Kurt Godel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein's general relativity, as he proved that Einstein's theory allows for time machines. The Godel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin's groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Godel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life.This accessible book gives a new, detailed and elementary explanation of the Godel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book's writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8

Kurt Godel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein s general relativity, as he proved that Einstein s theory allows for time machines.
The Godel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Godel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life.
This accessible book gives a new, detailed and elementary explanation of the Godel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences.

See also: http: //www.youtube.com/watch?v=REy9noY5Sg8

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One of the world's greatest mathematicians explains his revolutionary hypothesis about the enigma at the heart of maths: omega. 'Chaitin comes across as a kind of mathematical Richard Feynman, intuitive and high-spirited, irreverent and plain-spoken.' -- Peter Pesic, TLS Meta Maths is Gregory Chaitin's exuberant account of his discovery of 'omega': the infinitely long, exquisitely complex and utterly incalculable representation of randomness and unknowability in mathematics. From Euclid to Goedel to Turing, Chaitin's infectious narrative guides us on a spellbinding journey through the historical advances in maths and science that led to his breakthrough discovery. Once there he takes us further, to the very frontiers of scientific thinking. Meta Maths shows that mathematics is as much art form as logic, as much science as pure reasoning, and sheds light on what we can ultimately hope to know about the universe and the very nature of life.

Gregory Chaitin, one of the world's foremost mathematicians, leads us on a spellbinding journey, illuminating the process by which he arrived at his groundbreaking theory.
Chaitin's revolutionary discovery, the Omega number, is an exquisitely complex representation of unknowability in mathematics. His investigations shed light on what we can ultimately know about the universe and the very nature of life. In an infectious and enthusiastic narrative, Chaitin delineates the specific intellectual and intuitive steps he took toward the discovery. He takes us to the very frontiers of scientific thinking, and helps us to appreciate the art--and the sheer beauty--in the science of math.

Groundbreaking mathematician Gregory Chaitin gives us the first book to posit that we can prove how Darwin's theory of evolution works on a mathematical level.
For years it has been received wisdom among most scientists that, just as Darwin claimed, all of the Earth's life-forms evolved by blind chance. But does Darwin's theory function on a purely mathematical level? Has there been enough time for evolution to produce the remarkable biological diversity we see around us? It's a question no one has yet answered--in fact, no one has attempted to answer it until now. In this illuminating and provocative book, Gregory Chaitin elucidates the mathematical scheme he's developed that can explain life itself, and examines the works of mathematical pioneers John von Neumann and Alan Turing through the lens of biology. Fascinating and thought-provoking, "Proving Darwin" makes clear how biology may have found its greatest ally in mathematics.