What are some examples of mathematicians who had an unconventional education? 
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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.
 A: Alexander Pell seems to be a good example of someone who did other exciting things before taking up mathematics, see his wikipedia page.
A: 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.
A: 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.  
A: 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. 
A: I read 14 previous answers and did not find the most evident example: Ramanujan:-)
A: 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 :)
A: I. M. Gelfand proceeded to postgraduate study bypassing high school
http://en.wikipedia.org/wiki/Israel_Gelfand 
A: 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.
A: 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).
A: 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.

A: 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.
A:  Raoul Bott's undergraduate studies were in electrical engineering.
A: George Boole had an unusual mathematical background:  see http://www-history.mcs.st-andrews.ac.uk/Biographies/Boole.html.
A: And of course there was Stefan Banach:
Who wrote up Banach's Thesis? 
A: 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.
A: 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.

A: 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.
A: 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
A: 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.
A: 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.
A: 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
