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What is it that French people
do better than all the others?
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If you take polls,
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the top three answers might be:
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love, wine and whining.
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(Laughter)
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Maybe.
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But let me suggest a fourth one:
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mathematics.
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Did you know that Paris
has more mathematicians
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than any other city in the world?
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And the most streets
with mathematician's names, too.
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And if you look at the statistics
of the Fields Medal,
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often called the Nobel Prize
for mathematics,
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and always awarded to mathematicians
under the age of 40,
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you will find that France has more
[......]
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than any other country.
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What is it that we find so sexy in math?
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After all, it seems to be
dull and abstract,
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just numbers and computations
and rules to apply.
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Mathematics may be abstract,
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but it's not dull
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and it's not about computing.
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It is about reasoning
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and proving our core activity.
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It is about imagination,
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the talent which we most praise.
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It is about finding the truth.
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There's nothing like the feeling
which invades you
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when after months of hard thinking,
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you finally understand the right
reasoning to solve your problem.
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The great mathematician
André Weil liked this --
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no kidding --
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to sexual pleasure.
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But noted that this feeling could
last for hours or even days.
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The reward may be big,
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[......] [mathematic ... ] choose
to permeate our whole physical world.
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They are inaccessible to our senses,
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but can be seen
through mathematical lenses.
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Close your eyes for moment
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and think of what is occurring
right now around you.
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Invisible particles from the air
are bumping on you
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by the billions and billions
at each second.
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[All in complete cause]
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and still,
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their statistics can be accurately
predicted by mathematical physics.
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And open your eyes now
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to the statistics of the velocities
of these particles.
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The famous bell-shaped Gauss Curve,
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or the Law of Errors,
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of deviations [in] respect
to the mean behavior.
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This curve [tells] about the statistics
of velocities of particles
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in the same way as a demographic curve
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would tell about the statistics
of ages of individuals.
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It's one of the most
important curves ever.
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It keeps on occurring again and again,
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from many theories and many experiments,
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as a great example of the universality,
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which is so dear to us mathematicians.
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Of this curve,
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the famous scientist Francis Galton said,
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"It would have been deified by the Greeks
if they had known it.
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It is the supreme law of Unreason."
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And there's no better way to materialize
that supreme goddess than Galton's board.
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Inside this board are narrow tunnels
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for which tiny balls
will fall down randomly,
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going right or left, or left, etc ...
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All in complete randomness and [cause].
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Let's see what happens when we look
at all these random trajectories together.
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This is a bit of a sport,
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because we need to resolve
traffic jams in there.
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Aha.
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We see that randomness
is going to play me a tick on stage.
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There it is.
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Our supreme goddess of unreason.
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The Gauss Curve,
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trapped here inside this transparent box
as Dream in "The Sandman" comics.
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For you I have shown it,
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but to my students I explain why
it could not be any other curve.
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And this is touching
the mystery of that goddess;
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replacing a beautiful coincidence
by a beautiful explanation.
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All of science is like this.
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And beautiful, mathematical explanations
are not only for our pleasure,
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they also change our vision of the world.
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For instance,
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Einstein,
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Perrin,
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Smoluchowski,
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they used the mathematical analysis
of random trajectories
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and the Gauss Curve
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to explain and prove that our
world is made of atoms.
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And it was not the first time
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that mathematics was revolutionizing
our view of the world.
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More than 2,000 years ago,
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at the time of the Ancient Greeks,
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it always occurred.
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In those days,
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only a small fraction of the world
had been explored,
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and the Earth might have seemed infinite.
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But clever Eratosthenes,
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using mathematics,
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was able to measure the Earth
with an amazing accuracy of two percent.
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Here's another example.
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In 1673, Jean Richer noticed
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that the pendulum swings slightly slower
in Cayenne than in Paris.
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From this observation alone
and clever mathematics,
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Newton rightly deduced that the Earth
is a wee bit flattened at the poles,
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like point three percent,
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so tiny that you wouldn't even
notice it on the real view of the Earth.
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These stories show
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that mathematics is able to make us
go out of our intuition,
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measure the Earth which seems infinite,
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see atoms which are invisible,
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or detect an imperceptible
variation of shape.
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And if there is just one thing that you
should take home from this talk,
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it is this:
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mathematics allows us
to go beyond the intuition,
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and explore territories which do not
fit within our grasp.
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Here's a modern example
you will all relate to ...
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searching the Internet.
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The world wide web,
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more than one billion web pages --
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do you want to go through them all?
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Computing power helps,
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but it would be useless without
the mathematical modeling.
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To find the information
hidden in the data.
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Let's work out a baby problem.
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Imagine that you're a detective
working on a crime case,
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and there are many people
who have their version of the facts.
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Who do you want to interview first?
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Sensible answer:
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prime witnesses.
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You see,
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suppose that there is person number seven,
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tells you a story,
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but when you ask where he got if from,
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he points to person
number three as a source,
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and maybe person number three, in turn,
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points at person number one
as the primary source.
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Now number one is a prime witness,
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so I definitely want to interview him --
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priority.
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And from the graph
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we also see that person
number four is a prime witness.
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And maybe I even want
to interview him first,
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because there are more
people who refer to him.
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OK, that was easy,
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but now what about if you have big
bunch of people who will testify?
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And this graph,
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I may think of it as
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all people who testify
in a complicated crime case,
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but it may just as well be web pages
pointing to each other,
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referring to each other for contents.
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Which ones are the most authoritative?
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Not so clear.
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Enter page rank,
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one of the early cornerstones of Google.
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This algorithm uses the laws
of mathematical randomness
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to determine automatically
the most relevant web pages,
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in the same way that we used randomness
in the Galton Board experiment.
