Claude Elwood Shannon. Do I need to say more?!
Shannon has single-handedly both introduced a new mathematical theory, Information Theory and was the author of the first and fundamental results on his Information Theory. Other theories were introduced by a crowd where one or two people stand out and get extra credit. In the case of Shannon's Information Theory, there was nothing like this.
Information Theory has exciting chapters:
- data compression;
- error-correcting codes;
- encryption
Each of these three theories assists the respective technologies.
Shannon is known also for very practical financial activities like making fun of the casino business, where he induced certain casino modifications, etc.
Shannon's 1940 PhD Thesis at MIT was entitled An Algebra for Theoretical Genetics, and I've heard that its content kept on getting rediscovered in the 60s by multiple researchers.
Kolmogorov had a very high opinion on Shannon. Kolmogorov applied Shannon's ideas (Shannon's entropy function) to solve an old and outstanding problem of classification of Bernoulli shifts (he got half of it, which was a wonderful achievement).