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Рыться в пыльных старых журналах
Feb. 8th, 2014 01:18 amThe history of mathematics is replete with injustice. There is a tendency to exhibit towards the past a forgetful, oversimplifying, hero-worshipping attitude that we have come to identify with mass behavior. Great advances in science are pinned on a few extraordinary white-maned individuals. By the magic powers of genius denied to ordinary mortals (thus safely getting us off the hook), they alone are made responsible for Progress.
The public abhors detail. Revealing that behind every great man one can find a beehive of lesser-known individuals who paved his way and obtained most of the results for which he is known is a crime of lèse majesté. Whoever dares associate Appollonius with Euclid, Cavalieri with Leibniz, Saccheri with Lobachevski, Kohn with Hilbert, MacMahon with Ramanujan should stand ready for the scornful reaction of the disappointed majority.
One consequence of this sociological law is that whenever a forgotten branch of mathematics comes back into fashion after a period of neglect only the main outlines of the theory are remembered, those you would find in the works of the Great Men. The bulk of the theory is likely to be rediscovered from scratch by smart young mathematicians who have realized that their future careers depend on publishing research papers rather than on rummaging through dusty old journals.
In all mathematics, it would be hard to find a more blatant instance of this regrettable state of affairs than the theory of symmetric functions. Each generation rediscovers them and presents them in the latest jargon. Today it is K-theory, yesterday it was categories and functors, and the day before, group representations. Behind these and several other attractive theories stands one immutable source: the ordinary, crude definition of symmetric functions and the identities they satisfy.
(G.-C. Rota, "A mathematician's gossip", Indiscrete thoughts, p.211-212.)
***
У меня все вышло по-другому. Эйленберг и Мур, придумавшие контрамодули, были именно что "великие люди", а не "менее известные индивидуумы". Это не помешало их изобретению быть совершенно забытым на несколько десятилетий. Я не был таким умным, чтобы уметь думать о карьере или переоткрывать подобные вещи с нуля. Но нашел я, заметил и запомнил их определение в пыльном старом журнале потому, что знал, где примерно мне нужно искать то, что мне может понадобиться. И тогда, когда узнал это.
The public abhors detail. Revealing that behind every great man one can find a beehive of lesser-known individuals who paved his way and obtained most of the results for which he is known is a crime of lèse majesté. Whoever dares associate Appollonius with Euclid, Cavalieri with Leibniz, Saccheri with Lobachevski, Kohn with Hilbert, MacMahon with Ramanujan should stand ready for the scornful reaction of the disappointed majority.
One consequence of this sociological law is that whenever a forgotten branch of mathematics comes back into fashion after a period of neglect only the main outlines of the theory are remembered, those you would find in the works of the Great Men. The bulk of the theory is likely to be rediscovered from scratch by smart young mathematicians who have realized that their future careers depend on publishing research papers rather than on rummaging through dusty old journals.
In all mathematics, it would be hard to find a more blatant instance of this regrettable state of affairs than the theory of symmetric functions. Each generation rediscovers them and presents them in the latest jargon. Today it is K-theory, yesterday it was categories and functors, and the day before, group representations. Behind these and several other attractive theories stands one immutable source: the ordinary, crude definition of symmetric functions and the identities they satisfy.
(G.-C. Rota, "A mathematician's gossip", Indiscrete thoughts, p.211-212.)
***
У меня все вышло по-другому. Эйленберг и Мур, придумавшие контрамодули, были именно что "великие люди", а не "менее известные индивидуумы". Это не помешало их изобретению быть совершенно забытым на несколько десятилетий. Я не был таким умным, чтобы уметь думать о карьере или переоткрывать подобные вещи с нуля. Но нашел я, заметил и запомнил их определение в пыльном старом журнале потому, что знал, где примерно мне нужно искать то, что мне может понадобиться. И тогда, когда узнал это.
