Notable math from those without math PhDs 
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What recent discoveries have amateur mathematicians made? 

Can anyone give historical examples of people outside of mathematics that have contributed to the literature?  I'm particularly interested in academics from distant fields (humanities, social sciences) who have developed their hobby into a noteworthy contribution, but would also be interested in those from nearer fields (sciences), where the math was not part of their area of research, and those not affiliated with academia at all.
I'm a math graduate student with hopes to contribute to philosophy or humanities someday.  I'm just curious how impenetrable different disciplines are, and realised I know of no examples like this.
Please forgive me if this is a duplicate, I couldn't find another like it, and think others may find it interesting as well.
 A: Buffon(Georges-Louis Leclerc, Comte de Buffon; 1707 – 1788) is a towering figure in biology.
As a mathematical hobbyist he invented geometric probability theory.
His method  of calculating $\pi$ by throwing pins on a floor ruled by parallel lines and recording the number of  throws in which  the pin crosses one of those lines must surely count as one ot the most extraordinary ideas ever in mathematics.
A: To answer your second paragraph rather than the first, the best way to break into a field other than your own is to form a collaboration with someone already in the field. Doing it on your own could be too difficult as you will be unknown and your writing will feel alien to people who grew up in the field (even if it is technically excellent). Once you establish a reputation as a collaborator, you will be better placed to strike out on your own if you wish.
A: Heegner from the Stark–Heegner theorem
A: Raymond Quenau, the French writer, published
Raymond Queneau, « Sur les suites s-additives », Journal of Combinatory Theory, 12, 1972, pp.31-71.
with an introduction by Gian Carlo Rota.  This maybe does not qualify as "notable" but still is not so bad for an amateur...
A: To answer the question in the title: Andy Gleason never bothered with a PhD. One could speculate his service to the US Navy in WWII was the reason, and that ordinarily he would have gone through the "ordinary" channels. He became famous for his contribution, along with Deane Montgomery and Leo Zippin, to the solution to Hilbert's fifth problem. 
A: Edward Witten is a winner of  the Fields Medal and he's a physicist. Nor so far from mathemathics but he doesn't have a Math PhD.
A: Hilary Putnam is a philosopher who played a key role in the solution of Hilbert's 10th problem.
http://en.wikipedia.org/wiki/Hilary_Putnam
