Mathematics and Its History

From the reviews of the first edition:
"There are many books on the history of mathematics in which mathematics is subordinated to history. This is a book in which history is definitely subordinated to mathematics. It can be described as a collection of critical historical essays dealing with a large variety of mathematical disciplines and issues, and intended for a broad audience. ... we know of no book on mathematics and its history that covers half as much nonstandard material. Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many." (Mathematical Intelligencer)

"The discussion is at a deep enough level that I suspect most trained mathematicians will find much that they do not know, as well as good intuitive explanations of familiar facts. The careful exposition, lightness of touch, and the absence of technicalities should make the book accessible to most senior undergraduates." (American Mathematical Monthly)

• algebraic number theory
• elliptic function
• history of mathematics
• number theory

From the reviews of the first edition:

"There are many books on the history of mathematics in which mathematics is subordinated to history. This is a book in which history is definitely subordinated to mathematics. It can be described as a collection of critical historical essays dealing with a large variety of mathematical disciplines and issues, and intended for a broad audience...we know of no book on mathematics and its history that covers half as much nonstandard material. Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many." (Mathematical Intelligencer)

"The discussion is at a deep enough level that I suspect most trained mathematicians will find much that they do not know, as well as good intuitive explanations of familiar facts. The careful exposition, lightness of touch, and the absence of technicalities should make the book accessible to most senior undergraduates." (American Mathematical Monthly)

"...The book is a treasure, which deserves wide adoption as a text and much consultation by historians and mathematicians alike." Physis - Revista Internazionale di Storia della Scienza
"A beautiful little book, certain to be treasured by several generations of mathematics lovers, by students and teachers so enlightened as to think of mathematics not as a forest of technical details but as the beautiful coherent creation of a richly diverse population of extraordinary people...His writing is so luminous as to engage the interest of utter novices, yet so dense with particulars as to stimulate the imagination of professionals." (Book News, Inc.)

From the reviews of the second edition:

"The author discusses many subjects by tracing their historical developments and showing their interactions. … Eachchapter includes biographical notes, describing briefly the life of the main contributors. Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students … and will give them a good account of how the different branches of mathematics interact." (Dennis Bonheure, Bulletin of the Belgian Mathematical Society, 10:4, 2003)

"The book is focused on the mathematics, which is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. … This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." (European Mathematical Society Newsletter, September 2002)

"This book covers many interesting topics not usually covered in a present day undergraduate course … . The fact that the topics are introduced in their historical context will enable students to better appreciate and understand the mathematical ideas involved. … Topics are presented mainly in a present-day context, using modern terminology and notation. … All of the chapters contain a number of interesting mathematical concepts, results and exercises. … I can suggest no better text than Stillwell’s excellent book." (David Parrott, The Australian Mathematical Society Gazette, 29:5, 2002)

"This successful book appeared in 1989 and has been reprinted several times … . The new edition is substantially longer than its predecessor, mainly due to some new chapters, more exercises, a larger bibliography (which contains several little-known items, both primary and secondary), and an elaborated index. … An impressive range of topics is covered …" (Ivor Grattan-Guinness, Zentralblatt MATH, 985, 2002)

• Department of Mathematics, University of San Francisco, San Francisco, USA

  John Stillwell

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