For very general Z, it is known that [N.sup.2][H.sup.4](X) (which is the subspace of Hodge classes, as the Hodge conjecture
is known for X) has dimension 2.
Heck, how can you expect to solve the "Hodge conjecture
" without it?
Specifically, they are the Riemann hypothesis, which lingers from Hilbert's list, Yang-Mills theory and the mass gap hypothesis, the P Versus NP problem, the Navier-Stokes equations, the Poincaire conjecture, the Birch and Swinnerton-Dyer conjecture, and the Hodge conjecture
. Devlin profiles each problem and offers insight into how it came about and its significance.
Professor Miles Reid, of Warwick University, has spent more than 30 years mulling over the Hodge Conjecture which has baffled academics for decades.
But Prof Reid, 52, claims the Hodge Conjecture will never be solved and has instead channelled his efforts into disproving the complex algebraic theory.