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› Find signed collectible books: 'Godel's Proof'
Gödel's incompleteness theorem--which showed that any robust mathematical system contains statements that are true yet unprovable within the system--is an anomaly in 20th-century mathematics. Its conclusions are as strange as they are profound, but, unlike other recent theorems of comparable importance, grasping the main steps of the proof requires little more than high school algebra and a bit of patience. Ernest Nagel and James Newman's original text was one of the first (and best) to bring Gödel's ideas to a mass audience. With brevity and clarity, the volume described the historical context that made Gödel's theorem so paradigm-shattering. Where the first edition fell down, however, was in the guts of the proof itself; the brevity that served so well in defining the problem made their rendering of Gödel's solution so dense as to be nearly indigestible. This reissuance of Nagel and Newman's classic has been vastly improved by the deft editing of Douglas Hofstadter, a protégé of Nagel's and himself a popularizer of Gödel's work. In the second edition, Hofstadter reworks significant sections of the book, clarifying and correcting here, adding necessary detail there. In the few instances in which his writing diverges from the spirit of the original, it is to emphasize the interplay between formal mathematical deduction and meta-mathematical reasoning--a subject explored in greater depth in Hofstadter's other delightful writings. --Clark Williams-Derry --This text refers to the Hardcover edition.
› Find signed collectible books: 'Godel's: Proof (Routledge Classics)'
'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 was partly based on propositions not provable within the mathematical system. The importance of Godel's Proof rests upon its radical implications and has echoed throughout many fields, from maths to science to philosophy, computer design, artificial intelligence, even religion and psychology. While others such as Douglas Hofstadter and Roger Penrose have published bestsellers based on Godels theorem, this is the first book to present a readable explanation to both scholars and non-specialists alike. A gripping combination of science and accessibility, Godels Proof by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.
Kurt Godel (1906 1978) Born in Brunn, he was a colleague of physicist Albert Einstein and professor at the Institute for Advanced Study in Princeton, N.J.
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› Find signed collectible books: 'Mathematics and the Imagination'
Emphasizes the approach to mathematics rather than an explanation of the hows and whys of the subject. The author argues that maths is analogous to a fairyland ruled by logic, and that the only restraint on what math can provide is the reader's lack of imagination in using its principles.
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› Find signed collectible books: 'The Rule of Folly'
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› Find signed collectible books: 'What Is Science'
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› Find signed collectible books: 'The World of Mathematics'
The objective of this anthology is to introduce intelligent laypersons to the scope, power, significance and beauty of mathematics. It comprises a four-volume set with the selection of articles arranged within topic groupings.
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› Find signed collectible books: 'Der Gödelsche Beweis.'
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› Find signed collectible books: 'Der Gödelsche Beweis. Scientia Nova'
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