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I just read something about Rüdiger Gamm, who recited $81^{100}$ (191 digits), which took approximately 2 minutes and 30 seconds. So I asked myself:

Are there any kind of mathematical discoveries (proofs, theorems,...) that were made or supported by savants?

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What are the advantages of savants over computers for the purpose of mathematical discoveries? Of course, according to Roger Penrose they should have some, but in this case the savants are probably real mathematicians and will be able to successfully hide that they are savants. –  Thomas Klimpel Jun 25 '12 at 22:42
According to the Oxford English Dictionary, a savant is "A man of learning or science; esp. one professionally engaged in learned or scientific research". Someone coined the term "idiot-savant" and somehow in popular speech that gets abbreviated (and in this case even spelled with an inexplicably capitalized initial "s" in the subject line). So that usage convention does exist, but should it? –  Michael Hardy Jun 25 '12 at 23:06
My first thought was Ramanujan, but though many sources stress that his mathematical insights were reached in mysterious ways, it doesn't appear that he displayed the lack of functioning outside his particular area of genius that one typically associates with the "savant" moniker -- or at least not more than most other mathematicians. So exactly what are your criteria for being a "savant"? –  Henning Makholm Jun 26 '12 at 0:31
If you are interested, here it is dicussed, how are autistic savants able to perform certain mathematical computations so quickly? –  draks ... Jun 27 '12 at 10:12
@janmarqz let's see what cogsi.SE says, see here... –  draks ... Jan 9 '14 at 0:41

3 Answers 3

Although not mathematical, but worth to mention:

Mental calculators were in great demand in research centers such as CERN before the advent of modern electronic calculators and computers. See, for instance, the 1983 book The Great Mental Calculators, whose introduction was written by Hans Eberstark.

from Mental calculator

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According to Wikipedia, Zacharias Dase "calculated a 7-digit logarithm table and extended a table of integer factorizations from 7,000,000 to 10,000,000." It also says he "calculated $\pi$ to 200 decimal places in his head, a record for the time," but it's not clear to me whether that was a record for calculating $\pi$, or just a record for calculating $\pi$ in one's head. I don't know whether Dase qualifies as a savant.

EDIT: Perhaps I should have mentioned that Dase did this in the 1830s or thereabouts, hence, without mechanical aids to computation.

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I don't know if he qualifies as a savant, but Simon Plouffe (of the Bailey–Borwein–Plouffe formula) has also held a world record in reciting the digits of $\pi$.

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