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So let's send into this graph
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a bunch of tiny, digital marbles
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and let them go randomly
through the graph.
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Each time they arrive at some site,
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they will go out through some link
chosen at random to the next one.
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And again, and again, and again.
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And with small, growing piles,
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we keep the record of how many times
each site has been visited
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by these digital marbles.
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Here we go.
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Randomness, randomness ...
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and from time to time,
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also let's make jumps completely
randomly to increase the fun.
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And look at this:
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from the curves will emerge the solution.
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The highest piles
correspond to those sites
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which somehow are better
connected than the others,
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more pointed than the others.
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And here we see clearly
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which are the web pages
we want to first try.
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Once again,
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the solution emerges from the randomness.
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Of course since that time,
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Google has come up with much more
sophisticated algorithms,
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but already this was beautiful,
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and still,
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just one problem in a million.
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With the event of digital area,
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more and more problems lend
themselves to mathematical analysis,
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making the job of mathematicians
a more and more useful one.
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To the extent that a few years ago,
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it was ranked number one among
hundreds of jobs
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in a study about the best and worst jobs
-
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published by the Wall Street
Journal in 2009.
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Mathematician --
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best job in the world.
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That's because of the applications ...
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communication theory,
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information theory,
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game theory.
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Compressed sensing,
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machine learning,
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graph analysis,
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[....] analysis.
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And why not [....] processes,
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linear programming,
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or [fruit] simulation?
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Each of these fields have monster
industry reputations.
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And through them,
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there is big money in mathematics.
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And let me concede
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that when it comes to making
money from the math,
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the Americans are by a long shot
the world champions,
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with clever, emblematic billionaires
and amazing, giant companies,
-
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all resting, ultimately, on algorithm.
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Now with all this beauty,
usefulness and wealth,
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mathematics does look more sexy,
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but don't you think
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that the life a mathematical
researcher is an easy one.
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It is filled with perplexity,
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frustration --
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(Laughter)
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A desperate fight for understanding.
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Let me evoke for you
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one of the most striking days
in my mathematician's life.
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Or should I say,
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one of the most striking nights.
-
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And that time,
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I was staying at the Institute
for Advanced Studies in Princeton --
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for many years,
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the home of Albert Einstein,
-
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and arguably the most holy place
for mathematical research in the world.
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And that night I was working and working
on an elusive proof,
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which was incomplete.
-
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It was all about understanding
-
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the paradoxical stability
property of plasmas,
-
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which are a crowd of electrons.
-
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In the perfect world of plasma,
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there are no collisions and no friction
-
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to provide the stability
like we are used to.
-
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But still,
-
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if you slightly perturb
a plasma equilibrium,
-
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you will find that the
resulting electric shield
-
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spontaneously vanishes,
-
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or damps out,
-
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as if by some mysterious friction force,
-
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this paradoxical effect,
-
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called the Landau damping,
-
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is one of the most important
in plasma physics,
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and it was discovered
through mathematical ideas.
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But still,
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a full mathematical understanding
of this phenomenon was missing.
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And together with my former student,
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and main collaborator Clément Mouhot,
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in Paris at the time,
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we had been working for months
and months on such a proof.
-
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Actually,
-
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I had already announced by mistake
that we could solve it,
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but the truth is,
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the proof was just not working.
-
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In spite of more than 100 pages
of complicated, mathematical arguments,
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and a bunch discoveries,
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and huge calculation,
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it was not working.
-
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And that night in Princeton,
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a certain gap in the chain of arguments
was driving me crazy.
-
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I was putting in there all my energy
and experience and tricks,
-
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and still nothing was working.
-
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1am, 2am, 3am,
-
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not working.
-
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Around 4am I go to bed in low spirits.
-
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Then a few hours later,
-
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waking up and go,
-
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"Ah it's time to get
the kids to school --"
-
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What is this?
-
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There was this voice in my head, I swear.
-
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"Take the second term to the other side,
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fully transform and invert [near two]."
-
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(Laughter)
-
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Damnit,
-
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that was the start of the solution.
-
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You see,
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I thought I had taken some rest,
-
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but really my brain had
continued to work on it.
-
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In those moments,
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you don't think of your career
or your colleagues,
-
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it's just a complete battle
between the problem and you.
-
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That being said,
-
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it does not harm when you do get
a promotion in reward for your hard work.
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And after we completed our huge
analysis of the Landau damping,
-
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I was lucky enough
-
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to get the most coveted Fields Medal
-
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from the hands of the President of India,
-
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in Hyderabad on 19 August, 2010.
-
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An honor that mathematicians
never dare to dream.
-
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A day that I will remember until I [die].
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What do you think,
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on such an occasion,
-
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pride, yes?
-
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And gratitude to the man collaborators
who made this possible.
-
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And because it was a collective adventure,
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you need to share it,
-
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not just with your collaborators.
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I believe that everybody can appreciate
the [freedom] of mathematical research,
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and share the passionate stories
of humans and ideas behind it.
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And I've been working with my staff
at Institute Henri Poincaré,
-
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together with partners and artists
of mathematical communication worldwide,
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so that we can found our own,
very special museum of mathematics there.
-
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So in a few years,
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when you come to Paris,
-
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after tasting the great crispy baguette
and macaroons,
-
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please come visit us
at Institute Henri Poincaré,
-
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and share the mathematical dream with us.
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Thank you.
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(Applause)
Natasha Murashkina
The following subtitle has a typo. It should be “many” instead of “man.”
15:08 - 15:11
And gratitude to the man collaborators
who made this possible.
Retired user
7:46 should be: so I definitely want to interview him IN priority. (dot is also missing)
Brian Greene
This transcript was updated on 8/17/16.
At 15:08, the phrase "man collaborators" was changed to "many collaborators."