Posts
How easy can it be to get a miilion dollars? In fact by January, you could be in your own yatch with yoour own victoria's secret girl somewhere in the carribeans.
Truly, there are easier ways of making a million dollars, but if you're down to solve some mathematics, you could be in for some cash.
TheMillennium Prize Problemsare seven problems in mathematicsthat were stated by the Clay Mathematics Institutein 2000. As of August 2010, six of the problems remain unsolved. A correct solution to any of the problems results in a US$1,000,000 prize (sometimes called aMillennium Prize) being awarded by the institute. Only the Poincaré conjecturehas been solved, by Grigori Perelman, who declined the award.
The seven problems are:
Contents
1 P versus NP
2 The Hodge conjecture
3 The Poincaré conjecture (proven)
4 The Riemann hypothesis
5 Yang–Mills existence and mass gap
6 Navier–Stokes existence and smoothness
7 The Birch and Swinnerton-Dyer conjecture
And here's a lil explanation of the first 2 question(you'll have to google the rest)
P versus NP
The question is whether, for all problems for which a computer canverifya given solution quickly (that is, in polynomial time), it can alsofindthat solution quickly. The former describes the class of problems termed NP, whilst the latter describes P. The question is whether or not all problems in NP are also in P. This is generally considered the most important open question in mathematicsand theoretical computer scienceas it has far-reaching consequences in mathematics, biology, philosophy[ citation needed]and cryptography(see P versus NP problem proof consequences).
If the question of whether P=NP were to be answered affirmatively it would trivialise the rest of the Millenium Prize Problems (and indeed all but the unprovable propositionsin mathematics) because they would all have direct solutions easily solvableby a formal system.
Mathematicians and Computer Scientists expect that the statement 'P=NP' will be shown to be false.
The official statement of the problem was given by Stephen Cook.
The Hodge conjecture
The Hodge conjecture is that for projective algebraic varieties, Hodge cyclesare rational linear combinationsof algebraic cycles.
