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Famous mathematicians with background in arts/humanities/law etc

What are some examples of mathematicians who had an unconventional education and yet, went on to make an impact on mathematics? Here is an example: Edward Witten. He does not have a formal undergraduate degree in mathematics or physics but won the Fields medal.

More precisely, I am looking for examples of mathematicians whose undergraduate mathematical education was in a different field or was hindered by circumstances like war and poverty or did not have a formal degree as was the case of Srinivasa Ramanujan.

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marked as duplicate by Felipe Voloch, Andres Caicedo, Daniel Moskovich, Qiaochu Yuan, S. Carnahan Jun 13 '13 at 3:56

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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Since this question doesn't have a single correct answer, it should be community-wiki. –  HJRW Jun 12 '13 at 11:03
    
I have made it community wiki. –  Sabyasachi Mukherjee Jun 12 '13 at 13:27
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Some time limit should be put on such stories, since "undergraduate mathematical education" does not make sense before some point in the 19th century, at least not without several history books' worth of qualifying context. –  Yemon Choi Jun 12 '13 at 19:41
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Regarding continental Europe up to most of the 20th century, "undergraduate education" does not make sense at all. –  Margaret Friedland Jun 13 '13 at 1:29

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my favorite: George Green: his entire formal education consisted of one year of school at age 8; he started to work as a baker at age 5 (!), and devoted much of his working life to the operation of a wind mill near Nottingham. Wikipedia gives a nice overview of this remarkable life:

It is unclear to historians exactly where Green obtained information on current developments in mathematics, as Nottingham had little in the way of intellectual resources. What is even more mysterious is that Green had used "the Mathematical Analysis", a form of calculus derived from Leibniz that was virtually unheard of, or even actively discouraged, in England at the time (due to Leibniz being a contemporary of Newton who had his own methods that were thus championed in England). This form of calculus, and the developments of mathematicians such as Laplace, Lacroix and Poisson were not taught even at Cambridge, let alone Nottingham, and yet Green had not only heard of these developments, but also improved upon them.

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It might be worth reading more about his life on The MacTutor History of Mathematics archive: www-history.mcs.st-andrews.ac.uk/Biographies/Green.html . Especially because wiki doesn't give any references for the above paragraph. –  Oldřich Spáčil Jun 12 '13 at 11:58
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The windmill in Nottingham operated by Green (no relation) can still be visited: en.wikipedia.org/wiki/Green's_Mill,_Sneinton though it is something of a detour even if one happens to be in Nottingham. Isaac Newton's home, 28 miles away, could be ticked off too for a mathematical tour of the East Midlands of England. –  Ben Green Jun 12 '13 at 13:56
    
Here is a short video about Green and his functions, featuring the windmill: youtube.com/watch?v=ji-i6XCkgC0 –  Finn Lawler Jun 12 '13 at 15:20
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A good account and a good read: MR1829410 (2002i:01019) Cannell, D. M. George Green. (English summary) Mathematician & physicist 1793–1841. The background to his life and work. Second edition. With a foreword and an obituary of Cannell by Lawrie Challis. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2001. xxxiv+316 pp. ISBN: 0-89871-463-X –  Margaret Friedland Jun 12 '13 at 17:33

I am surprised that Persi Diaconis has not made this list. Persi left formal education at the age of 14 to join a magician on the road. He later returned to to formal education and completed an undergraduate degree at the age of 26.

Thereafter he traveled the more conventional route but it certainly was a formative diversion to Persi considering his later work.

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Hua Luogeng ( Hua Lo-keng,or Loo-Keng Hua), a number theorist ,

did not receive a formal university education and never got a formal degree from any university,his formal education only consisted of six years of primary school and three years of middle school.

see:

http://en.wikipedia.org/wiki/Hua_Luogeng

http://www-history.mcs.st-and.ac.uk/Biographies/Hua.html

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In wiki,there are some details in Hua's story that are not precise:Yang Wu-zhi ,who was Chenning Yang the famous physicist(the Yang-Mills equation is named after him) 's father and who was a math professor at Tsinghua university was amaze by Hua's article and asked a lecturer who was from Hua's hometown to invite Hua to Tsinghua University. –  XL _at_China Jun 12 '13 at 14:00

Alexander Pell seems to be a good example of someone who did other exciting things before taking up mathematics, see his wikipedia page.

