'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.' - "The Guardian". In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of physicist Albert Einstein, his theorem proved that mathematics wa...(展开全部)

Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable". His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fa...(展开全部)

Following the death of her brilliant mathematician father, Catherine struggles to come to terms with his legacy. Inheriting some of both his brilliance and his instability, she is torn between her sister, Claire, who wants to take her back to New York, and Hal, a former student of her father's, who tests both her knowledge and her emotions. In Proof, David Auburn has fashioned ...(展开全部)

In 1931 Kurt Godel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems". This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Godel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the n...(展开全部)

This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear...(展开全部)

Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics. Suitable for advanced undergraduates and graduate students of mathematics, this long-out-of-print monograph forms a cornerst...(展开全部)

Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics. Suitable for advanced undergraduates and graduate students of mathematics, this long-out-of-print monograph forms a cornerst...(展开全部)

In 1931 Kurt Godel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems". This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Godel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the n...(展开全部)

Math - the application of reasonable logic to reasonable assumptions - usually produces reasonable results. But sometimes math generates astonishing paradoxes - conclusions that seem completely unreasonable or just plain impossible but that are nevertheless demonstrably true. Did you know that a losing sports team can become a winning one by adding worse players than its oppone...(展开全部)

An introduction to writing proofs, presented through compelling mathematical statements with interesting elementary proofs. This book offers an introduction to the art and craft of proof-writing. The author, a leading research mathematician, presents a series of engaging and compelling mathematical statements with interesting elementary proofs. These proofs capture a wide range...(展开全部)