But in order to solve a problem, you’ve got to know at the outset exactly what the problem is! In mathematical research, clearly identifying what it is you are trying to do is a crucial, and often very tricky, first step.
Humbly, without pretending to know much of anything, I’m teaching myself basic concepts that physicists have known for half a century.…
The complexity and the confusion of the adventure put me in a good mood: I take such dreams as a sign that my brain is in good working order.
And even if the problem is simple to state, it’s probably difficult to prove. What’s more, it asks an original question about a well-known model. So far, so good; I’m very pleased.
Conclusion: We’ll have to go on being devious.
Scientists who worked on the Manhattan Project in the 1940s were fond of saying that Martians really do exist: they have superhuman intelligence, speak an incomprehensible language, and claim to come from a place called Hungary.
I still vividly recall the amusing anecdotes recounted by the speakers that day. One in particular of Kruskal and two colleagues talking in an elevator, so deeply immersed in conversation that they went up and down for twenty minutes, oblivious to the people getting on and off.
John Nash, my mathematical hero, is said to have regularly put himself under fantastic pressure by announcing results that he did not yet know how to prove.
But then … suddenly, in 1993, Scheffer showed that Euler’s equations in the plane are consistent with the spontaneous creation of energy!
One way or another the Problem simply has got to be tamed, even if it means going without sleep. I’m going to take Landau with me everywhere—in the woods, on the beach, even to bed. Time now for him to watch out!
Every mathematician worthy of the name has experienced, if only rarely, the state of lucid exaltation in which one thought succeeds another as if miraculously.… Unlike sexual pleasure, this feeling may last for hours at a time, even for days. [André Weil]
“Hmmmm, now that resembles a Young inequality … and then it’s like proving Minkowski’s inequality … you change the variables, separate the integrals.…” * * * I went into semi-automatic pilot, drawing on the whole of my accumulated experience … but in order to be able to do this, first you’ve got to tap into a certain line —the famous direct line, the one that connects you to God, or at least the god of mathematics. Suddenly you hear a voice echoing in your head. It’s not the sort of thing that happens every day, I grant you. But it does happen.
Doing mathematics is no different, really. You’re constantly exploring, your eyes and ears are always open, and then every once in a while you’re completely smitten by something and you pour your heart and soul into it, you tell yourself over and over again, hundreds and hundreds of times, that nothing else matters. Well, almost nothing else.
In the world of Paris rapid transit, each of the RER lines is remarkable in its own way. In the case of the RER B, the line I take to go to work, it would not be an exaggeration to say that it breaks down every day, and that most days it is packed until midnight or one in the morning. To be fair, it also has its virtues: it assures its passengers of regular physical exercise by making them change trains frequently, and it improves their mental agility by keeping them in suspense as to exactly when a train will reach its destination and where it will stop along the way.
(always fly economy class, by the way, the girls are statistically cuter).
And then, after day has broken, after the sun has climbed high into the sky, a phase of depression inevitably follows. You lose all faith in the importance of what you’ve achieved. Any idiot could have done what you’ve done, go find yourself a more worthwhile problem and make something of your life.
Cédric, you’re a father—ritual suicide is not an option.