This book presents a concise unified view of mathematics and its historical development. It is aimed at senior undergraduates - or other mathematicians - who have mastered the basic topics but wish to gain a better grasp of mathematics as a whole. Reasons for the emergence of the main fields of modern mathematics are identified, and connections between them are explained, by tracing the course of a few mathematical themes from ancient times down to the 20th century.

The emphasis is on history as a method for unifying and motivating mathematics, rather than as an end in iteself, and there is more mathematical detail than in other general histories. No historical expertise is assumed, and classical mathematics is rephrased in modern terms whenever it seems desirable. Nevertheless, there are copious references to original sources, and readers wishing to explore the classics for themselves will find it a useful guide.

An advantage of the unified approach is that it ties up loose ends and fills gaps in the standard undergraudate curriculum. Thus, readers can expect to add to their mathematical knowledge as well as gaining a new perspective on what they already know.

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From the reviews of the second edition:

"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."

(David Parrott, Australian Mathematical Society)

"The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... 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)

"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 that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact."

(Denis Bonheure, Bulletin of the Belgian Society)

This third edition includes new chapters on simple groups and combinatorics, and new sections on several topics, including the Poincare conjecture. The book has also been enriched by added exercises.

John Stillwell is a professor of mathematics at the University of San Francisco. He is also an accomplished author, having published several books with Springer, including The Four Pillars of Geometry; Elements of Algebra; Numbers and Geometry; and many more.

*"About this title" may belong to another edition of this title.*

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