Translator: PhAnh MAC Reviewer: Denise RQ
Hello.
As a very true proverb goes,
prediction is a difficult art form, mostly when it is about the future.
And it's perfectly accurate.
It is very difficult to predict what science will be in 2030,
which is, of course, one of the topics that we can address in this TEDx.
When asked about this in 1900, Henri Poincaré
- the greatest mathematician of his time - got away with it by dint of a pirouette.
"If, in 1800, we'd asked any scholar
what science would be in the 19th century,
what nonsense he would have said, great God!
That thought keeps me from answering you.
I believe that we will get surprising results.
This is exactly why I can't tell you anything,
because if I foresaw it, what surprise would there be left about it?"
Today, I could very well take this quote
from the great man for myself, stop here,
and defer to the next speaker,
enabling an appreciable gain of time.
(Laughter)
Do you agree?
You don't seem to agree. Then we shall go on.
Poincaré makes a prediction for us, actually, without appearing to.
A prediction that surprising things will happen,
and that tomorrow, like today, like yesterday,
innovative ideas will play a vital role.
Discoveries that we cannot foresee, but for which we can prepare.
Ideas are extremely powerful -- this is well known here at TED.
Ideas can make you change your opinion,
win you a war, change the fate of humanity.
Among several highly representative examples from the 20th century,
we have here, to your right, the English mathematician Alan Turing,
born 100 years ago, whose mathematical ideas,
during the Second World War, allowed the allies
to crack Germans' secret code -- the German Marine's secret code,
and whose researches led to the development of computers.
To his left, Paul Erdős, the errant mathematician,
a Hungarian Jew, uprooted by the war, wandering with no luggage,
no money, no job, no car,
nothing else but the richness of his ideas
and the solidarity of his friends
who made him the most prolific mathematician of the 20th century.
At the center, you have Leó Szilárd, his compatriot,
the first to have the idea of a chain reaction,
which, for good or for evil, led to the atomic bomb.
We can see it through these examples: an idea can change the whole world.
And all higher education institutions
in the world, in the US, in Europe, and everywhere else, pride themselves
not only on the knowledge they pass on
but on the ability to have innovative ideas that they teach.
That, is true wealth!
But ideas, how does it work?
What happens when we have an idea? Let's give the floor back to Poincaré.
Poincaré is one of the few scientists to have written in the first person
about the process of discovering great ideas.
A very famous text, which, to sciences, is a little like
what Proust's Madeleine is to literature.
In a very famous text,
he talks about an inspiration that comes to him suddenly
when he puts his foot on a step during a bus ride,
bringing the solution he was looking for.
Let's take a look at another example, where he talks about
how he resolved a problem in which he took great interest
and which he had been fighting in vain.
"Having enough of my failure, I went to spend a few days at the seaside,
and thought about something completely different.
One day, while walking along a cliff,
the idea came to me, always with the same characteristics of brevity,
suddenness and immediate certainty,
- excuse the big words -
that the arithmetic transformations of ternary indefinite quadratic forms
are identical to those of the non-Euclidean geometry."
(Laughter)
Even if you didn't grasp the entire subtlety and poetry
of the last lines, you understand
that it has nothing to do with the cliffs, or walking.
That's precisely the point.
What Poincaré describes to us is a complex process
in which periods of intense and conscious work
alternate with sudden aspirations that come without warning,
absolutely unrelated to what you're doing
- walking a cliff for instance -
because there was an unconscious and very poorly understood brain work.
The younger of you, keep this in mind --
if one night you have a rebellious math assignment
and you want to go meet your friends
in a nightclub,
try using the Poincaré method with your parents.
Tell them, a mathematician has explained in a large conference
that in order to solve problems, you should go out
and wait for the inspiration to come.
Let me know if that works.
So, we don't have a lot of testimonials like Poincaré's.
I tried to make mine, it's called "Living theorem,"
and it's the story of an idea from the viewpoint of one of those
who gave birth to it.
The story of an idea between the story of a theorem,
an assembly, and an innovative assembly of mathematical concepts,
to solve a problem of plasma physics -- I won't tell you which one.
The book is not about the problem, it's about the resolution.
From the first moment when a fruitful conversation
between two mathematicians marks the beginning of the project
until the moment when the consolidated discovery is ready to be born.
That is to say, to be published as a research paper.
Between these two moments, there's a long and non-linear quest
of two years and a half, with joy and sorrow,
moments of exaltation and depression,
unexpected rebounds, illuminations --
a bit like the one described by Poincaré, lows and highs,
and phases of extremely hard work.
A complex, a little chaotic process which represents what may be
the birth of an idea.
In this book, the hero is an idea, but, also, it is clear
that mathematical ideas aren't born mathematically.
Mathematicians' brain, like everyone's,
is built upon emotions, analogies, and feelings,
and one must manage to bring the logical idea
into this biological and emotional matrix.
A biological brain carries the idea,
sometimes it's the idea that carries human beings when it's strong.
That's the story told by author Francis Spufford
in a fascinating historical novel, Red Plenty,
the story of an idea which was thought to be able
to revolutionize Soviet Russia in the 50s.
Linear programming,
with genius mathematicians in control,
and all the social and political impacts that this idea could bring about.
As says Spufford in his book's introduction,
the hero of this book is an idea.
And we could spend hours talking about ideas and their adventures,
their history, geography, exchanges,
all kinds of things related to them.
I'm just going, in the few remaining minutes,
to identify some ingredients necessary for the emergence of ideas.
To have good ideas, a well trained brain is perhaps necessary;
and even that is not enough to have good ideas.
To have the ideas and theorems which earned me the Fields medal in 2010,
the brain was not the only factor, there were a lot of other ingredients
found in all ideas.
