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Who developed the mathematical incompleteness theorem?
Who developed the mathematical incompleteness theorem?
Godel gave us the incompleteness theorem.
He showed that there can be no consistant and complete set of theorems. That is any set of theorems that is complete can not be consistant and any that is consistant can not be complete.
In Euuclidian geometry we accept some axioms as true without proof. If we elmininated these axioms would we still be able to make proofs (sometimes we can, see non-Eucliidian geometry but other times we can’t).
The gist of all of this are there are true theorms that are unprovable and there are false theorems that can not be disproven. Prior mathemeticians assumed that given enough time everything could be proven or disproven. Godel turned mathematics on its ear when he proved that not everything is proveable. The Book “Gödel, Escher, Bach: an Eternal Golden Braid: A metaphorical fugue on minds and machines in the spirit of Lewis Carroll” spends quite a few pages explaining how revolutionary Godel’s work was in mathematics.
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