Re:It's the Times... (Score 2, Informative)

"...I believe the Clay Mathematics Institute award specifically excludes refutation." That is partially correct. The paragraph from the rules concerning counter-examples at http://www.claymath.org/prizeproblems/rules.htm states: "In the case that a mathematician discovers a proposed counterexample to a prize problem, the SAB will consider this counterexample after publication and the same two-year waiting period as for a proposed solution will apply. If the counterexample shows that the original problem survives after reformulation or elimination of some special case, then the SAB may recommend that a small prize be awarded to the author. The money for this prize will not be taken from the Millennium Prize Problem fund, but from other CMI funds. In the case of the P versus NP problem, the SAB may recommend the award of the Millennium Prize for deciding the question in either direction." The "fine print" here is the phrase: "If the counterexample shows that the original problem survives..." If it turns out that the counter-example totally blows away the hypothesis, then it seems that the full prize could be awarded. The actual determination of the quality of the proof or counter-example comes from extensive peer review of the submitter's published work, so any submissions, postive or negative, will be carefully scrutinized (at least that's what the Clay Institute is counting on!). Cheers!