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"Exciting" sounds just wrong in this case, as Pell's carrear until age 27 was: terrorist->police informer->terrorist->refugee, while getting PhD in math at age 40. Kids, do not try this at home. –  Misha Jun 12 '13 at 17:04
    
Misha: maybe "exciting" was the wrong term, would "eventful" be ok? –  Jean-Marc Schlenker Jun 13 '13 at 11:02
    
Misha has a point; 40 is damn late for getting a PhD. –  darij grinberg Jun 13 '13 at 17:24
    
Jean-Marc: I meant to say ...exciting is "a bit" of an understatement in this case... Incidentally, I read about Degayev --- a terrorist, when I was still in the Soviet Union, never realized that he had a 2nd carrear as a mathematician. –  Misha Jun 13 '13 at 18:40

Otto Grün seems to fit the bill. Here's the abstract of From FLT to finite groups. The remarkable career of Otto Grün by Peter Roquette:

Every student who starts to learn group theory will soon be confronted with the theorems of Grün. Immediately after their publication in the mid 1930s these theorems found their way into group theory textbooks, with the comment that those theorems are of fundamental importance in connection with the classical Sylow theorems. But little is known about the mathematician whose name is connected with those theorems. In the following we shall report about the remarkable mathematical career of Otto Grün who, as an amateur mathematician without having had the opportunity to attend university, published his first paper (out of 26) when he was 46. The results of that first paper belong to the realm of Fermat’s Last Theorem (abbreviated: FLT). Later Gr¨un switched to group theory.

(emphasis by me)

I ran into this article through this answer to this question on MO.

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From what I understand Sophie Germain was by and large self-taught and corresponded with other mathematicians under the name of a man due to misogynistic practices in the academy at the time.

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Although, strictly speaking, he actually learned mathematics at university, the way Alexandre Grothendieck entered into the research world, and the way he had to see structures, is quite fascinating to me.

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To see how unconventional was Alexander Grothdndieck's background and education, see the book "Who is Alexander Grothendieck? Part 1: Anarchy" Winfried Scharlau , available from amazon. –  Ronnie Brown Jun 12 '13 at 16:55

I read 14 previous answers and did not find the most evident example: Ramanujan:-)

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That may be because he was listed by the person who asked the question, but you are right, he is one of the most well-known examples. –  Sean Lawton Jun 12 '13 at 18:48

I am not sure if it's a good example, but Sophus Lie studied a broad science course, so his specialty wasn't mathematics. Even after he graduated he didn't know what to do, so he tried learning some mechanics, astronomy, zoology et.c. Only after some period of time he became interested in maths, and we all know that he succeded in it :)

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Well, at his time, all university students had to follow a quite broad field of study! When S Lie entered the University of Oslo in 1859, the number of new students pr year was around 100! so early specialization was obviously not possible. –  kjetil b halvorsen Jun 13 '13 at 13:28

D’Alembert, he studied law and medicine, but then he learned mathematics and physics. He also published the most famous encyclopedia of that time together with Diderot where he wrote about mathematics and physics.

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Raoul Bott's undergraduate studies were in electrical engineering.

