most recent 30 from http://mathoverflow.net 2013-05-18T22:28:17Z http://mathoverflow.net/feeds/question/3591 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list Abel 2009-10-31T20:34:53Z 2012-02-03T00:14:12Z

<p>It is well-known that many great mathematicians were prodigies. </p> <p>Were there any great mathematicians who started off later in life? </p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/3592#3592 Qiaochu Yuan 2009-10-31T20:38:15Z 2009-10-31T20:38:15Z

<p><a href="http://www.gap-system.org/~history/Biographies/Lie.html" rel="nofollow">Sophus Lie</a> didn't become interested in mathematics until after university, and before then didn't seem to have shown significant aptitude for it.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/3594#3594 Jose Capco 2009-10-31T20:50:56Z 2009-10-31T20:50:56Z

<p>You could read the autobiography of Paul Halmos (RIP- he died just a few years ago) "<a href="http://www.amazon.com/I-Want-Be-Mathematician-Automathography/dp/0387960783" rel="nofollow">I want to be a mathematician</a>". He started mathematics much later in life, first he did chemical engineering then philosophy then mathematics. Halmos wasn't quite the genius in mathematics (as he has described it) but later in life he got into it and succeeded. John von Neumann (who was Halmos' countryman) also started from chemical engineering before going to mathematics.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/3595#3595 Ben Linowitz 2009-10-31T20:52:27Z 2009-10-31T20:52:27Z

<p>I don't think that <a href="http://en.wikipedia.org/wiki/Stephen%5FSmale" rel="nofollow">Stephen Smale</a> really distinguished himself until after graduate school. </p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/3599#3599 Anna Varvak 2009-10-31T21:05:32Z 2009-10-31T21:05:32Z

<p><a href="http://www.math.columbia.edu/~jb/" rel="nofollow">Joan Birman</a> went back to grad school in math in her forties, and is now one of the top researchers in knot theory.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/3600#3600 Richard Kent 2009-10-31T21:08:59Z 2009-10-31T21:08:59Z

<p>She didn't get started late, but I do know that Alice Roth wrote an important thesis in 1938, took 35 years off from research, and then did very beautiful and influential work in complex approximation starting at age 66.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/3606#3606 Charles Siegel 2009-10-31T21:46:00Z 2009-10-31T21:46:00Z

<p>Well, there's Witten. He got his degree in history, then attempted to be a political journalist and get a grad degree in econ before looking into physics and math, but got the Fields Medal.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/3607#3607 Ari Shnidman 2009-10-31T21:51:36Z 2009-10-31T21:51:36Z

<p>Dwork started out as an electrical engineer and was 31 when he received his PhD. The memorial article by Tate and Katz gives the interesting details. </p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/3612#3612 Julián Aguirre 2009-10-31T22:43:27Z 2009-11-11T03:18:59Z

<p>Misha Cotlar, born in 1912 in Ukraine, emigrated to Uruguay in 1928. He never had a formal education. He got his PhD from Chicago University in 1953. Hi died in 2007. He is well known for his work in harmonic and functional analysis.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/3613#3613 Terry Tao 2009-10-31T22:49:33Z 2009-10-31T22:49:33Z

<p>According to <a href="http://www.ams.org/notices/200605/fea-bott.pdf" rel="nofollow">this Notices article</a>, Raoul Bott was undistinguished in high school, but displayed impressive talent once he reached graduate school (though his thesis was actually in electrical engineering, rather than mathematics).</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/3632#3632 Mark Lewko 2009-11-01T02:27:49Z 2010-03-04T01:36:29Z

<p>A similar question was discussed some time ago over at <a href="http://quomodocumque.wordpress.com/2009/01/21/claimed-proof-of-the-abc-conjecture/#comment-3179" rel="nofollow">http://quomodocumque.wordpress.com/2009/01/21/claimed-proof-of-the-abc-conjecture/#comment-3179</a>. There it was pointed out that <a href="http://en.wikipedia.org/wiki/William_Henry_Young" rel="nofollow">William H. Young</a> (of, say, Hausdorff-Young fame) didn't publish much before 40. After 40 he had a successful career, with a prolific publication record. This said, <a href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Young.html" rel="nofollow">it is reported</a> that he was a very talented student.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/3654#3654 Thomas Sauvaget 2009-11-01T09:45:39Z 2009-11-01T09:45:39Z