They're found through the centuries,
always the same ones, I think,
but evolving according to culture and technology,
and each of these ingredients is a research topic on its own,
mingling hard and social sciences.
First ingredient: documentation.
Encyclopedias, experimental results,
information, results representations,
everything that will feed your brain.
This has been revolutionized by computing.
Nowadays, with an electronic encyclopedia,
you can retrieve a formula that you forgot,
of which you forgot even the name,
as long as you vaguely know what it's about. It's a revolution.
Second fundamental ingredient, without which nothing's done:
motivation.
It's something not to be neglected.
This is probably the most serious threat
to science in the industrialized countries nowadays --
the lack of motivation of the young generations
for science professions,
exciting professions though --
a problem that affects all industrialized countries.
Where does motivation come from? We'd be happy if we knew.
It comes and it's sometimes passed on from teacher to student,
from parent to child.
It can be discovered in an illustrated book,
through a cartoon, like some of those I used to watch when I was a child.
It can be found in experiments such as the one depicted here --
the experiment conducted by a professor
with his primary school students in England on bees' behavior.
The bees, which will integrate color and pattern recognition
to choose where to forage.
It's a topic for a class to work on
as a research theme,
which leads to the publication of an article in a journal.
All authors, except one, are children of primary school.
In the conclusions of the study, they discovered some things about bees,
and they say, "We also found out that science is fun."
There you have a conclusion that I hope will be discovered times and again
by numbers of children in the coming decades.
Our future depends on it.
Third ingredient without which you can't do anything:
an enabling environment which allows you to develop your ideas.
Material and intellectual conditions.
People with whom to discuss, it can be a laboratory with colleagues,
an institute such as the one I'm honored to direct
- the Henri Poincaré Institute - one that receives researchers
from all horizons and all countries in mathematics and theoretical physics.
It can also be the city environment with the encounters it enables.
The science historian Marc Giget, specializing in innovations,
has analyzed the role of cities as innovation units through the centuries,
going back up to ancient examples such as the legendary city of Persepolis
- an innovation phenomenon - and many others.
Other examples of cities with an extremely innovative climate
include Budapest of the years 1920 to 1930,
with its extremely tolerant climate, where prevailed an intellectual richness
that led to the emergence of these famous Martians --
these scientists speaking an incomprehensible language,
of whom we have already seen two,
and who have revolutionized the world with their discoveries in mathematics
and theoretical physics.
It can be an encounter in a city,
it can be an encounter like this TED conference in Paris.
It can also be an encounter like the one that led me
to find myself at the dinner table of a literary editor one night
and that resulted in the publication of the book I introduced earlier.
Without this encounter in this city, no book.
You see on what an idea depends --
on your environment, not just on you.
Fourth ingredient: exchanges.
Face to face exchanges are fundamental
to the start of a project, but to develop the idea, propel it,
you have all kinds of possibility of exchange.
Nowadays it can be through emails.
And during months, with a main contributor in particular,
we exchanged hundreds of emails,
creating a sort of delocalized brain
on both sides of the Atlantic.
The mathematician Tim Gowers conducted much more impressive experiments
with hundreds of mathematicians working together
to solve a theorem on his blog.
Fifth ingredient: constraints.
They are mostly expected to be of scientific nature
but they can also be at the creativity level.
Their roles in artistic co-creation has often been highlighted.
Two noteworthy examples that I am presenting --
the musical piece written by György Ligeti
entirely in A, with one exception,
and, on the right, an excerpt from this famous novel by Georges Perec
in which the constraint was to never use the letter 'e'.
Constraint as an element of creation.
Sixth ingredient, as we have seen with Poincaré -- this mix
and wise dosage of work and intuition
where hard work and unexplained illumination alternate.
And then, the seventh ingredient: perseverance and luck.
The nanny working for a famous mathematician
once described the work of her employer to her friends,
"I don't understand what he does.
He spends his day scribbling on paper sheets.
As evening falls, he crumples everything and throw it away." And that says it all.
Because in the same way 99% of patents won't result in any yielding invention,
most ideas don't work out.
It's normal and it's the way it is.
The researcher spends his time sending his brilliant ideas to the bin
because they don't work out.
From time to time luck saves one of them
and there starts a great adventure.
You see all that is needed for an idea to emerge?
We get that it's precious, but it's not the end of the adventure
once you realised your idea.
And both today and tomorrow, dissemination of ideas
will be a key challenge.
Ideas are normally meant to be exchanged freely.
Let's quote Thomas Jefferson, one of the Founding Fathers of the USA,
"If nature has made any one thing less susceptible than all others
of exclusive property, it is the action of the thinking power called an idea,
which an individual may exclusively possess as long as he keeps it to himself;
but the moment it is divulged, it forces itself into the possession of every one,
and the receiver cannot dispossess himself of it.
Its peculiar character, too, is that no one possesses the less,
because every other possesses the whole of it.
He who receives an idea from me, receives instruction himself without lessening mine
as he who lights his taper at mine, receives light without darkening me."
Words worth remembering today
and not necessarily understood by all, as shows the following anecdote.
As a lot of my colleagues do, I publish my articles on my website,
all with free access for my colleagues, and, a few weeks ago,
a platform for the dissemination of ideas contacted me to collect some
and post them on its platform.
And the manager receives, several weeks later,
a comminatory letter with a plethora of names of lawyers
representing a great number of scientific editions
mentioning infringement of intellectual property
and explaining that damages and interests are claimed.
Today, in 2012, Jefferson's words are still relevant.
We have to be reminded of them, and will have to, again, in 20 years.
To protect ideas, which are as powerful as they are precious and fragile.
I'll leave the concluding word to Henri Poincaré --
"Ideas are thoughts.
Thought is like a flash in a long night; but it is this flash that is everything."
Thank you.
(Applause)