Slashdot Mirror
Professor Receives Praise for 40 Year Old Problem
An anonymous reader writes "The Kansas City Star is reporting that Steven Hofmann is in line to receive accolades from his peers this coming year in Madrid, Spain for solving a mathematical problem that has baffled mathematicians for over 40 years. Hofmann, a professor at the University of Missouri-Columbia, solved the 3 dimensional version of the 'Kato problem for divergence form elliptic operators with Gaussian heat kernel bounds' (say that 10 times fast!). From the article: 'For three years, starting in 1996, Hofmann worked on the problem for two to eight hours every day [...] Hofmann said the solution could allow mathematicians to better describe the behavior of waves traveling through a medium that changes over time. But beyond that, he said, it is impossible for him to explain all the real-world applications.'"
It really doesn't explain much about the problem, but it does do a nice job of explaining how some people wind up in mathematics:
"Hofmann majored in math, he said, "because it was the path of least resistance." While his friends were writing history papers that were many pages long or spending hours in a computer lab, "all I had to do was solve math problems, and it was something that came to me naturally," he said.
"By the time you get to graduate school, even if it comes naturally, it gets hard, and that is when you begin to develop a skill to go with the ability.""
It's nice to see an article about a mathematician that isn't a "look at the freaky math guy" or "look at the useless thing we're paying people to do" kind of writeup, but just about someone who was enjoyed playing with mathematics, and has done well by it.
Anyone have a better explanation of what he did or where it fits in? Is it more theoretical or applied? What stuff is it related to?
Why is the first question about a mathematical breakthrough always "What are the applications?" Why can people not accept that mathematics is interesting in its own right?
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
Now if that doesn't give him a good pickup line, I don't know what will.
When people hear of something like this, oftentimes they can feel threatened that someone is so much more intelligent then they are. (If this is true or not, or if intelligence is even quantifiable doesn't matter -- That's how they're feeling.) As a defense, they pose the question "what is this actually good for". They take comfort in that the answer is "not much", hence allowing them to know that at least they're not wasting their time on such useless nonsense, and no matter how "intelligent" the discoverer is, he's still an "idiot" for "wasting his time" on it.
That's effectively the nearest equivalent except for a few differences. First among them is that the price is given to people _under_ 40. Second the price is given every 4 years. So the Fields is way more difficult to get because of those additional constraints.
Math is related to itself in so many ways that even the most abstract of problems can have benefits in seemingly unrelated areas. For example, if you can prove a certain bound on the divisor function (lowercase sigma), you'll be able to prove the Riemann hypothesis. These are two seemingly unrelated problems, but solving one will yield a solution to the other.
There's nothing too impressive about solving a 40 year-old problem, though: Some problems went unsolved for hundreds of years. Still, I can't even understand this problem, let alone attempt a solution at it (and I studied math), so bravo!