From: rusin@vesuvius.math.niu.edu (Dave Rusin) Newsgroups: sci.math Subject: You know you've made it in mathematics when... Date: 15 Feb 1998 04:14:32 GMT Musings on a quiet Saturday afternoon: One sign of a mathematician's success is to have his or her name identified with an object of study, or indeed a whole area of study. I looked to see who is mentioned by name in the Mathematics Subject Classification scheme. (I had the 1980 scheme at home.) There were many more names than I would have expected, and more than I could identify! A few observations: Abel is bestowed the unique honor of having his name used without capitalization. (A few mathematicians are known through abbreviations, e.g. KdV, but these seem all to be spelled out in the MSC.) Lie and Fourier are the two people mentioned by name in the top-level (2-digit) classifications: Lie Groups - 22, and Fourier Analysis - 42. At the next level (3-digit headings) we have also Boole, Diophantus, Artin, Jordan, Abel, Riemann, Banach, Hilbert, von Neumann, Caratheordory, Hamilton, Jacobi, Markov, Lagrange, the K-theorists Grothendieck, Whitehead, Steinberg, and the geometers Hjelmslev, Barbilian. Archimedes is referred to only in the negative! (Non-Archimedean XXX). A few others are known in both positive and negative form (Newton, Euclid, Abel, Desargues, ...). How many Neumann's are there? We have von Neumann (mentioned in 16E50, 46L, 47B10, 47C15), and these others: * 20E06 Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations * 32F20 \overline\partial- and \overline\partial_b-Neumann problems; also * 35N15 \overline\partial-Neumann problem and generalizations; formal complexes There are also Fuchs and Fuks, and Schwartz and Schwarz. I'm _guessing_ that other occurrences of identical names represent the same person, active in several areas, but in some cases I'm not so sure. (There _seem to be_ no references to Noether's father, for example.) The fields of algebra and topology seem more inclined to use people's names to identify a field; analysis and applications less so. Indeed, in the applications to physics (areas 70-86) almost all the names mentioned are from fairly far back in mathematical history. There are quite a few more names in the reorganized number theory (section 11) than in its older presentation (section 10). Generally, newer areas tend to name-drop more frequently. The most heavily-used names include Galois and Riemann (no surprise there) as well as Hermite (much more than I would have guessed). Of course, there are a lot of references to Herr Dr. Eigen, too... I noticed Mersenne and Pascal to be among the missing despite having their names used as common mathematical adjectives. Of course, there are plenty of first-rate mathematicians (e.g. most of the newer Field's medalists) who are not mentioned. I suppose it's only a matter of time until we have "Atiyah theory", say. I was sorry not to see "student" listed among the Statistics topics :-( Attached below are the 285 names I spotted (I may have missed some, especially those only added in the 1991 revisions of the MSC). If you'd like to know who these people are and what their niches are, try this word-lookup server for the MSC: http://www.ams.org/mathweb/mi-msc_keyword.html Many of them have short bios at the MacTutor History of Mathematics Archive: http://www-groups.dcs.st-andrews.ac.uk/~history/ You can look over the MCS yourself; it's available through http://www.ams.org/mathweb/mi-classification.html When you find names I failed to notice, please let me know. dave Abel Adams Aleksandrov Anosov Archimedes Aronszajn Artin Azumaya Baire Baker Banach Barbilian Bayes Bell Bergman Bernoulli Bernstein Bessel Bethe Birch Blaschke Bockstein Boole Borel Bott Brauer Brewer Brown Burgers Burkill Burnside Busemann Calderon Cantor Caratheodory Cartan Cauchy Cesaro Chebyshev Chern Choquet Chow Clifford Cremona Daniell Darboux deRham Dedekind Dehn DeMorgan Denjoy Desargues Descartes deVries Diophantus Dirac Dirichlet Ditkin Drinfeld Dyer Eckmann Eilenberg Einstein Engel Epstein Erdos Euclid Euler Fatou Fermat Feynman Finsler Fitting Fourier Franz Frattini Frechet Fredholm Frobenius Fuchs Fuks Gabriel Gale Galerkin Galois Galton Gateaux Gauss Gegenbauer Gel'fand Gersten Godel Goldbach Goldie Gordon Gorenstein Grassmann Green Grothendieck Haar Hadamard Hamilton Hardy Hartogs Hausdorff Hecke Helly Helmholtz Helson Hermite Heyting Higman Hilbert Hill Hilton Hjelmslev Hodge Holder Hopf Iwasawa Jackson Jacobi Jacobsthal James Jordan Kaehler Kan Karman Karoubi Kasparov Klein Kleisli Kloosterman Kolmogorov Korteweg