Steven Hoffman is a professor at the University of Missouri at Columbia. In 2001, he and his colleagues (Pascal Auscher, Michael Lacey, John Lewis, Alan McIntosh, and Philippe Tchamitchian) published a 120-page long paper that solved Kato's Conjecture, a math problem first proposed by Tosio Kato in 1953.
Kato's Conjecture deals with waves traveling through different media (e.g. seismic waves traveling through different types of rocks). According to Wikipedia, "Kato asked whether the square root of certain elliptic operators, defined via functional calculus, is analytic." I really don't know what that means, but Hoffman figured it out. Prior to his work, the problem had been solved in one-dimension, but the work of he and his colleagues solved it in all dimensions.
Since this is about Hoffman, I'll try to stick to talking about him. He was first intrigued by the problem when a professor introduced him, as an undergraduate student, to it. Before solving it, he would think about it a lot. "I could be out for a bike ride, and I would be thinking about it," he said.
For his work on Kato's Conjecture, he has been chosen to speak at the 2006 International Congress of Mathematicians in Madrid, Spain. If you're in the area around August, check it out and tell us other nerds what it's like.