<p>According to an <a href="http://www.ams.org/notices/199704/arnold.pdf" rel="nofollow">interview of Arnold in Notices</a> (p437), both Whitney and Kolmogorov switched subject at university after a couple years and chose mathematics (Whitney was studying violin, Kolmogorov was into history). So they discovered math after high school, but the interview makes it clear both were very smart (not late bloomers).</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/3664#3664 Kevin Lin 2009-11-01T13:34:14Z 2009-11-02T16:50:55Z

<p><a href="http://books.google.com/books?id=Xnv5fXu1vFoC&amp;lpg=PP1&amp;pg=PA119#v=onepage&amp;q=&amp;f=false" rel="nofollow">Here</a>, Rob Kirby describes some of his experiences as an undergraduate at Chicago, and how he "snuck into graduate school".</p> <blockquote> <p>As an undergraduate, I'd been far more interested in chess, poker, and almost any sport, than in the game of mathematics. I had little chance of getting into a good graduate school. However, I failed German and didn't get a B.S. in four years, so in my fifth year I took most of the graduate courses on which the Masters Exam (really a Ph.D. prelim) was based. With a B.S. I asked to be admitted to graduate school so as to take the Exam. They cautiously said yes if I got grades closer to B than C in the fall quarter. I got a B and a C (measure theory from Halmos and algebraic topology from Dyer) and a Pass, and no one told me to leave.</p> <p>The Masters Exam could have four outcomes: you could pass with financial aid, pass without aid but with encouragement, pass with advice to pursue studies elsewhere, and fail. I got the third pass, but really liked Chicago and turned up the next year (1960) anyway.</p> </blockquote>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/3720#3720 shenghao 2009-11-02T01:06:50Z 2011-05-16T19:37:24Z

<p>Lefschetz didn't move to math until he lost both of his hands in an industrial accident at the age of 23.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/3829#3829 DoubleJay 2009-11-02T17:55:33Z 2009-11-02T17:55:33Z

<p>I've always heard that Hilbert was unexceptional (not bad, but not genius) as a student. He gained steam throughout his career, rather than bursting into prominence.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/3832#3832 1-- 2009-11-02T18:26:42Z 2009-11-02T18:26:42Z

<p>There's <a href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Lang.html" rel="nofollow">Serge Lang</a>. Apparently, he finished his undergraduate degree in physics at CalTech, before a short tour of duty in Europe. When he returned for graduate studies, he was initially enrolled in Princeton's philosophy department. According to the biography, he switched to mathematics after his first year, and worked with Emil Artin.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/4166#4166 Proportional 2009-11-04T23:15:35Z 2009-11-04T23:15:35Z

<p>Karl Theodor Wilhelm Weierstrass (Weierstraß) Follow this <a href="http://books.google.com/books?id=BCMLOp6DyFIC&amp;lpg=RA1-PA462&amp;ots=fXU9hNyNmn&amp;dq=Weierstrass%20beer%20late&amp;pg=RA1-PA462#v=onepage&amp;q=Weierstrass%20&amp;f=false" rel="nofollow">link</a></p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/17079#17079 dke 2010-03-04T12:40:29Z 2010-03-04T12:40:29Z

<p>Somebody who probably fits the bill here is <a href="http://en.wikipedia.org/wiki/Albrecht_Fr%C3%B6hlich" rel="nofollow">Albrecht Fröhlich</a> who after fleeing Nazi Germany as a teenager, eventually attended university only when he was about 30. He later went on to jointly organize the Brighton conference which put class field theory on the mathematical map, essentially create a new branch of number theory and produce his most important work well into his fifties.</p> <p>There's a biographical memoir <a href="http://rsbm.royalsocietypublishing.org/content/51/149.abstract?sid=fd93959e-ca80-497f-a045-750e46bb7ffa" rel="nofollow">here</a>.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/17108#17108 Richard Stanley 2010-03-04T16:50:17Z 2010-03-04T16:50:17Z