Kothe Kovalevskaya Krasner Kronecker Krull Kummer Kunneth Lagrange Laguerre Lame Langlands Laplace Lashof Lebesgue Lefschetz Legendre Lerch Lidstone Lie Lindelof Liouville Lipschitz Littlewood Ljusternik Lorentz Lucas Lukasiewicz Lyapunov Macaulay MacLane MacLaurin Maeda Mal'cev Marin Markov Massey Mathieu Mikunski Mills Milnor Minkowski Moebius Montel Moore Morse Nash Navier Neumann Nevanlinna Newton Nikodym Nikolski Noether Norlund Orlicz Pade Paley Pappus Pareto Peano Perron Petersson Pfaff Picard Poincare Poinsot Poisson Popov Post Postnikov Pruefer Radon Ramsey Raphson Rayleigh Reidemeister Reinhardt Ridge Riemann Riesz Ritz Roch Rossby Runge Saint-Venant Salpeter Sasaki Schmidt Schnirelman Schoenflies Schroedinger Schubert Schur Schwartz Schwarz Selberg Serre Shannon Shimura Sidon Siegel Silva Sitnikov Smale Sobolev Spanier Spenser Steenrod Stein Steinberg Steinger Stieltjes Stirling Stokes Sturm Suslin Swinnerton Sylow Tate Tauber Taylor Teichmuller Thue Toeplitz Tricomi Tsien Turan Turing Ulm Vekua Verma Veronese Villamayor Volterra von Neumann Wall Walsh Watson Weierstrass Weil Weiner Weinstein Weyl Whitehead Wiener Witt Yang Zorn Zygmund and I already see I missed Boltzman ============================================================================== From: rusin@vesuvius.math.niu.edu (Dave Rusin) Newsgroups: sci.math Subject: Re: You know you've made it in mathematics when... Date: 16 Feb 1998 01:58:43 GMT Jos Horikx wrote: >> Brauer Brewer Brown ... etc. > >'Brauwer' has to be spelled as: > >Brouwer > * Rotterdam 1881 > + Blaricum 1966) You're confusing LEJ Brouwer (Brouwer Fixed Point Theorem, Intuitionism debate, etc.) with Richard Brauer (modular group representations, Brauer Group in ring theory, etc.) Allow me to respond to a couple of other posters as well: My list was intended to reflect the AMS/Zbl Math Subject Classifications. In particular, while _other mathematicians_ may frequently fail to capitalize names, or use people's names as familiar adjectives, I was trying to keep to a well-defined dataset. Here, Hausdorff is always capitalized, Shelah/Lax/Milgram/... do not appear, and "Archimedean" is used only preceded by "non-". On the other hand, it appears the 1980 list I was working from differs more from the current list than I had thought. I had looked at the updated list in some areas which I knew had undergone significant revisions, but failed to check others. Thus there are indeed more names in the 1991 and 1995 updates to the MSC (and presumably more will be added when the 2000 scheme comes out). Among those names now present are several in ring theory and related fields, brought to my attention in email: Auslander Cohen Hochshild Jacobson Kac Kirillov Moody Ore Peirce Reiten Sylvester Virasoro Fibonacci is indeed included in area 11 now; I suppose it's a compliment to him that I could look right at his name and not even think of it as a proper name, but rather just a term in mathematics. I will have to remember Leibniz as a notable omission from the MSC, where his name indeed does not appear! dave ============================================================================== From: rusin@vesuvius.math.niu.edu (Dave Rusin) Newsgroups: sci.math Subject: Re: You know you've made it in mathematics when... Date: 16 Feb 1998 23:08:28 GMT Dave Rusin wrote: >Musings on a quiet Saturday afternoon: Since it seems to be the case that quite a few names were added in the 1985 and 1990 revisions of the Mathematics Subject Classifications, and since I seem to have introduced a few spelling and transcription errors into the list, I decided to try a more methodical approach. At http://www.zblmath.fiz-karlsruhe.de/class/msc.html I found the whole 1991 MSC in one file. I inserted a linefeed before each capital letter, sorted, and hand-edited to get a better list of who's in the MSC. Rather than repost the list, I've left the names at 98/MSC.names A few other tidbits emerged: Abel is treated in another unique way: his name is combined as the root in the word "metabelian". Those whose names appear more than 10 times are Lie [54] Fourier [35] Banach [27] Riemann [24] Hilbert [23] Abel [23] Markov [20] Galois [13] Hermite [13] Boole [11] Euclid [11] Among those whose names are included in a non-obvious way are al'Khwarizmi ("algorithm") and Amerigo Vespucci ("Americas"). I'm assuming words like Creep, Radical, Peculiar, etc. are not references to anyone in particular :-). Markov can be added to those whose name is also used in the negative. The MSC refers both to Gelfand and to Gelfond; I assume these are the same person. On the