Irreducible Complexity in Pure Mathematics

Gregory Chaitin

Abstract


I'll review the history of metamathematics, including the ideas of David Hilbert, Kurt Goedel, Alan Turing, and Emile Borel, leading to my own work on incompleteness, randomness, algorithmic information and complexity, that can be traced back to Leibniz's 1686 Discours de metaphysique.

Keywords


20th century philosophy; logic; philosophy; Wittgenstein Ludwig; algorithmic information; algorithmic irreducibility; experimental mathematics; halting probability Omega; halting problem; Leibniz Gottfried Wilhelm; Turing Alan; quasi empirical mathematics

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