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Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable O number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as Gödel and Turing.This book contains 23 non-technical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of program-size co

Godel's theorem. --- Incompleteness theorems. --- Logic, Symbolic and mathematical. --- Metamathematics. --- Computational complexity. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Theorems, Incompleteness --- Constructive mathematics --- Proof theory --- Complexity, Computational --- Electronic data processing --- Machine theory --- Logic, Symbolic and mathematical --- Gödel's incompleteness theorem --- Undecidable theories --- Arithmetic --- Completeness theorem --- Incompleteness theorems --- Number theory --- Decidability (Mathematical logic) --- Philosophy --- Foundations --- Gödel's theorem.