IT’S NOT ALL IN THE NUMBERS: GREGORY CHAITIN EXPLAINS GÖDEL’S MATHEMATICAL COMPLEXITIES
Gregory Chaitin“In any non-trivial axiomatic system,” stated Austrian mathematician and logician Kurt Gödel (1906 – 1978), “there are true theorems which cannot be proven.”
This finding forms the basis of Gödel’s groundbreaking Incompleteness Theorem, demonstrating that the establishment of a set of axioms encompassing all of mathematics would never succeed.
When it was first made public in 1931, the theorem revolutionized the field of mathematics and logic, disproving the prevailing belief that mathematics could be explained with the correct set of axioms.
Gregory Chaitin is at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York. He is the discoverer of the celebrated Omega number, and has devoted his life to developing a complexity-based view of incompleteness. He calls this subject “algorithmic information theory,” and has published eleven books and numerous papers, some of which may be found on his website at http://www.cs.umaine.edu/~chaitin.
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