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Von Neumann's were in chemical engineering IIRC. –  Steve Huntsman Jun 12 '13 at 10:58
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Von Neumann actually first did a Ph.D. in mathematics, and then followed that up with studies in chemical engineering to please his father (who was worried that math would not provide a decent job for his son) –  Carlo Beenakker Jun 12 '13 at 11:12
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Bronisław Knaster studied medicine in Paris and served as a doctor in the Polish Army during the Polish–Soviet War in 1920. Although, I am not sure whether Knaster really counts because later on he had received a PhD in mathematics. –  Tomek Kania Jun 12 '13 at 11:13
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Bernard Dwork undergraduate studies were also in electrical engineering. –  Lennart Meier Jun 12 '13 at 11:19

I. M. Gelfand proceeded to postgraduate study bypassing high school http://en.wikipedia.org/wiki/Israel_Gelfand

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Misha Cotlar (Cotlar-Stein lemma and other important contributions to harmonic analysis) started by earning his life playing the piano at bars in Buenos Aires and his first degree was a doctorate in U. of Chicago with Zygmund as advisor.

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Jakob Steiner did not learn to read and write until he was 14. At the age of 18, against the wishes of his parents, he left home to attend Johann Heinrich Pestalozzi's school at Yverdom at the south-east end of the Lake of Neuchâtel. (From mathtutor biography).

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Hermann Grassmann is a notable example.

Grassmann was an undistinguished student until he obtained a high mark on the examinations for admission to Prussian universities. Beginning in 1827, he studied theology at the University of Berlin, also taking classes in classical languages, philosophy, and literature. He does not appear to have taken courses in mathematics or physics.

See http://en.wikipedia.org/wiki/Hermann_Grassmann

Also "A Metaphor for Mathematics Education" written by Greg McColm (Notices, April 2007; www.ams.org/notices/200704/fea-mccolm-web.pdf) This one is not about Grassmann as such. But it gives an interesting account of why he went unnoticed by his contemporaries (including Gauss, Mobius, Cauchy, Hamilton):

Grassman’s problem may have been his lack of students and credentials (he studied philology and theology in Berlin and taught at technical schools, but never got a university post) and the novelty of his approach. And there was the opacity of his exposition.

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Anastacio da Cunha is a rather unknown eighteen century portuguese mathematician who published a significant encyclopedia on elements of calculus, algebra and geometry. His innovative contributions were mainly on Calculus. He was unusually rigorous for his time (http://www-history.mcs.st-andrews.ac.uk/Biographies/Cunha.html)

This mathematician did not learn much about mathematics and physics in school. In these subjects he was an auto-didact (http://www-history.mcs.st-andrews.ac.uk/Biographies/Cunha.html)

Anastácio da Cunha survived the terrible 1755 Lisbon earthquake. He was in the army for 10 years. One day he was arrested and imprisioned by the inquisition during three years for his heretical views. Apparently his health did not recover from that period and he died some years after (http://www-history.mcs.st-andrews.ac.uk/Biographies/Cunha.html).

Maybe one can say that he had not only an unconventional education but also an unconventional life.

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Barry Mazur was never awarded an undergraduate degree from MIT because he never completed the ROTC requirements. Nevertheless, he was deemed talented enough to be admitted to the graduate program at Princeton, so perhaps this doesn't fit the mold you're looking for.

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The "unconventional" aspect includes not getting the piece of paper from high school as well, but the educational aspect is indeed entirely conventional (and even exceptional): taking classes as a registered student for a few years at each of Bronx High School of Science and MIT. –  user29720 Jun 12 '13 at 17:09

Lucjan Emil Boettcher (1872-1937) started studying mathematics at (then Russian-dominated) Imperial University in Warsaw in the year 1893/94, but was soon expelled from it for participating in a political manifestation. He then moved to Lvov (in Austro-Hungarian empire) and studied in the Division of Machine Construction at the Lvov Polytechnic School, getting his so-called half-diploma in this area in 1897. The same year he moved to Leipzig to continue his studies in mathematics, getting his PhD with Sophus Lie in 1898.

For more information about Boettcher (including his not-so-successful academic career) see e.g. my answer to this MO question: Mathematicians whose works were criticized by contemporaries but became widely accepted later

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Dwork did his undergrad in EE. Started math seriously relatively late. Proved first two statements of the Weil conjectures using padic methods. Went on to win the Cole prize.

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