel.
An uncertain world where people kill and die.
Where children suffer.
This world will soon be theirs.
We must adapt education to the world of tomorrow.
The recently proposed reform has caused reaction.
Modern mathematics, the reform that has confused
students and parents alike.
Modern mathematics should provide us
with a universal tool
that will enable us to adapt to new situations.
In the '70s there was a desire to modernize
and industrialize France.
To do that we needed engineers,
more than the number graduating from university.
Historian of Mathematics
We needed a large pool of them. Mathematics was considered the means
by which to train them.
It was the baby boom, the population had soared.
The birthrate had risen,
and classes were filled to the brim.
The problem was how to offer opportunity
to everyone.
The modern mathematics reform
was thought to be
the most effective means to teach the masses.
Access to mathematical knowledge
was thought to be something natural to man,
while literary knowledge, theater, poetry, music
was learned socially.
This viewpoint was not entirely sound
but it was workable.
First, programs were revised.
Mathematics had to be conceived differently.
Mathematics is a logical, clear, distinct process
and was thus deemed the "least worst" means of selection.
The math curriculum was inspired
by the work of top mathematicians who had influenced their era.
It was a group of mathematicians,
young professors who would get together
and prepare their courses.
"Let's work up next year's courses."
Before they knew it, they were rewriting mathematics.
It was a time in the field
where some order needed to be restored.
Notations needed reviewing, interdisciplinary relations assessed.
They had to start from scratch, and it took years.
This group of mathematicians
published under the pseudonym Nicolas Bourbaki.
Though it started in France, within a few years
it had become a worldwide movement.
It was quite a phenomenon.
Conferences were held on "modern math"
in South-East Asia,
in Brazil,
and, of course, "new math" in England and the United States.
Yes, it was new mathematics,
with an emphasis on modern.
In other words, mathematics truly of the time.
The modern mathematics reform echoed, in the events of May '68,
the demands for more freedom in the classroom.
People felt they had been liberated
from so many constraints,
especially those of authority.
They were breaking with a restrictive culture
that had so encumbered them
and didn't allow them
to be truly themselves.
I was at school during the reform and loved it.
It created a real opening, which was fabulous.
It led to a generation of mathematicians
with the highest qualifications
and a solid foundation.
It's true.
But generations since
have been either disgusted or overwhelmed,
when they could've learned math,
or at least not rejected it.
That's truly sad. It's still a heavy price to pay.
A number of politicians and journalists were so traumatized
they still can't say they enjoy math.
If you don't get it, you're in trouble.
You're not doing any more calculations?
We don't know how to do them anymore.
Calculations with decimals, numerals, division...
I'm completely lost.
The big problem is the language.
Math terms are super complicated.
Math has become so abstract, it's a joke.
The new definition of a straight line
makes no sense.
You learn it by heart and mindlessly recite it.
You get the gist of it,
but the terms are incomprehensible.
Even parents have to go back to school.
95 percent of parents
can't make sense of the new textbooks.
Kindergarteners were told not to finger-count.
They had to identify commonalities between...
3 isn't the number anymore.
It's 3 shoes, 3 pants, 3 crayons.
And the link between them? The number 3!
Except kids already know what the number 3 is.
Likewise,
you don't draw a line
because the act of drawing has been corrupted by the senses.
It needs to be defined abstractly.
The idea behind the reform was
to make kids understand before actually drawing.
Understand first then feel, and only then.
On top of it, teachers hadn't been trained.
At the time there was a shortage of high school teachers
so we had to hire teachers from grade school
who hadn't studied science at college.
They were good teachers
but had no scientific basis.
And they were supposed to teach this new math
with its extreme level of abstraction.
So as not lose grip, they went strictly by the book.
They understood nothing.
- So their students didn't either? - Exactly.
Teaching methods changed.
Completely. I was a teacher back then.
It helped me improve my teaching skills.
How have kids reacted to the changes?
They love their new math lessons.
They can't wait for class.
They don't get tired during the lesson.
It's a game.
It's quite amusing to read
the modern mathematics textbooks.
The explanations kept getting longer.
They had to learn to "speak well" even if it concerned mathematics.
That hadn't been planned.
What was supposed to be a sphere of creativity and freedom
became something that petrified everyone.
"I don't understand anything. I'm completely lost."
It created bewilderment instead of creativity,
like a rabbit caught in headlights. "What's this truck going to do to me?"
A school curriculum
can't be conceived on paper.
It has to be tested.
You have to experiment when it comes to child education.
You first test a program, see how kids fare
then go from there.
We're limited in our understanding of how the brain works.
All we can do is experiment.
Modern mathematics was full of honorable intentions.
It was developed by the best mathematicians of the day.
It just wasn't the right reform at the right time.
Nowadays,
people use the word "Bourbakist" as an insult.
A kind insult, it you will.
"You're abstract. What are you, a Bourbakist?"
For a time people criticized Bourbaki,
but now I think there's a general consensus
that Bourbaki had a big impact on mathematics.
There's no denying or idealizing it.
