Jim Choate
From: Tim May
"Name me one..."? How about Gauss, who didn't publish many of his results. Or, of course, Fermat, ironically linked to Wiles.
True, Gauss didn't publish many of his results and he wasn't famed for that either. He *was* famed because he *did* publish some of his works. In fact, if you study Gauss you find a insecure introvert who in general hated his competition. He lied in his correspondance about work he supposedly did (see his relations with Bolyai who was a friend of his from school - "Non-euclidean Geometry" by Roberto Bonola; Dover ISBN 0-486-60027-0 $5.50). Yes, Gauss was respected for his math, he was hated for his humanity, or lack thereof. If anything Gauss' bahaviour held back science because of his self-interest.
Janos Bolyai was the son of the math professor Farkas B. in Buda(best). While an undergraduate, he was working with a fellow named Szasz on non-euclidean geometry. In 1832 he published his findings as an appendix to his father's textbook. he did show that Euclid's axiom about parallel lines is independent of the others and did explore the geometry that arises if you omit this axiom. According to my sources, the appendix is "Wronski-like" to the point of unreadability. Apparently no one actually read it until B. started arguing about who did what first. The Russian mathematician Lobachavsky, in Kazan, came up with very similar results at the same time. He announced them at a talk in 1826 and published them in 1829. he was clearly first. There's no evidence that B. knew of L.'s results; these ideas were coming naturally from the work of the other mathematicians at this time. In 1837 B. submitted a paper on quaternions to some sort of competition; it received a very nagative review, which caused him to go crazy. He started working on logical foundations of geometry in weird ways, setting himself goals that he couldn't achieve. Then in 1940 he came across a German translation of Lobachevsky's paper on non-eucldiean geometry. he went totally bonkers, claiming that a) Lobachevsky is not a real person, but a "tentacle" of Gauss; b) that gauss is out to nail him, b) that their result is wrong anyway (although he never explained how). He died relatively young and totally insane. As someone pointed out, much of gauss's writings were not published until after his death. The folsk researching his notes were shocked to discover that Gauss did actually come up with very similar non-euclidean geometry ideas as early as 1818 (not surprisingly - these ideas were literally floating in the air). However he chose not to publish them, not realizing how important they would be, and also fearing that they woudn't be well accepted by his peers. Neither Bolyai nor Lobachevsky knew about Gauss's work. I have no idea what Bonola wrote, but if he's just repeating the allegations Bolyai made about Gauss while suffering from depression and paranoia, they have no more truth in them than the Timmy May rants on this mailing list. By the way, the same gossip prompted the Tom Lehrer song about Lobachevsky. I also don't see how Bolyai could have been gauss's chool friend, being 25 years younger than K.F. And it's not a dichotomy; it's a trichotomy: one can * do research and publish the results in a refereed journal. This is of use only for tenue-track faculty who need to publish to get tenured. Many refereed journals are extrmely political, with "friends" being published ahead of the queue, and "strangers" kept waiting for a couple of years while the "friends" can be advised of the manuscripts and publish their own version of the results. * do research on some practical problems whose solution interests some wealthy folks. Most tenured faculty dream of doing that; many actually do. * do research for fun/as a hobby; some wealthy folks do that, or pay others to do that.
Fermat in general published most of his work, however, much of it was lost including his proof. His statement was that it was too long to be written in the margin of the book, not that he didn't write it down. The implication being that he *had* written it down and it got misplaced or lost it.
Fermat was a judge. He did math for fun. (Strictly speaking, he did a lot his mathematical research to facilitate his gambling hobby - at the time when securities investment was viewed as a form of gambling no different from cards, dice, horse races, dog fights/races, cock fights, etc. How is Timmy's bet that INTC will fall (and shorting it, if he's got any brains) different from some Jose's bet that the rooster named Pedro will rip out the guts of the rooster named Jorge? I've known sports gamblers who would bet tens of thusands of dollars on a single game, and they also invested in securities; and the research they did before betting $40K on a basketball game was comparable to the research before taking a similar risk on stocks or bonds. --- Dr.Dimitri Vulis KOTM Brighton Beach Boardwalk BBS, Forest Hills, N.Y.: +1-718-261-2013, 14.4Kbps