MHB Favorite Mathematician: Rene Descartes

[topsquark]

I don't have much to say on the subject but because it's me...

I'd like to nominate not a Mathematician, but a Physicist. Some of Hawking's landmark works in Physics are showing some cracks, and there are a number of Physicists (and certainly Mathematicians) that can do everything that he can do, but there's one thought that makes me propose him:

He used to do most or all of it in his head.

-Dan

 

[youth4ever]

I like very much Euler.
Imagine how limited mathematics would be without the Euler formula.

I remained impressed for the rest of my life when I saw how he solved the famous limit

$$Sum from 0 to Infinity 1/x^2$$

A Famous Infinite Series

 

[Deveno]

I have 2 (both algebraists, of course):

Evariste Galois. He was misunderstood in his own lifetime, never got the education nor the recognition he wanted, was in and out of jail, and died tragically young, allegedly over the honor of a young lady (the truth about the duel, and even who he dueled, may never be known).

He was passionate, pig-headed, arrogant, and foolish. He died at 20 having a scant 60 pages of work to his name, almost all of it published posthumously. Oh, and he revolutionized mathematics.

Emmy Noether. A victim of sexual discrimination for most of her life, whose penetrating insight into algebraic structures gave abstract algebra the form we know it as today. I believed she casually remarked at a dinner party once that topology could be viewed in a more cohesive light by categorizing spaces by their associated topological groups. Reputedly one of the best lecturers and teachers ever, who often let her students and collaborators take credit for her work. Her first few years as a professor were unpaid.

Like so many other German intellectuals of the 20-th century, Emmy Noether was persecuted for being Jewish, eventually stripped of her position, and forced to flee her country. Noetherian rings are named after her.

Taken together, these two mathematicians remind me that mathematicians are exquisitely HUMAN, and possesses individual quirks that give them character, not only just genius.

 

[mathbalarka]

Paul Erdos.

Apparently a story I recall posted here about him and his collaborator Graham explains how sane minded he was. The one and only who can match the works of Euler (who, in turn, matches the works of Ramanujan - though of course not the age which is challenged by Terry Tao lately) the establisher of something I call TheBook-ism, a kind of a religion I believe in. The Number Theorist Extraordinaire, analytic, algebraic, transcendental, diophantine and combinatorial all the same; and the man whom communists feared, being one and only of the Hungarians to be able to go anywhere out and in of Hungary he and do anything he wants. Locally mad, totally genius and who accused of the supreme fascist of stealing his socks.

 

[ModusPonens]

I have to review my previous list. Not the names, but the order. Grothendieck must come first. He is the mathematician who has fascinated me the most, both on a professional level, and on a human level. Here's a quote from the short biography published on a AMS magazine:

Schwartz [Grothendieck's PhD advisor] gave Grothendieck a paper to read that he had just written with Dieudonné, which ended with a list of fourteen unsolved problems. After a few months, Grothendieck had solved all of them. Try to visualize the situation: On one side, Schwartz, who had just received a Fields Medal and was at the top of his scientific career, and on the other side the unknown student from the provinces, who had a rather inadequate and unorthodox education.

If you're so inclined, find the biographical articles from the AMS. There are several. The best one is divided in two parts. It's like reading the biography of an extraterrestial superior mind.

 

[Prometheus1]

I've heard so many amazing stories about Grothendieck. What's amazing is that he was able to view mathematics from bird's-eye view. Even when I'm learning elementary results I learn by considering specific examples, and find generality bit of an effort. He seems to have been completely the other way round. Consider, for example, the story of the Grothendieck prime (57):

One striking characteristic of Grothendieck’s mode of thinking is that it seemed to rely so little on examples. This can be seen in the legend of the so-called “Grothendieck prime”. In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57.”

But Grothendieck must have known that 57 is not prime, right? Absolutely not, said David Mumford of Brown University. “He doesn’t think concretely.” Consider by contrast the Indian mathematician Ramanujan, who was intimately familiar with properties of many numbers, some of them huge. That way of thinking represents a world antipodal to that of Grothendieck. “He really never worked on examples,” Mumford observed. “I only understand things through examples and then gradually make them more abstract. I don’t think it helped Grothendieck in the least to look at an example. He really got control of the situation by thinking of it in absolutely the most abstract possible way. It’s just very strange. That’s the way his mind worked.