Changes

'''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]].

'''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]] posting the solution directly on the internet rather than seeking publication by a peer-reviewed mathematical journal.

==The Millennium problems==

==The Millennium problems==

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.)

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.

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.  In August 2010, Vinay Deolalikar posted on the internet a proposed proof that P≠NP.

4. The ''Hodge conjecture'', which identifies algebraic structures on certain kinds of complex manifolds.

4. The ''Hodge conjecture'', which identifies algebraic structures on certain kinds of complex manifolds.