Prof Honored for Solving Old Math Problem (Kato's Conjecture)

Still more proof that I was and am not smart enough to work in pure math!

:-)


http://hosted.ap.org/dynamic/stories/M/MATH_PROBLEM?SITE=FLTAM&SECTION=US
http://www.kcstar.com/
http://cnn.netscape.cnn.com/story.jsp?id=2005122704220001702241&dt=20051227042200&w=APO&coview=
Dec 27, 7:22 PM EST

Prof Honored for Solving Old Math Problem

KANSAS CITY, Mo. (AP) -- 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.<snip>

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 - Pascal Auscher, Michael Lacey, John Lewis, Alan McIntosh and Philippe Tchamitchian.<snip>


---
harmonic analysis
http://www.math.sciences.univ-nantes.fr/edpa/2001/pdf/tchami.pdf
http://archive.numdam.org/article/JEDP_2001____A14_0.pdf
Kato's conjecture, stating that the domain of the square root of any accretive operator $L=-\dive(A\nabla)$ with bounded measurable coefficients in $\mathbb{R}^n$ is the Sobolev space $H^1(\mathbb{R}^n)$, i.e. the domain of the underlying sesquilinear form, has recently been obtained by Auscher, Hofmann, Lacey, M\texsuperscript^{c}Intosh and the author. These notes present the result and explain the strategy of proof.

Maybe because I got a B- in Algebra II.

:-)

I had a penchant for math all through K-12, though it seemed like the math teachers I had did everything they could to discourage mathematical curiosity. I had a great Geometry teacher, as a result I became fascinated with geometric proofs, which is one of the things that led to my interest in coding. I think, though, that given the importance of math (that is, everything boils down to math), that it's taught from a pragmatic rather than conceptual-contextual (e.g. useful) point of view.

That may or may not be why you got a 'B', but I just thought I'd toss in my two cents. ;-)

high school. I didn't get interested in it again until fractal geometry hit it big in the popular science magazines (80s). That's when I was reminded of the beauty and wonder in math that I'd seen as a kid.
My two cents. :P

In 10th grade Geometry (which was, as taught, the most worthless course in my entire K-12 experience), I was introduced to the concept of skew lines. That is, non-coplanar lines that are not parallel and do not intersect. Intrigued, and making my first baby steps into theoretical higher-dimensional technobabble, I asked in all sincerity if you could have "skew planes" in four dimensions, since planes in three dimensions are either parallel or intersecting.

"After you've mastered three dimensions," came the answer, "ask me about four."

Way to quench the fires of curiosity. Hey, I wasn't looking to split the atom, but I thought that the question merited more than a "fuck you, wise-ass" dismissal.

Of course, that's not why I failed to achieve glory in my later mathematics courses, but I recall it with clarity to this day ~20 years hence.

I had this worked out in the third grade, but I forgot to carry the one.

Crap.

and the Rubik's Cube.

Is there a connection between one's natural mathematical ability and solving the Rubik's cube.

Our little girl (adopted) when first picking up a Rubik's cube solved it a couple of minutes. She was about eight years old. It was not a fluke. She found it boring. As she progressed in life she had no real interest in school or learning.

Later in life, and a high school drop out she decided to go to college. She prepared herself for nursing school. On the way she discovered she had earned enough credits in math to earn an associate degree in (Math Science?).

I wonder if somehow she might be wasting her time in continuing in nursing?

Just a curious father.

180

math is a tough profession to make a living in.

I went the actuarial route but that involves giving up 10 years of life outside of your job as you get through the exams - and it is solid, but not heavy, math.

I know of no math ability correlation with Rubik's cube solving.

However math is the one pure science - there is no other.

And there is a great deal of satisfaction to be had in applied math by folks that are not all that smart - like myself.

But I stand in Awe of the pure math folks.

So do I.

180

HAHAHAHAHAHAHAHA! Faked you out! :evilgrin:

Oh, um, **120-word** paper????

Of a solution to Fermat's theroem. Fermat said there would be an elegant solution however. The found one required many pages. Fermat had implied that his approach to solving the theorem would only take a short while to prove. All told, this process took 300 years.