Jim Choate <ravage@ssz.com> writes:

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From: dlv@bwalk.dm.com (Dr.Dimitri Vulis KOTM) Date: Thu, 08 Jan 98 23:45:25 EST

Janos Bolyai was the son of the math professor Farkas B. in Buda(best).

Who also worked with Gauss and probably beat Gauss to any solution to the problem of non-euclidean geometry (see Kurzer Grundriss eines Versuchs, p. 46).

I'm sorry, I don't have the time to look this up. If you're trying to prove that Gauss was not a nice person, I don't believe it. And if the best argument you can make is to cite Bolyai's claims that Lobachevsky was not a real person but a "tentacle" of Gauss, created to persecute Bolyai (gee, that sounds vaguely familiar...), and you can't find any more dirt on Gauss, then it proves to me that he was indeed a remarkably nice person. Gauss rose from poverty to become one of the premier mathematicians of his time - in the era when sciences were considered a hobby suitable only for the noble-born and wealthy. Gauss did a lot to help other people in many ways, both as individuals, and in targeting his research to solve practical problems for good of the humanity. I was very fortunate to have met Paul Erdos and some living people whom I regard as mathematicial geniuses (not necessarily on par with Gauss); without exception their talents make them wonderful helpful people. You also haven't explained how Bolyai could have been Gauss's school friend, being 25 years younger. Crypto-relevant stuff: In 11-17 centuries, mathematicians who weren't independently wealthy, made their living by selling their service to/as "reckoners" (computers), accountants, bookkeepers, and astrologers. There was, you may recall, a similar dispute between Tartagla and some other Italian about who first discovered the formula for roots of 3rd order polynomials. This problem had some use in computing the internal rate of return (a practical accounting problem of interest at that time), but the main reason why each wanted to claim priority was for marketing reason: being its inventor would have enhanced their reputation and allowed them to charge higher fees or to get new clients for their bookkeeping businesses (because that's what they did for a living). So, the following technique emerged and was widely used by mathematicians at that time to claim the peiority. They would write out their result (or the proof); they would make an anagram, or take the first letter of each (latin) word, etc; and they would mass-mail it to every mathematician they knew, so they'd receive it at about the same time; then they'd publish it at leisure, knowing that once they decode the anagram or publish the proof whose first letters coincide with their broadcast, it will be evident that they had it on the date it was first mailed, yet they haven't revealed enough information for anyone to steal the result. The nice folks in goettingen who kept publishing Gauss's papers up until WW2 found that he too came up with a non-Euclidean geometry in 1818 (when Bolyai was 16 years old). They did not report finding any communications from Bolyai to Gauss about non-euclidean geometry in that time frame. Unfortunately if Bolyai makes the claims that he communicated his results privately to Gauss and that Gauss then concocted a tentacle named Lobachevsky, who's not a real person, then I have to discard the entire claim as a figment of his psychotic imagination.

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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.

Both John Bolyai's "The Science of Absolute Space" and Nicholas Lobachevski's "The Theory of Parallels" are included in Roberto Bonola's "Non-euclidean Geometry" (Dover, ISBN 0-486-60027-0 $5.50). I certainly had no problem reading the 3 combined books.

I was just looking at the translators notes to Lobachevski, it was done by George Bruce Halsted of 2407 San Marcos St, Austin, Tx. May 1, 1891.

What's your point? Are you suggesting that Lobachevsky first published it that year? He was long dead by then. He first gave a talk on non-euclidean geometry in 1825 and published the seminal paper in 1829 - before Bolyai's work was published in 1832 as an appendix to his father's textbook. Bolyai saw the German translation of Lobachevsky's paper in 1840. Are you trying to say that a paper's not really published until it's translated into english by some guy in Texas? :-)

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well accepted by his peers. Neither Bolyai nor Lobachevsky knew about Gauss's work.

Not true, Bolyai wrote him several letters as described in his book and the various prefaces. Lobachevski's book was promoted by Gauss as the first and truely critical work on non-euclidean geometry. In a rare show of magnamity Gauss even admits that Lobachevski's work exceeded his own.

What exactly is your beef with Gauss promoting Lobachevsky? When Lobachevsky's paper reached Europe, the "consensus" (I hate consensuses) among the working mathematicians was that non-euclidean geometry was nuts. Incidentally, Bolyai was among the people screaming that it was all wrong and renouncing his own 1832 publication. Gauss could have announced that he came up with the same results before Lobachevsky, but never bothered to publish them. Gauss could have also announced that he's gone through Lobachevsky's papers and endorses the results. His reputation capital was such that either claim would have been accepted by the mathematical community. He did neither. He endorsed Lobachevsky's paper as being sufficiently interesting to be translated and studied and checked; perhaps he himself was not sure that it was error-free. He also pushed for Lobachevsky's election into the Hannover academy of sciences - not just for the non-euclidean theory, for for his many other interesting results. Gauss also promoted many other people who did outstanding mathematical work. There wasn't a "consensus" that non-euclidean geometry was kosher until about 1865, by which time all 3 were dead or retired. Likewise when Kantor first announced that the infinite number of real numbers is greater that the infinite number of integers, the "consensus" among working mathematicians was that this was crazy. Likewise when a certain well-known Dutch mathematician mass-mailed many people a few years ago announcing that he's been having sex with the mother goddess, the "consensus" was that he's gone nuts. Finally, if Gauss said that Lobechevsky's paper was more complete and detailed than Gauss's unpublished notes from 1818, it may very well have been true.

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I have no idea what Bonola wrote, but if he's just repeating the allegation 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.

He wrote a classic work on non-euclidean geometry that was quite popular in 1912 when it was printed.

If the book repeats the bizarre claims made by Bolyai, when he was paranoid, depressed, and outright psychotic - such as the claim that Lobachevsky was not a real person, but a "tentacle" of Gauss created to torture Bolyai - then it's not worth reading. Sadly, some people do go insane. Trying to find the truth in their paranoid rants is a waste of time, just like reading Timmy May's rants is a waste of time. --- Dr.Dimitri Vulis KOTM Brighton Beach Boardwalk BBS, Forest Hills, N.Y.: +1-718-261-2013, 14.4Kbps