Wednesday, August 17, 2011

Good Will Hunting versus the Millennium Seven

Back in the year 2000, I read about a big prize for some math problems.  Specifically, the Clay Mathematics Institute compiled a list of seven difficult math problems, and they offered one million dollars for each problem solved.  Eleven years later, I wondered if anyone had won a prize?

In 1900 at a meeting of the International Congress of Mathematicians in Paris, David Hilbert presented a list of 23 math problems that no one had figured out.  By 2000, ten of those problems had been solved, and another seven have solutions but not everyone agrees if they are correct.  Only one of Hilbert's problems, the Riemann hypothesis, made the Millennium list.

Reading the summaries of the seven Millennium problems was bewildering.  I don't understand the symbols, and even the written explanations baffled me.  But the idea that these problems remain unbroken is intriguing.

So how many of the Big Seven have been solved in the last 11 years?

One.

In 2010, the Clay Mathematic Institute awarded Dr. Grigoriy Perelman of St. Petersburg, Russia for solving Poincare's Conjecture, a problem having to do with three dimensional spheres in four dimensional space.  (The picture above is of a Poincare sphere.)  Perelman felt that Richard Hamilton of Columbia University in the US had made an equal contribution, so in 2011 the Clay committee split the prize between the two men. 

Poincare's Conjecture has been around since 1904, but these two finally cracked it.  It makes you wonder how long the other problems will resist solving. 

These problems may sound like the height of theory, and it's natural to wonder what their practical applications are.  I don't know and really cannot even imagine what we can accomplish if we solve them.  But sometimes you have to invent something before you can decide what to do with it.  Like fire.  I figure we had fire before we had cooking.  Maybe before fire it was just a theoretical problem, but after fire, people started finding ways to use it--like cooking, clearing fields, baking clay pots and lighting up the family cave.

So maybe there is fire in one of these math problems, and I wish anyone luck who takes a crack at them. 

(Sources for this article include the Clay Mathematics Institute, Wolfram Alpha, Wikipedia, and Antigravitypower.  The picture is from:  http://spie.org/x32375.xml)

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