other hand, I must wonder if there are two Steins 32E10 Stein spaces, Stein manifolds 62J07 Ridge regression; James-Stein estimators and two Martins 03E50 Continuum hypothesis and Martin's axiom, See also 04A30,54A25 31C35 Martin boundary theory, See also 60J50 A number of names which I posted previously have been removed from the MSC; fame is so fleeting! Kummer was dropped in 1985 and Burkill, Gabriel, Peano, Poinsot, Silva, Tricomi, Tsien in 1991. Even better than being attached to "XXX spaces" or "of XXX type" is to play the title role in "XXX theory". Those so honored in the MSC are Arakelov deRham Cartan Galois Hodge Iwasawa Kasparov Littlewood-Paley Morse Nevanlinna Ramsey Riemann Shannon Smith Sturm-Liouville Teichmuller Turan Weyl There are now 349 names on the list I culled from the MSC. dave ============================================================================== From: rusin@vesuvius.math.niu.edu (Dave Rusin) Newsgroups: sci.math Subject: More mathematical biography Date: 2 Mar 1998 15:28:10 GMT I'd like to update a recent conversation regarding biographies of mathematicians, and then start a new one. A couple of weeks ago I asked about the people whose names are used in the Mathematics Subject Classification to identify parts of mathematics (e.g. Lie groups, Fourier analysis). This engendered some very interesting conversations here and in email. Evidently I am easily entertained: I worked on the list a bit more on succeeding weekends and collected the results in 98/MSC.names The file includes more chatter, too. (e.g. I found a paper which uses both classifications referring to the two different Martins!). The list is still incomplete and possibly erroneous, so I welcome continued feedback. There are two kinds of problems: 1. Only the authors of the MSC can be certain whom they intended with the references; the rest of us merely guess with greater or lesser certainty. I'm not really very confident about some of my guesses, e.g. 17B67 Kac-Moody algebras (structure and representation theory) is Victor Kac not Mark? 49R15 Weinstein and Aronszajn methods, intermediate problems is Alexander (1897-1979) Weinstein? 22E47 ... (Verma modules, etc.) is Daya-Nand Verma? Of the hundreds of such references in the MSC I'm sure I must have goofed in at least a few cases. 2. The other kind of problem comes from inadequate or conflicting biographical data. For example, what do we know of the Farey of Farey sequences? I take it his name was John and he was alive in 1816; more details? How about H.Schunck in 20D10 Solvable groups, theory of formations, Schunck classes, .. He seems to have published only one paper (1967). Or what of the Gateaux of 49J50 Frechet and Gateaux differentiability, (Also in 58C20) R. Gateaux worked with Levy during this century's second decade. Has anyone a pointer to a biography? Ernst Ising 82B20 Lattice systems (Ising, dimer, Potts..)(also 82B44, 82C20, 82C44) was born in 1900; is he still alive? I found no bio stating a year of death. I've got dozens of such holes in the file; citations for bios solicited. .............................................................................. A number of people commented to me that mathematician X is remembered by the use of his/her name in the literature; the fact that X didn't make it into the MSC (yet) is perhaps a fluke. Very well then: but the set of X such that the term "X's theorem" is used in papers is quite large. Still, this can be fun. I would like to start several threads of this type -- one at a time, please! -- and learn of other uses of people's names. I have a number of suggestions in mind, but today I'll start with just one: Q: Whose name is used repeatedly in the phrase "X's thesis"? My first candidate would be Alonzo Church: Church's thesis (Princeton, 1927) established that several notions of what is computable coincide. Moreso than in any other example that comes to mind, the phrase "Church's thesis" is used as a _thesis_, that is, a position or opinion which needs to be defended (a la Luther), rather than proved. Other examples I have heard repeatedly are "by Serre's thesis" and "by Tate's thesis", but perhaps other topologists and number theorists (respectively) would like to comment on how they are used. OK, who's next? Whose theses are not just _in_ the literature but are used to _define_ the literature? Whose theses are listed in book indices under "X's thesis"? (Please support your nominees with a few words of context or history.) dave ============================================================================== From: Robin Chapman