Hodges Conjecture Clay Institute Millennium Problem Solution

Paul T E Cusack*

Citation: Hodges Conjecture Clay Institute Millennium Problem Solution. American Research Journal of Mathematics. vol 3, no. 1, 2017, pp. 1-4.

Copyright This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Here we consider the Hodge’s Conjecture that expresses when a projective manifold coincides with a sum of algebraic cycles. More generally, this entails the convergence of geometry and calculus which has been discussed in this author’s previous paper.

Keywords: Hodge’s Conjecture; Polynomials; Analytic sums; Geometry; Calculus.



In his paper, we consider the Hodge’s Conject Clay Institute Millennium Problem solution.That problem is described as follows:


Let X be a non-singular complex projective manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cosmology classes of complex sub varieties of X.

Therefore, roots are always even.


We have worked out a possible set of solutions to the Hodges Conjecture. We have considered Analytic functions, C, summed into the general polynomial, P. This allows us to mold geometry and calculus together.


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