<p>Eugene Ehrhart (of Ehrhart polynomial fame) was born in 1906, taught in various French lycees (high schools), began his work on geometry in the 1950's, did his best work in the 1960's, and received a Ph.D. in 1966. See <a href="http://icps.u-strasbg.fr/~clauss/Ehrhart.html" rel="nofollow">http://icps.u-strasbg.fr/~clauss/Ehrhart.html</a>.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/19350#19350 dke 2010-03-25T20:15:53Z 2010-03-25T20:15:53Z

<p>I've just been reading Peter Roquette's entertaining account of the remarkable career of <a href="http://www.rzuser.uni-heidelberg.de/~ci3/manu.html#gruen" rel="nofollow">Otto Grün</a>. Grün was an amateur, never attended university but at the age of 44 sent some results around FLT to Helmut Hasse. There were considerable errors, but Hasse spotted enough originality to keep up a correspondence and helped guide Grün into becoming a highly respected group theorist with work fundamental enough to find it's way straight into group theory text books.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/22436#22436 ogerard 2010-04-24T15:52:45Z 2010-05-11T05:21:46Z

<p>One could perhaps also cite George Green, miller and mainly autodidact mathematician as an unconventional and relatively late bloomer. He entered University only at 40, one year or so before his death. See for instance Green's Biography at MathTutor</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/22443#22443 Bill Johnson 2010-04-24T17:22:51Z 2010-04-24T17:22:51Z

<p>R. H. Bing taught high school for several years before entering graduate school.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/22446#22446 Eric Zaslow 2010-04-24T18:03:15Z 2010-04-24T18:03:15Z

<p>Unfortunately, all these exceptions appear to be reaches, thus proving the rule.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/22461#22461 Andrew L 2010-04-24T23:01:55Z 2010-04-24T23:01:55Z

<p>Here's a great example:Makus Fisz. "Who?!?" An expert in probability and statistics who was born in 1910 and grew up in war-torn Poland-and as a result,his career kept getting interrupted. He finally got his doctorate at the age of 40 and published a number of well known papers as well as an acclaimed text on the subject that was translated into a half a dozen languages and became very popular in Europe.He was finally appointed full professor of mathematics at New York University after many visiting positions. Tragically,he died of a heart attack at the age of 54. A great story and career with a very sad ending. </p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/22991#22991 Physicsfreak 2010-04-29T15:17:21Z 2010-04-29T15:17:21Z

<p>There's Thomas Kirkman of <a href="http://en.wikipedia.org/wiki/Kirkman%2527s_schoolgirl_problem" rel="nofollow">Kirkman's schoolgirl problem</a>, who didn't start studying mathematics until he was into his forties. Aside from the problem that bears his name he went on to work publish papers in extremal set theory, finite geometries and the like, he was also one of the first to write about group theory in English. </p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/23018#23018 Joseph Malkevitch 2010-04-29T18:34:42Z 2010-04-29T18:34:42Z

<p>Dennis Sullivan who won the 2010 Wolf Prize comments on this in his own words in the magazine published by the New York Academy of Sciences:</p> <p><a href="http://www.nyas.org/Publications/Detail.aspx?cid=14047af0-9f26-481c-9b50-9434130c89db" rel="nofollow">http://www.nyas.org/Publications/Detail.aspx?cid=14047af0-9f26-481c-9b50-9434130c89db</a></p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/23117#23117 Victor Miller 2010-04-30T15:05:42Z 2010-04-30T15:05:42Z

