Proofs and Disproof of the Hodge Conjecture from 2016-2017- 2018
Journal Title: International Journal of Modern Research In Engineering & Management. - Year 2018, Vol 1, Issue 6
Abstract
The Godel incompleteness Theorem argues “your set of axioms will always be incomplete-they won’t be sufficient to prove all the facts. In mathematics as in life, parts of the truth are destined to remain forever elusive.” [1] Kurt Godel was a famous Austrian Mathematician and some appreciation for his incompleteness theorem should be given. Hodge Conjecture could be disproved in a few words, as axioms often are incomplete. If we take a set of irrational algebraic cycles, the result will be an irrational combination of classes. We cannot add irrational algebraic cycles and make up a rational linear combination. Yes, Hodge as we show can make up fantasies, inventions, or ideas like the Hodge Class, but that is only a definitional proof. When tested on real irrational algebraic cycles, the definition is just that a definition and not really a description of all algebraic geometric cycles like irrational shapes. The irrational algebraic cycle easily disproves the conjecture, as combinations will not be rational!
Authors and Affiliations
James T. Struck BA
Keywords
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