Thread: Math question
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Old March 2 2013, 11:33 AM   #44
Asbo Zaprudder
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Re: Math question

Everybody has a limit to their understanding. Many mathematicians wouldn't be able to get their heads around the Hodge conjecture:

"Let X be a projective complex manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X."

which Keith Devlin in "The Millennium Problems" restates as:

"Every harmonic differential form (of a certain type) on a non-singular projective algebraic variety is a rational combination of cohomology classes of algebraic cycles."

but which has yet to be proved. There is a Millennium Prize worth $1 million if you can prove it. I haven't much of a clue about what most of the individual terms mean so I won't be trying for the prize ever.

There are seven Millennium Prize problems, each worth $1 million, of which six remain to be proved:
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