<p>Persi Diaconis had two careers -- the first as a violin prodigy studying at Julliard, and then as a world famous magician who performed for the crowned heads of Europe. In his early twenties he decided that he wanted to learn enough math to understand Feller's two volume treatise, so enrolled at CCNY. His beginning was rocky (by his own admission), but he finished there well enough to be admitted to the Ph.D. program in Statistics at Harvard, and, the rest, shall we say, is history. He also worked as an advertising copywrighter while he was attending CCNY.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/27395#27395 Bman 2010-06-07T21:22:47Z 2010-06-07T21:22:47Z

<p>In May 2006, the AMS Notices printed a remembrance article for Serge Lang. Dorian Goldfield was one of the contributors, and as an undergraduate, he described himself as follows:</p> <blockquote> <p>Of the many people who had serious interactions with Serge, I am one of those who came away with fierce admiration and loyalty. In the mid-1960s, I was an undergraduate in the Columbia engineering school on academic probation with a C–average. In my senior year I had an idea for a theorem which combined ergodic theory and number theory in a new way, and I approached Serge and showed him what I was doing. Although I was only a C–level student in his undergraduate analysis class he took an immediate interest in my work and asked Lorch if he thought there was anything in it. When Lorch came back with a positive response, Lang immediately invited me to join the graduate program at Columbia the next year, September 1967.</p> </blockquote> <p>Then again, Goldfield was not a "late learner" as he was 20 when he finished college and 22 when he earned his PhD. But...</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/47101#47101 anon 2010-11-23T14:25:08Z 2010-11-23T14:25:08Z

<p>I don't know if Jean van Heijenoort counts as great, but his life story is amazing.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/47102#47102 Pablo Shmerkin 2010-11-23T14:48:42Z 2010-11-23T14:48:42Z

<p><a href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Calderon.html" rel="nofollow">Alberto Calderón</a> (of Calderón-Zygmund Theory/operators - one of the great analysts of the 20th century by any account). He studied Electrical Engineering in Buenos Aires, graduating at age 27. Zygmund met him during a visit to Buenos Aires and was very impressed with his mathematical originality, so he invited him to pursue a PhD in Chicago, which Calderón completed when he was 30.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/47108#47108 Sky 2010-11-23T15:40:05Z 2010-11-23T15:40:05Z

<p>In my opinion the right answer is why are you asking that question? (no need to answer to this one in public by the way, but i do think that great insight can come from it)</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/64105#64105 Denis Serre 2011-05-06T10:21:44Z 2011-05-06T10:21:44Z

<p>In the early 90's, I had a colleague who had been a professional tennis player before going back to a PhD thesis in mathematics. I'll hide his name since he is now in the middle of his career.</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/64108#64108 Michael Renardy 2011-05-06T10:41:52Z 2011-05-06T10:41:52Z

<p>Ludolph van Ceulen (1540-1610) was 60 when he became professor of mathematics. Prior to that, he was a fencing instructor. He is known for calculating pi to 35 digits (not easy without calculus!).</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/64137#64137 Zsbán Ambrus 2011-05-06T17:21:05Z 2011-05-06T17:21:05Z

<p>How about <b>Raymond Smullyan</b>? According to his autobiography[1], he has published his first mathematical article at the age of 35, to which Marvin Minsky has reacted by saying Ray has decided to become a child prodigy at the age of 35. Does this count as starting off late in life?</p> <p>[1] Raymond Smullyan, <em>Emlékek, történetek, paradoxonok.</em> TyopTeX, 2004, original title "Some Interesting Memories. A Paradoxical Life".</p>

http://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list/65173#65173 Marc Palm 2011-05-16T20:27:53Z 2012-02-03T00:14:12Z

<p>Preda Milhaescu is a good example http://en.wikipedia.org/wiki/Preda_Mihăilescu.</p> <p>He received his PhD with 42, and proved the Catalan conjecture 5 years later.</p> <p>The Catalan conjecture was open for 160 years.</p> <p>He proposed in 2009 a proof of the Leopoldt conjecture, but I am not sure about the status of this.</p>