Mind Boggling Math Puzzles: Millennium Prize Problems

Quicker Maths offers regular tips and tricks for zooming through some arithmetic problems, as well as giving us fascinating puzzles that offer some solid food for mathematical thought. But what if you were given the opportunity to earn one million dollars to solve one math problem? That’s exactly the deal that the Clay Mathematics Institute in Cambridge Massachusetts has offered. And pretty much anyone can enter to win.

The Millennium Problems, as they are known, were originally seven math problems that had existed for several years and remained unsolved. Most recently, one problem–the Poincare Conjecture–was successfully solved by Dr. Grigory Perelman of St. Petersburg, Russia. Perelman worked on and solved the problem in 2002 and 2003, and was thereafter awarded the CMI one million dollar prize in 2010, although he ended up turning down the prize money.

The Poincare Conjecture was a problem proposed in 1904 and left unsolved by French mathematician and theoretical physicist Henri Poincare. Although the details of the problem and the process of solving it are quite complex, essentially what Poincare was asking had to do with three-dimensional spheres.

In layman’s terms, Poincare wanted to know why one could strap a rubber band around an apple and shrink the band down to a certain point without the band breaking or leaving the surface of the apple, whereas if you were to do the same with a rubber band and a doughnut, either the doughnut or the band would break.

Although several had attempted to figure out the mathematical details of this problem, Perelman successfully connected all the dots, so to speak, by building on the work of Richard Hamilton and his theory of the Ricci flow. Perelman also employed previous work on the spaces of metrics devised over the years by Cheeger, Gromov, and Perelman himself.

When Perelman solved the prize problem, aside from the CMI prize, he also received other accolades, including Science Magazine’s 2006 Breakthrough of the Year award and the International Congress of Mathematicians’ Fields Medal. As of now, the Poincare Conjecture is the only Millennium Prize problem that has been solved. The remaining six problems–the Birch and Swinnerton Dyer Conjecture, the Hodge Conjecture, the Navier-Stokes Equations, P vs. NP, the Riemann Hypothesis, and the Yang-Mills Theory–are yet to be resolved.

If you think you may want to someday take a crack at these “unsolvables”, you can find more information on the CMI website, including the rules and information on each problem. Even though they may seem impossible, just like with any puzzle, it wouldn’t hurt to try.


This guest post is contributed by Lauren Bailey, who writes on the topics of online colleges. She welcomes your comments at her email Id: blauren99 @gmail.com

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