Impossible ProblemsDate: 08/07/2001 at 17:22:22 From: David Khourshid Subject: Impossible Problems Is there a cash prize for finding solutions to impossible problems? If so, what are they? Date: 08/08/2001 at 13:34:23 From: Doctor Rick Subject: Re: Impossible Problems Hi, David. No one can earn a prize by finding a solution to an impossible problem. If he finds a solution to a problem, then that problem is not impossible. Certain easily stated problems have been *proved* to be impossible. Take a look in our Dr. Math FAQ: "Impossible" Geometric Constructions http://mathforum.org/dr.math/faq/faq.impossible.construct.html There is no point in asking about prizes for solving these problems. The proof that they are impossible is the only solution they can have, and that's been done. You could learn more about geometry, for instance, by trying, but you won't solve the problem, and you won't get money out of it. There are other problems that are not necessarily impossible, but (so far) unsolved. Some may have solutions that no one has found yet, and some may be truly impossible. Of these, some may one day be *proved* impossible like the impossible geometrical constructions, but some impossible problems can't even be proved to be impossible. A mathematician named Kurt Goedel proved that there must be at least one such problem: Goedel's Incompleteness Theorem http://mathforum.org/dr.math/problems/seldon2.8.8.97.html Some significant previously unsolved problems have been solved in recent years: the four-color map problem and Fermat's last "theorem," which you can read about in the MacTutor Math History archives: Fermat's last theorem http://www-history.mcs.st-and.ac.uk/history/HistTopics/Fermat's_last_theorem.html The four colour theorem http://www-history.mcs.st-and.ac.uk/history/HistTopics/The_four_colour_theorem.html A quick Web search on the words "unsolved problem" and prize, brought up this site listing some major unsolved problems, and giving the rules for winning a $7 million prize: Clay Mathematics Institute Millennium Prize Problems http://www.claymath.org/prizeproblems/index.htm These are not simple problems! You might deserve a prize at your age just for understanding what the problem means, let alone solving it. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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