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.
A Concise History of Mathematics for Philosophers (Elements
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.
Foundations of mathematics - Wikipedia
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
The History of Mathematical Proof in Ancient - Mathematics
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，
History of logic | Math Wiki - Fandom
The history of logic is the study of the development of the science of valid inference (logic). Many cultures have employed intricate systems of reasoning,
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John Stillwell, "The Story of Proof: Logic and the History of Mathematics" (Princeton UP, 2022) · PLAY · 57 min.
John Stillwell, "The Story Of Proof: Logic And The - Player FM
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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Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being
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