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The Story of Proof - Logic and the History of Mathematics (Hardcover)
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The Story of Proof - Logic and the History of Mathematics (Hardcover)
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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, Goedel, 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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