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The Story of Proof: Logic and the History of Mathematics

Description:

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.


Editorial Reviews

Review

"This book could well serve as a history of mathematics. … [Stillwell] has done an amazing job of collecting and categorizing many of the most important ideas in this area."---Jim Stein, New Books in Mathematics

"Stillwell’s
[The Story of Proof] joins his two other Princeton University Press books in having my highest recommendation. I just wish they had been around when I was a student."---George Hacken, Computing Reviews

"I hugely enjoyed this book."
---Jonathan Shock, Mathemafrica

"This book would be perfect for any keen undergraduate, keen amateur, or indeed a teacher of mathematics, who wants a book to dip into to use for the classroom."
---Jonathan Shock, Mathemafrica

"

A well-crafted, thought-provoking meditation on the concept of proof in mathematics. . . .It is a substantive book that deserves to be read and reflected upon.

"---Tommy Murphy, Irish Mathematical Society Bulletin

"This is a work that mathematicians, historians, and philosophers will find especially engaging, as will anyone with a serious interest in mathematics and the limits of certainty that it is constantly probing."
---J.W. Dauben, Choice

"Stillwell's book is fundamentally an ode to mathematical progress and a retrospective on how far we have come in developing a mathematically sound theory of proof itself."
---Alexi Block Gorman, The Mathematical Intelligencer

Review

“I am a great admirer of Stillwell’s writing, and this book does not disappoint. Ranging broadly and authoritatively over the history of mathematics, he takes the reader into those places where proofs have been innovative and have played a critical role.”―David M. Bressoud, author of Calculus Reordered: A History of the Big Ideas



"This is a lively story of the way that mathematics develops new concepts and ideas in order to solve hard problems. It is, at the same time, a story of the way that logic and the theory of computability emerged organically from reflection on mathematical method and thought. This book will be highly valuable to anyone interested in contemporary mathematics and how it came to be."
―Jeremy Avigad, Carnegie Mellon University

The Story of Proof―a book about mathematics as proof, and proof as mathematics, through the ages―is unique and enjoyable."―Anil Nerode, Cornell University

Details:

The Story of Proof: Logic and the History of Mathematics

Product ID: U0691234361
Condition: New

QAR25993

Price includes VAT & Import Duties
Type: Hardcover
Availability: In Stock

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Order today to get by 7-14 business days

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Every product in the BOLO catalogue is sourced through our Verified Global Supply Network of verified sellers, authorized distributors or directly from the manufacturer.

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Unless otherwise stated, all prices displayed on the product page include applicable taxes and import duties.

BOLO operates in accordance with the laws and regulations of Qatar. Any items found to be restricted or prohibited for sale within the Qatar will be cancelled prior to shipment. We take proactive measures to ensure that only products permitted for sale in Qatar are listed on our website.

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Similar suggestions by Bolo

The Story of Proof: Logic and the History of Mathematics

Product ID: U0691234361
Condition: New
The Story of Proof: Logic and the History of Mathematics-0
Type: Hardcover

QAR25993

Price includes VAT & Import Duties
Availability: In Stock

Quantity:

|

Order today to get by 7-14 business days

This item qualifies for free delivery

Returns & Warranty policies

Imported From: United States

At BOLO, we work hard to ensure the products you receive are new, genuine, and sourced from reputable suppliers.

Every product in the BOLO catalogue is sourced through our Verified Global Supply Network of verified sellers, authorized distributors or directly from the manufacturer.

Each product undergoes thorough inspection and verification at our consolidation and fulfilment centers to ensure it meets our strict authenticity and quality standards before being shipped and delivered to you.

If you ever have concerns regarding the authenticity of a product purchased from us, please contact Bolo Support. We will review your inquiry promptly and, if necessary, provide documentation verifying authenticity or offer a suitable resolution.

Your trust is our top priority, and we are committed to maintaining transparency and integrity in every transaction.

While we strive to display accurate information, variations in packaging, labeling, instructions, or formulation may occasionally occur due to regional differences or supplier updates. For detailed or manufacturer-specific information, please contact the brand directly or reach out to BOLO Support for assistance.

Unless otherwise stated, all prices displayed on the product page include applicable taxes and import duties.

BOLO operates in accordance with the laws and regulations of Qatar. Any items found to be restricted or prohibited for sale within the Qatar will be cancelled prior to shipment. We take proactive measures to ensure that only products permitted for sale in Qatar are listed on our website.

All items are shipped by air, and any products classified as “Dangerous Goods (DG)” under IATA regulations will be removed from the order and cancelled.

All orders are processed manually, and we make every effort to process them promptly once confirmed. Products cancelled due to the above reasons will be permanently removed from listings across the website.

Description:

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.


Editorial Reviews

Review

"This book could well serve as a history of mathematics. … [Stillwell] has done an amazing job of collecting and categorizing many of the most important ideas in this area."---Jim Stein, New Books in Mathematics

"Stillwell’s
[The Story of Proof] joins his two other Princeton University Press books in having my highest recommendation. I just wish they had been around when I was a student."---George Hacken, Computing Reviews

"I hugely enjoyed this book."
---Jonathan Shock, Mathemafrica

"This book would be perfect for any keen undergraduate, keen amateur, or indeed a teacher of mathematics, who wants a book to dip into to use for the classroom."
---Jonathan Shock, Mathemafrica

"

A well-crafted, thought-provoking meditation on the concept of proof in mathematics. . . .It is a substantive book that deserves to be read and reflected upon.

"---Tommy Murphy, Irish Mathematical Society Bulletin

"This is a work that mathematicians, historians, and philosophers will find especially engaging, as will anyone with a serious interest in mathematics and the limits of certainty that it is constantly probing."
---J.W. Dauben, Choice

"Stillwell's book is fundamentally an ode to mathematical progress and a retrospective on how far we have come in developing a mathematically sound theory of proof itself."
---Alexi Block Gorman, The Mathematical Intelligencer

Review

“I am a great admirer of Stillwell’s writing, and this book does not disappoint. Ranging broadly and authoritatively over the history of mathematics, he takes the reader into those places where proofs have been innovative and have played a critical role.”―David M. Bressoud, author of Calculus Reordered: A History of the Big Ideas



"This is a lively story of the way that mathematics develops new concepts and ideas in order to solve hard problems. It is, at the same time, a story of the way that logic and the theory of computability emerged organically from reflection on mathematical method and thought. This book will be highly valuable to anyone interested in contemporary mathematics and how it came to be."
―Jeremy Avigad, Carnegie Mellon University

The Story of Proof―a book about mathematics as proof, and proof as mathematics, through the ages―is unique and enjoyable."―Anil Nerode, Cornell University

Details:

Similar suggestions by Bolo