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Tracking the World's Great Unsolved Math Mysteries
coondoggie writes "Some math problems are as old as the wind, experts say, and many remain truly unsolved. But a new open source-based site from the American Institute of Mathematics looks to help track work done and solve long-standing and difficult math problems. The Institute, along with the National Science Foundation, has opened the AIM Problem Lists site to offer an organized and annotated collection of unsolved problems, and previously unsolved problems, in a specialized area of mathematics research. The problem list provides a snapshot of the current state of research in a particular research area, letting experts track new developments, and newcomers gain a perspective on the subject."
It's even worse than that. The problem of counting lattice points is closely related to the Riemann Hypothesis, the "most" important unsolved math problem. Clearly that is what Shaneson and Cappell are after. I've looked at the paper, and it is only 40 pages (compare with the 200+ of Wiles work), and these guys are respected mathematicians. No one has said it is wrong. I don't know the area, but it shouldn't be as hard to check as the Wiles paper. Maybe people are waiting to see if they announce a proof of the Riemann-Hypothesis.
See http://rjlipton.wordpress.com/2009/11/12/more-on-mathematical-diseases/ for unsolved problems which are all really simple and also really addicting to think about. For many of these, the best way to stop thinking about one of them is to start thinking about another.
I'm actually a bit puzzled as to why this is a Slashdot article. If I wanted to point to something new in the way people are doing math I'd point to Math Overflow http://mathoverflow.net/ where many professional mathematicians, grad students and others are active. It is essentially a centralized system for people to post math questions and get math answers from people who know. It is very cool. It also is highly addictive to read.