Posted on 08/22/2006 7:48:41 PM PDT by SJackson
A RECLUSIVE Russian has won the mathematical world's highest honour for solving a problem that has stumped some of the discipline's greatest minds for a century - but refused the award.
Grigory Perelman, 40, from St Petersburg, won a Fields Medal - often described as mathematics' equivalent of the Nobel prize - for a breakthrough that experts say might help scientists work out the shape of the universe.
Besides shunning the award, colleagues say he also seems uninterested in a separate $1 million prize for which he is eligible for his feat of apparently proving the Poincaré conjecture, a theorem about the nature of multi- dimensional space.
The award, given only every four years, was announced at the International Congress of Mathematicians.
Three other men - Russian Andrei Okounkov, Frenchman Wendelin Werner and Australian Terence Tao - also won Fields medals in other areas of mathematics. They received their awards from King Juan Carlos. But Dr Perelman was not present.
"I regret that Dr Perelman has declined to accept the medal," said John Ball, the president of the International Mathematical Union, which is holding the convention, in Madrid.
Professor Ball said later that he had met Dr Perelman in St Petersburg in June, told him he had won a Fields medal and urged him to accept it.
But Dr Perelman said he felt isolated from the mathematics community and refused the medal because "he does not want to be seen as its figurehead", Prof Ball said.
The $1 million prize in the Poincaré case is separate, and will be announced in about two years by a private foundation called the Clay Mathematics Institute in Cambridge, Massachusetts . If his proof stands the test of time, Dr Perelman - whose work is still under review - will win all or part of the money.
Academics have been studying Dr Perelman's proof ever since he left the first of three papers of it on an internet maths archive in November 2002 - itself an odd gesture, because normal procedure would have been to seek publication in a peer-approved journal.
Three separate teams have now presented papers or books explaining the details of Perelman's work, and two weeks ago the two-year countdown set by the Clay institute began. During it academics have a final chance to challenge the proof.
The Poincaré conjecture essentially says that in three dimensions you cannot transform a doughnut shape into a sphere without ripping it, although any shape without a hole can be stretched or shrunk into a sphere.
Proving the Poincaré conjecture - an exercise in acrobatics with mindboggling imaginary doughnuts and balls - is anything but trivial.
Colleagues say Dr Perelman's work gives mathematical descriptions of what the universe might look like and promises exciting applications in physics and other fields.
The problem is that home-schooling parents are unlikely to know much about math. (Except in the A in algebra sense.)
Why can't you just role the doughnut into a ball with your two palms?
And you think the average high school teacher is capable of really working with, accomodating and encouraging a math prodigy? Better than home schooling parents? REALLY?
First of all, high school students are lucky to get into calculus. And the high school structure is almost perfectly designed to limit the better students to the pace of everybody else.
For example, I wanted to learn calculus when I was around 12 years old. In a decent home schooling environment, with even a little encouragement or help, I probably would've been able to at least get going on that path. As it was, in the public school I had to wait another 6 or 7 years -- until I reached university.
Second, I think you deceive yourself in regard to the ranks of home schooling parents with math skills. There are quite a few. I don't even have to look out of our my own house to find a home-schooling mom who's studied calculus at the university level. As for the dad, I took around 40 or 50 credit hours of advanced mathematics, including at graduate level. Advanced calc, ring theory, set theory, advanced probability theory, de, statistics...
But let's say you have a parent with a math whiz kid and NO math skills of his or her own. What's that parent likely to do? In that case, the parent will almost certainly draw upon other resources. And there are plenty of them out there. College courses, tutors, math study groups, coops where a math-knowledgeable parent will help kids in small groups with a lot of one-on-one.
Frankly, from my perspective the home-schooling environment has plenty of flexibility to accomodate prodigies -- if not quite a bit more than the school system. Looks to me like bright HS kids are likely to be quite a bit better off than if they were stuck in a high-school class where they have neither much individual attention nor the opportunity to pursue what they would like to.
The ability of HSers to focus on a topic of interest is one reason why HSers, for their population percentage, tend to dominate things like the National Spelling Bee. Yes, you do have to pull in more outside resources, but the same dynamics can work with math.
In any event, it turns according to the available research that not only do HS kids as a group perform significantly better academically, they're less limited than PS kids by any educational deficiencies on the part of their parents. In other words, the research indicates that if the parent of a PS didn't do well academically, the kid isn't likely to either -- but if the parent of a HS kid didn't do well academically, it really doesn't matter very much.
So your supposition is simply one that might sound good in theory (like the wildly misguided theory that home-schooled kids are "missing out on socialization"), but it doesn't carry with it any real knowledge or experience of the subject.
Sorry to put it that way, but that's my view. :-)
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