Georg Cantor
Georg CantorGeorgCantor was one of the most stupefyingly original thinkers in all of mathematical history. He placed the study of the various degrees of infinity on a firm set theoretical basis.
He proved some amazing theorems, such as that the set of transcendental numbers is uncountable, whereas the set of algebraic numbers is countable. He did this at a time when the only examples of transcendental numbers were pi, e, and numbers based on them (2pi, e+2, etc). See CantorsProof for another of his celebrated results.
His theories were not easily accepted, and he suffered numerous bouts of extreme depression, finally dying in an asylum.
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