Russian Name Worshipper mystics and Cantor's set theory
in [Math]
|
Prev: PRIVATE NET TO EXPAND WEB SPACE: 'mmm.web(TM)' seeks to replace.com
Next: Solutions manual to Engineering Mechanics Statics 12th edition by Russell C. Hibbeler
From: Dave L. Renfro on 17 Sep 2009 14:49 Marko Amnell wrote (in part): > There is an interesting new book out about the > history of Cantor's set theory. [snip] > Naming Infinity: A True Story of Religious Mysticism > and Mathematical Creativity (Belknap Press) (Hardcover) > by Loren Graham (Author), Jean-Michel Kantor (Author) Thanks for mentioning this. I've read a lot about the Luzin [Lusin] mathematical school, both because of some interesting but little known real analysis work came out of it (see [1]) and because, off-and-on, I've been assembling/translating/organizing the historical development of real analysis and descriptive set theory (1870s to 1930s, mostly excluding the well worn paths that lead directly to the Lebesgue, Denjoy, etc. integrals during this time) -- see [2] for example. Although I can tell this book isn't going to tell me anything of significance mathematically, it definitely looks like it will be useful for some of the historical facts that can be very difficult to track down. [1] Kantorov wrote a paper in 1932 that made explicit use of what are now called porous sets. Kolmogorov wrote a couple of papers in the mid 1930s on are called contingents in Saks' "Theory of the Integral", and a lot of follow-up work was done by F. I. Smidov in the following decades, which also lead to some interesting but little known papers in the late 1950s and 1960s by Tuy Hoang and I. Ya. Plamennov and G. H. Sindalovskii). G. P. Tolstoff wrote several papers in the 1940s and 1950s, including one in 1942 that investigated fairly thoroughly what one can say about the rate at which the Lebesgue density converges to 1 for almost all points in a measurable set (some, but not all, of these were independently rediscovered by S. James Taylor in "On strengthening the Lebesgue density theorem", Fundamenta Mathematicae 46 (1959), 305-315; also, some of Tolstoff's results can be found on pp. 466-468 of Volume 2 of Nina Bary's "A Treatise on Trigonometric Series"). And there are many more examples I could give. [2] Mikhail Y. Suslin and Lebesgue's error http://groups.google.com/group/sci.math/msg/fb9d47de618ef57d Dave L. Renfro
From: Marko Amnell on 17 Sep 2009 15:32 On Sep 17, 9:49 pm, "Dave L. Renfro" <renfr...(a)cmich.edu> wrote: > Marko Amnell wrote (in part): > > > There is an interesting new book out about the > > history of Cantor's set theory. > > [snip] > > > Naming Infinity: A True Story of Religious Mysticism > > and Mathematical Creativity (Belknap Press) (Hardcover) > > by Loren Graham (Author), Jean-Michel Kantor (Author) > > Thanks for mentioning this. I've read a lot about the > Luzin [Lusin] mathematical school, both because of some > interesting but little known real analysis work came > out of it (see [1]) and because, off-and-on, I've been > assembling/translating/organizing the historical > development of real analysis and descriptive set > theory (1870s to 1930s, mostly excluding the well > worn paths that lead directly to the Lebesgue, Denjoy, > etc. integrals during this time) -- see [2] for example. > Although I can tell this book isn't going to tell me > anything of significance mathematically, it definitely > looks like it will be useful for some of the historical > facts that can be very difficult to track down. > > [1] Kantorov wrote a paper in 1932 that made explicit use > of what are now called porous sets. Kolmogorov wrote > a couple of papers in the mid 1930s on are called > contingents in Saks' "Theory of the Integral", and a lot > of follow-up work was done by F. I. Smidov in the following > decades, which also lead to some interesting but little > known papers in the late 1950s and 1960s by Tuy Hoang > and I. Ya. Plamennov and G. H. Sindalovskii). G. P. Tolstoff > wrote several papers in the 1940s and 1950s, including > one in 1942 that investigated fairly thoroughly what > one can say about the rate at which the Lebesgue density > converges to 1 for almost all points in a measurable set > (some, but not all, of these were independently rediscovered > by S. James Taylor in "On strengthening the Lebesgue density > theorem", Fundamenta Mathematicae 46 (1959), 305-315; > also, some of Tolstoff's results can be found on > pp. 466-468 of Volume 2 of Nina Bary's "A Treatise on > Trigonometric Series"). And there are many more examples > I could give. > > [2] Mikhail Y. Suslin and Lebesgue's error > http://groups.google.com/group/sci.math/msg/fb9d47de618ef57d Thanks for the link. Your [2] is an interesting post. There is a good review of this book by Jim Holt in the August 27 issue of the London Review of Books: http://www.lrb.co.uk/v31/n16/holt01_.html Unfortunately, the LRB no longer provides free access online to their articles. But you can buy it as a PDF for £2.75.
From: Dave L. Renfro on 17 Sep 2009 16:27 Marko Amnell wrote: > Thanks for the link. Your [2] is an interesting post. I just remembered that I made a more mathematical follow-up to that post, which is in the same thread, but in case anyone reading is interested and didn't think to look at the rest of the thread . . . http://groups.google.com/group/sci.math/msg/714f47a4a2edc7ae Dave L. Renfro
From: That One on 19 Sep 2009 21:10 The general impression I've been getting is that Greater Russia (for lack of a better term) was a hotbed of genius until Stalin fucked everything up. D.
From: Bappa on 20 Sep 2009 05:50
On Sep 18, 3:42 am, Marko Amnell <marko.amn...(a)kolumbus.fi> wrote: > There is an interesting new book out about the > history of Cantor's set theory. It seems to > me that the book lends support to Feyerabend's > philosophy of science in _Against Method_. > Science can progress through *any* method, Sorry, Marko, this is dead wrong. The only valid *method* in science is the *experimental* method - meaning, repeatability of results under controlled and same conditions. The rest is analysis and discussion. This is what I was taught in my engineering institute (First Year) by the profs. in the Humanities Dept. IIT Kharagur was the only IIT where there was a firmly established and motivated Humanities department. > including the paradoxical fact that the progress > of mathematics was aided by the mysticism > of Russian mathematicians who accepted > Cantor's set theory because it fit their > mystical beliefs. Now what has maths to do with science? The Queen of Arts is Mathematics, and Science pays the most humble homage to Her. Cheers, Arindam Banerjee. |