Birth of a Theorem: A Mathematical Adventure by Cédric Villani
Authors: Cédric Villani
indices …
I’ll think about it some more.
Best wishes,
Clement
Date: Fri, 26 Dec 2008 20:24:12 + 0100
From: Clement Mouhot
To: Cedric Villani
Subject: Re: parts 1 and 2, almost done
What I’ve been calling the “time boundary condition” is the fact that since the loss on the index due to scattering is linear with respect to time (as I put it in the assumption), that meant there had to be a time boundary if the loss wasn’t to be greater than a certain constant. But now it seems to me, having looked at your “analytic” file, that the assumption has to be strengthened, something like a loss
$$
\varepsilon \, \min \{1, (t-s) \}
$$
which allows the loss to remain small for large $t$ and for $s$ far from $t$ …
v. best, clement
NINE
Princeton
January 1, 2009
It’s pitch-dark; the taxi driver’s completely bewildered. His GPS is pointing in a plainly absurd direction: straight ahead into the trees.
I try appealing to his common sense. We’ve already passed by here once before, obviously the GPS is on the fritz, there’s no choice but to explore the surrounding area. In other words, we’re lost. The only thing that’s certain is that if we follow the machine’s instructions, we’ll wind up getting stuck in the mud and the melting snow!
In back, the children aren’t the least bit worried. My daughter is asleep, worn out by the plane trip and the change in time. My son is watching intently. He’s only eight years old but already he’s been to Taiwan, Japan, Italy, Australia, and California, so getting lost somewhere in New Jersey isn’t about to frighten him. He knows that everything’s going to turn out all right.
We drive around some more, see the twinkling lights of civilization in the distance, and then encounter a human being at a bus stop who gives us directions. A GPS has no monopoly on topographic truth.
Finally, the Institute for Advanced Study—the IAS, as everyone calls it—comes into view. A little like a castle rising up in the middle of a forest. We had to go around a large golf course in order to find it.…
* * *
It is here that Einstein spent the last twenty years of his life. True, by the time he came to America he was no longer the dashing young man who had revolutionized physics in 1905. Nevertheless, his influence on this place was deep and long-lasting, more so even than that of John von Neumann, Kurt Gödel, Hermann Weyl, Robert Oppenheimer, Ernst Kantorowicz, or John Nash—great thinkers all, whose very names send a shiver down the spine.
Their successors include Jean Bourgain, Enrico Bombieri, Freeman Dyson, Edward Witten, Vladimir Voevodsky, and many others. The IAS, more than Harvard, Berkeley, NYU, or any other institution of higher learning, can justly claim to be the earthly temple of mathematics and theoretical physics. Paris, the world capital of mathematics, has many more mathematicians. But at the IAS one finds the distillate, the crème de la crème. Permanent membership in the IAS is perhaps the most prestigious academic post in the world!
And, of course, Princeton University is just next door, with Charles Fefferman and Andrei Okounkov and all the rest. Fields medalists are nothing out of the ordinary at Princeton—you sometimes find yourself seated next to three or four of them at lunch! To say nothing of Andrew Wiles, who never won the Fields Medal but whose popular fame outstripped that of any other mathematician when he broke the spell cast by Fermat’s great enigma, which for more than three hundred years had awaited its Prince Charming. If paparazzi specialized in mathematical celebrities they’d camp outside the dining hall at the IAS and come away with a new batch of pictures every day. This is the stuff that dreams are made on.…
But first things first: we had to locate our apartment, our home for the next six months, and then get some
I’ll think about it some more.
Best wishes,
Clement
Date: Fri, 26 Dec 2008 20:24:12 + 0100
From: Clement Mouhot
To: Cedric Villani
Subject: Re: parts 1 and 2, almost done
What I’ve been calling the “time boundary condition” is the fact that since the loss on the index due to scattering is linear with respect to time (as I put it in the assumption), that meant there had to be a time boundary if the loss wasn’t to be greater than a certain constant. But now it seems to me, having looked at your “analytic” file, that the assumption has to be strengthened, something like a loss
$$
\varepsilon \, \min \{1, (t-s) \}
$$
which allows the loss to remain small for large $t$ and for $s$ far from $t$ …
v. best, clement
NINE
Princeton
January 1, 2009
It’s pitch-dark; the taxi driver’s completely bewildered. His GPS is pointing in a plainly absurd direction: straight ahead into the trees.
I try appealing to his common sense. We’ve already passed by here once before, obviously the GPS is on the fritz, there’s no choice but to explore the surrounding area. In other words, we’re lost. The only thing that’s certain is that if we follow the machine’s instructions, we’ll wind up getting stuck in the mud and the melting snow!
In back, the children aren’t the least bit worried. My daughter is asleep, worn out by the plane trip and the change in time. My son is watching intently. He’s only eight years old but already he’s been to Taiwan, Japan, Italy, Australia, and California, so getting lost somewhere in New Jersey isn’t about to frighten him. He knows that everything’s going to turn out all right.
We drive around some more, see the twinkling lights of civilization in the distance, and then encounter a human being at a bus stop who gives us directions. A GPS has no monopoly on topographic truth.
Finally, the Institute for Advanced Study—the IAS, as everyone calls it—comes into view. A little like a castle rising up in the middle of a forest. We had to go around a large golf course in order to find it.…
* * *
It is here that Einstein spent the last twenty years of his life. True, by the time he came to America he was no longer the dashing young man who had revolutionized physics in 1905. Nevertheless, his influence on this place was deep and long-lasting, more so even than that of John von Neumann, Kurt Gödel, Hermann Weyl, Robert Oppenheimer, Ernst Kantorowicz, or John Nash—great thinkers all, whose very names send a shiver down the spine.
Their successors include Jean Bourgain, Enrico Bombieri, Freeman Dyson, Edward Witten, Vladimir Voevodsky, and many others. The IAS, more than Harvard, Berkeley, NYU, or any other institution of higher learning, can justly claim to be the earthly temple of mathematics and theoretical physics. Paris, the world capital of mathematics, has many more mathematicians. But at the IAS one finds the distillate, the crème de la crème. Permanent membership in the IAS is perhaps the most prestigious academic post in the world!
And, of course, Princeton University is just next door, with Charles Fefferman and Andrei Okounkov and all the rest. Fields medalists are nothing out of the ordinary at Princeton—you sometimes find yourself seated next to three or four of them at lunch! To say nothing of Andrew Wiles, who never won the Fields Medal but whose popular fame outstripped that of any other mathematician when he broke the spell cast by Fermat’s great enigma, which for more than three hundred years had awaited its Prince Charming. If paparazzi specialized in mathematical celebrities they’d camp outside the dining hall at the IAS and come away with a new batch of pictures every day. This is the stuff that dreams are made on.…
But first things first: we had to locate our apartment, our home for the next six months, and then get some
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