Columbia, Mo. - A professor at the University of Missouri-Columbia is being recognized for solving a math problem that had stumped his peers for more than 40 years.

The achievement has landed Steven Hofmann an invitation to speak next spring at the 2006 International Congress of Mathematicians in Madrid, Spain.

[...] Hofmann became curious about the problem as an undergraduate when a professor introduced him to it.

The professor was unable to solve the problem. Hofmann, 47, would have more success when the problem began to take over his life in 1996. Until he solved it in 2000, it was the last thing he thought about before he went to bed and the first thing he thought about when he woke. He spent two to eight hours each day on the problem, working periodically with several colleagues. [...]

The problem, known as Kato's Conjecture, applies to the theory of waves moving through different media, such as seismic waves traveling through different types of rock. It bears the name of Tosio Kato, a now-deceased mathematician at the University of California-Berkeley, who posed the problem in research papers first written in 1953 and again in 1961.

Part of the problem, called the one-dimensional version, was solved about 20 years ago. Though it was a breakthrough, work remained. Hofmann solved the problem in all its dimensions in a 120-word paper that he wrote with several colleagues ย— Pascal Auscher, Michael Lacey, John Lewis, Alan McIntosh and Philippe Tchamitchian.

"Philosophically, the reason research in math matters is that by pursuing math ideas that are deep and interesting for their own sake, you will get real-world applications in the future," Hofmann said.

"It is like making investments." [...]