Now that the Andrew Wiles proof of Fermat's Conjecture has been
universally accepted, people are turning their attention to the large
number of other unsolved mathematical problems, and trying to order them
by priority.
The Clay Mathematics Institude recently picked the seven such problems it
considers most important, and put them on its web page, together with both
a layman's blurb, and a rigorous statement of the problem in .pdf format,
as the greatest unresolved problems of the 20th century.
They have also offered $7 million in prize money, one million per problem,
for a solutiion published in a peer-reviewed journal, which is still
standing two years later.
The problems are...
P versus NP
The Hodge Conjecture
The Poincaré Conjecture
The Riemann Hypothesis
Yang-Mills Existence and Mass Gap
Navier-Stokes Existence and Smoothness
The Birch and Swinnerton-Dyer Conjecture
The details can be found at
http://www.claymath.org/prize_problems/
and an AP account of the festivities at
http://www10.nytimes.com/aponline/i/AP-Million-Dollar-Math.html
Conspicuously absent is Goldbach's conjecture, which recently had a
prize offered for its solution, although I'm pretty sure someone was
advertising a solution a couple years back.
--
Eric Michael Cordian 0+
O:.T:.O:. Mathematical Munitions Division
"Do What Thou Wilt Shall Be The Whole Of The Law"
