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.'"

Comments

Why applications?

[siwelwerd]

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?

Re:Why applications?

[mooingyak]

What applications are there for this question?

Not sure what others would apply it to

[jd]

But if the summary of "waves in a changing medium" sums it up, then here are a few ideas. (Please note that if the summary I got is inaccurate or incomplete, then none of these examples would apply):

• Supersonic and hypersonic aircraft design: The shockwave is a wave (duh!) and the medium it travels through (the air) is certainly changing. This applies to the shock going through the air into the surroundings, so could modify models of aircraft noise.
  
• Vibrations within any aircraft: The vibrations are also a wave. The aircraft changes (as a medium) with temperature, also because it uses up fuel (and therefore changes in composition and distortion) but also as a result of the waves (stress in the metal, for example). The same will apply to any vehicle, provided there is sufficient change to the vehicle to be significant.
  
• Gravity waves: Gravity alters space, space alters the movement of the gravitational bodies, the gravitational bodies alter the waves.
  
• Microwave ovens: The microwaves heat the food. In so doing, you change the composition of the atmosphere through which the microwaves travel, thus absorbing some and potentially causing refraction.
  

Why? It's simple.

[John Nowak]

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.

Re:Why? It's simple.

[Anti_Climax]

To add to that, all too often it takes just as long to find uses for the solution as finding the solution itself. How long did we have Boolean mathematics before they wer put into use for digital compters? More than 70 years.

If we find more uses for it, great. If not, we have a better collective grasp of pure mathematics.

Don't ask what it's good for.

[Metasquares]

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!