Books › Science & Math › History & Philosophy

The Story of Proof: Logic and the History of Mathematics

Name: The Story of Proof: Logic and the History of Mathematics
Price: 36.17 USD
Availability: InStock
Rating: 4.4 (35 reviews)

4.4 of 5 Stars: History & Philosophy - The Story of Proof: Logic and the History of Mathematics

$36.17

Buying Options

Description

Book Synopsis: 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.

Details

Discover the fascinating journey of mathematical reasoning with The Story of Proof: Logic and the History of Mathematics. This captivating book explores the evolution of the concept of proof, unraveling its significance and impact on the development of mathematical thought. From ancient times to the present day, each chapter unveils critical episodes in the history of proof, showcasing its vital role in generating knowledge.

Step into the world of Euclid, the mastermind behind the foundation of geometry. Learn how his methods of proof paved the way for the development of this intricate discipline. Witness the rise of algebra, once considered a separate realm, but now a powerful force challenging the dominance of geometry. Dive into the complexities of calculus, where the infinite processes merge with algebraic proofs, reshaping the boundaries of mathematical exploration.

As the journey continues, explore the compelling domains of number theory, non-Euclidean geometry, topology, and logic. Delve into the profound connection between arithmetic and the concept of proof, as brilliant minds like Cantor, Gödel, Turing, and others uncover the fundamental limits of what can be proved and solved.

In The Story of Proof, John Stillwell sheds light on the inner workings of mathematics, revealing its power and progress at its most fundamental levels. Gain a fresh perspective on how proof inspires innovation and revolutionizes mathematical knowledge. Embrace the extraordinary journey that is mathematics and order your copy of The Story of Proof today!

Order Now and embark on an enlightening expedition through the history of mathematical thought!

See All Buying Options...

More Details...