Automoderated users, edit
3,552
edits
Changes
Jump to navigation
Jump to search
Line 1:
Line 1: − + + + + + + + + + + + + + + + + + +
no edit summary
'''Millennium problems''' are seven unsolved problems in [[mathematics]] identified around the year 2000 as the most significant challenges. [[Grigori Perelman]] solved one of them, despite resistance by university professors, leaving six.
'''Millennium problems''' are seven unsolved problems in [[mathematics]] identified around the year 2000 as the most significant challenges known to modern mathematics. Only one has been solved, the [[Poincare conjecture]], by [[Grigori Perelman]].
==The Millennium problems==
1. The [[Poincare conjecture]], which states that if certain algebraic structures associated with a space are equivalent to those associated with a kind of sphere, then the space itself must be that kind of sphere.
2. The [[Riemann hypothesis]], which states that a certain function investigated by Bernhard Riemann in the 19th century is only equal to zero for complex numbers with real part equal to 1/2. (The so-called trivial zeroes occur at -2, -4, etc.)
3. [[P=NP]], which states that the amount of time it takes to check a possible answer to a certain kind of problem is equal to the amount of time it takes to find that answer.
4. The [[Hodge Conjecture]], which identifies algebraic structures on certain kinds of complex manifolds.
5. The existence of infinitely differentiable solutions to the [[Navier-Stokes equations]], which would imply certain results about turbulence, an extremely common but not at all understood phenomenon.
6. The [[Birch and Swinnerton-Dyer conjecture]], which states there is a certain level of "simplicity" in the solutions to certain kinds of rational equations.
7. Investigation of the [[Standard Model|Yang-Mills existence and gap]]; specifically, whether Yang-Mills theory predicts particles with negative mass, and whether it contains any contradictions. Demonstrations of either negative-mass predictions or contradictions would provide clues as to how to build a more accurate theory.
[[Category:mathematics]]
[[Category:mathematics]]