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
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