Georg Cantor
The only true mathematician on my list of heroes, Cantor himself is a tragic figure, one romanticized by all mathematicians. He is the figure they champion for thinking outside of the box even when such thinking gets you ostracized by your own discipline because without his die-hard efforts to define numbers in terms of sets and his absolute conviction in the existence of infinite numbers, we would not have most modern mathematics at all, particularly group and category theory and topology.
Ridiculed, ostracized, and eventually driven insane for his radical challenge to the standard dogma that denies the existence of any number that does not easily fit on to the number line, Cantor was a rationalist to the extreme. He followed the math to its logical conclusion, rather than dismiss it as poppycock. Rather than deny his conclusions simply because convention and common sense said to, he embraced them. What he found was that transfinite numbers not only existed, but were more abundant than all of the finite numbers combined. He changed the way we actually defined something as basic as a number. Transfinite numbers were different kinds of numbers that did not follow or obey the usual laws of arithmetic. For example, unlike finite numbers, transfinite numbers are not the sum of two other numbers.
Again like so many of my intellectual heroes, Cantor dared to create a new vision for the universe that was not bound by the laws of common sense. And his vision was one that was at once more rational, and yet more humble. It was inclusive rather than exclusive. It helped, never hindered.
The best site on Cantor’s math: http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Cantor.html
A Good Fan Site: http://www.geocities.com/CollegePark/Union/3461/cantor.htm