It was a milestone.
The idea behind it was to convey
a maximum of knowledge to a maximum of kids.
But trends in math curriculum sort of betrayed the spirit of math.
It became hard,
severe, too abstract, completely based on objects...
independent of human beings.
Bit by bit, the idea of mathematics
as profitable, as functional prevailed.
Obviously,
Clemenceau High School Principal
science majors are eclipsing all the others.
It's terrible to see math being used as an assessment tool,
when many kids will never become scientists.
Since science is considered "the" field of study today,
landing a prestigious position is all but guaranteed.
Students major in math, even those graduating with a BA.
SCIENCE OF EDUCATION RESEARCHER
MSRI Director
Mathematical Research Institute of Oberwolfach
Germany
Director
Research can't be just summoned up.
You must rely on initiatives and the competence of experts.
There are those who suddenly have an idea.
They set it out. But no, it doesn't work.
The second time, it's still no.
The third time, yes! It finally works.
People have a hard time understanding creativity.
Artists function differently. They explore the unknown.
It's hard to find the right problem.
Those of no interest come by the dozen.
Asking the right question is a big chunk of the work.
It's the path taken that's important.
And there isn't one unique path.
Sometimes you find a shortcut,
a really simple shortcut.
Not as simple as an exercise, but close.
It's much less important.
The proof is simpler,
but a complex proof is much more profound and rich.
The mathematical result is important,
but the proof is often just as important.
So is the approach,
the arguments used, the interdisciplinary connections,
the developed theories, the tools.
A new way of seeing things, new connections.
They all lead to other ideas, other avenues, other techniques.
And this requires a lot of time.
In order to discover new fields of application,
or radically new concepts and phenomena,
highly developed research is required.
Unfortunately...
When we realized research, apart from the rising costs,
was having an impact,
and that science and industry were now connected through high-technology,
people said, "We're there.
"We're now one. We'll draw the consequences,
"and now function like companies."
That's a big mistake.
"We finance you, so we want to know what you're doing.
"We'll decide what you work on."
That's blatant abuse of power.
It kills the process we should be defending.
All countries do it except...
China.
The total counterexample.
The Chinese understood they couldn't meet
the expected levels of performance and development
without massively increasing pure research.
They'll have a labor shortage in 25 to 30 years.
They'll need to produce high value-added products
in order for the country to survive.
They recognized in order to achieve that
they'd need highly developed fundamental research.
However there is a consequence to this.
Most scientists are passionate about what they do.
Take away their freedom, tell them what to do every morning
and they'll up and leave.
Researchers aren't well paid, though I'm not complaining.
But most scientists are highly competent.
If they want to make money, they'll go elsewhere.
To get the most creative to stay leave them alone.
Institute of Advanced Scientific Studies (IHES), Bures-sur-Yvette, France
Mathematics works well with music and mountains.
Mathematics, mountain, music. M-M-M.
Alain, is your sense of orientation good?
Computational Science Researcher
We live in a world saturated with massive, complex data.
Any two individuals in the world
are connected by a chain of acquaintances.
This is known as discrete mathematics.
Everything today is done through data analysis.
Google's search engine
is a mathematical algorithm worth 200 billion dollars.
Cryptography Laboratory
Olivier, help Alexis out so he doesn't break anything.
Mathematicians remained craftsmen for a long time.
But the social impact of what they are now doing
is a radical shift.
Many hadn't much considered scientific responsibility.
They thought they lived in a world a bit apart.
They'd never had to choose, like some,
whether or not to join the Manhattan Project
and help in the making of the atomic bomb.
Suddenly there was a whole branch of mathematics
that found itself at the heart of economic activity,
an economic activity that was having a massive global impact.
Financial mathematics.
Professor of Financial Mathematics
The sophistication of the mathematics changed abruptly.
You now had mathematical products, like you have chemical products.
Banks were making a number of new offers.
New products, new ways of developing financing operations,
new profit-sharing plans.
Schemes that hadn't existed before.
These were new products
whose very existence depended on new mathematics.
Most models used by the banks
are based on random variables.
These models were built on statistical data
in order to calibrate the parameters.
Most of these banks, in feverish competition with each other,
never shared information.
From a scientific viewpoint, it was crucial
to have at one's disposal a vast pool of data.
And that was non-existent
because each bank jealously guarded its own information.
LaPlace said that if we knew everything
we could predict everything.
In the end,
our inclination for breaking "nature" down
into forms and numbers,
drawing conclusions, even predicting destiny
dates back to antiquity.
It's in our nature.
But it's important to learn to live fortuitously,
with uncertainty,
and to master it, to actually live it.
Our fascination with scientism has wreaked havoc.
"Science can solve everything."
Philosophically speaking, that's unacceptable.
Science doesn't have all the answers.
What science can give us
is the capacity to turn doubt into a virtue.
We all must doubt when it's appropriate,
but we can find certitude even in moments of doubt.
Subtitles by Theresa Murphy
Subtitling: C.M.C. - Paris
www.moviesubtitles.org