Read [pdf]> The Story of Proof: Logic and the

The Story of Proof: Logic and the History of Mathematics by John Stillwell, John Stillwell

• The Story of Proof: Logic and the History of Mathematics
• John Stillwell, John Stillwell
• Page: 456
• Format: pdf, ePub, mobi, fb2
• ISBN: 9780691234366
• Publisher: Princeton University Press

Download The Story of Proof: Logic and the History of Mathematics

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How the concept of proof has enabled the creation of mathematical knowledge The Story of Proof investigates the evolution of the concept of proof—one of the most significant and defining features of mathematical thought—through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge. Stillwell begins with Euclid and his influence on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as “infinitesimal algebra,” and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, Gödel, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems can be solved. Shedding light on the workings of mathematics at its most fundamental levels, The Story of Proof offers a compelling new perspective on the field’s power and progress.

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It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof.
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Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical 
The Story of Proof - John Stillwell - Booktopia
The Story of Proof investigates the evolution of the concept of proof-one of the most significant and defining features of mathematical thought-through critical 
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nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical 
The Story of Proof: Logic and the History of Mathematics - 博客來
書名：The Story of Proof: Logic and the History of Mathematics，語言：英文，ISBN：9780691234366，頁數：472，作者：Stillwell, John，出版日期：2022/11/15， 
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John Stillwell, "The Story of Proof: Logic and the History of Mathematics" (Princeton UP, 2022) · PLAY · 57 min.
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This book could well serve as a history of mathematics, because in developing the evolution of the concept of proof and how it has arisen in the 
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