Newsgroups: sci.math Subject: Re: More mathematical biography Date: Wed, 04 Mar 1998 02:23:56 -0600 In article <6dej6a$euk$1@gannett.math.niu.edu>, rusin@vesuvius.math.niu.edu (Dave Rusin) wrote: > > Other examples I have heard repeatedly are "by Serre's thesis" and > "by Tate's thesis", but perhaps other topologists and number theorists > (respectively) would like to comment on how they are used. > Tate's thesis is John Tate's 1950 Ph.D. thesis entitled "Fourier Analysis in Number Fields and Hecke's Zeta-Function". This was published in a volume called "Algebraic Number Theory" edited by J.W.S.Cassels and A.Fr"ohlich in 1967. To quote from the introduction "this volume also contains ..... Tate's doctoral thesis, which is for the first time published here after it had over many years had a deep influence on the subject as a piece of clandestine literature." Tate proves the functional equations for a very general class of zeta and L-functions by using a version of the Poisson summation formula for id`ele groups of algebraic number fields. Robin Chapman + "They did not have proper Department of Mathematics - palms at home in Exeter." University of Exeter, EX4 4QE, UK + rjc@maths.exeter.ac.uk - Peter Carey, http://www.maths.ex.ac.uk/~rjc/rjc.html + Oscar and Lucinda -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/ Now offering spam-free web-based newsreading ============================================================================== From: gerry@mpce.mq.edu.au (Gerry Myerson) Newsgroups: sci.math Subject: Re: Mathematical biography -- last call Date: Mon, 06 Apr 1998 16:52:30 +1100 In article <6g3f2v$a56$1@gannett.math.niu.edu>, rusin@vesuvius.math.niu.edu (Dave Rusin) wrote: > (*fl 1816*?) Farey, J. Beiler, Recreations in the Theory of Numbers, says, "John Farey was a somewhat versatile man who lived in the Napoleonic era. He was a surveyor who collected rocks and minerals and found time to write articles in the Philosophical Magazine on such diverse subjects as geology, music, decimal coinage, carriage wheels, comets---and Farey series!...One C. Haros apparently anticipated Farey by 14 years, but this fact was unknown to Cauchy, who attributed the discovery to Farey..." Hardy & Wright, The Theory of Numbers, say "Farey has a notice of twenty lines in the Dictionary of National Biography, where he is described as a geologist. As a geologist he is forgotten, and his biographer does not mention the one thing in his life which survives." My advice would be to track down the Dictionary of National Biography. Gerry Myerson (gerry@mpce.mq.edu.au) ============================================================================== From: rusin@vesuvius.math.niu.edu (Dave Rusin) Newsgroups: sci.math Subject: Mathematical biography -- last call Date: 3 Apr 1998 19:59:27 GMT Readers of this newsgroup may recall that I started a thread some time ago discussing the people whose names are used to describe a portion of mathematics in the Mathematics Subject Classifications. I have kept at this list in some delightful email exchanges, but things seem to have ground to a halt. Of the 351 names, there are 31 for whom I haven't found a reliable reference. (I can't claim to have looked all _that_ hard!) For the sake of completeness, I ask the readers of this group if they can identify these mathematicians. Here "identify" can be limited to providing Full name Years of birth (and death, where applicable) A citation for a bibliographic source A lengthy summary of the data found for these and the other 320 people is at 98/MSC.names Thank you dave (*fl 1816*?) Farey, J. (1858-1925~) Devries, Jan (*fl 1941*?) Martin, Robert S. : last paper 1941 (*fl 1919*?) Gateaux, R. (1880-1956) Riesz [or is it Riesz, Marcel (1886-1969)?] (*fl 1930*?) Vankampen, E.R. (1887-1970~) Fokker, Adriaan Daniel (*fl 1958*?) Bockstein, Meyer; last paper 1958 (1895-1982~) Burgers, Johannes Martinus (*fl 1970*?) Maeda, Fumitomo; last paper 1970 (1900~?-1975~?) Arakelov, S. Ju. (*fl 1940*?) Lidstone, G.J (1911-1980~?) Schatten, Robert (1912?-....) Sasaki, Shigeo (1917-1960~?) Cohen, Irvin Sol (1929~?-....) Maslov, Victor P (*fl 1961*?) James, W. (*fl 1967*?) Schunck, Hermann (1930~?-....) Kan, Daniel M. (1933~?-....) Popov, Vasile-Mihai (1934~?-....) Fuks, D.B. (1935~-....) Anosov, Dmitirii. (1938~?-....) Martin, Donald A. (1940~?-....) Kirillov, Alexandre (1941~?-....) Karoubi, Max (1942~?-....) Verma, Daya-Nand (1944~?-....) Virasoro, Miguel Angel (1945~?-....) Reiten, Idun (1947~?-....) Kasparov, Gennadi G (1950~?-....) Villamayor, Orlando Eugenio (1954~-....) Drinfeld, Vladimir