Computer as Crucible

Jonathan Borwein received his PhD from Oxford University as a Rhodes Scholar and is a professor of mathematics and computer science at Dalhousie University in Canada. He is the author of seminal works in the growing field of experimental mathematics, including Mathematics by Experiment (9781568814421) and Experimental Mathematics in Action (9781568812717), and more. Keith Devlin is Executive Director and Senior Researcher at the Center for the Study of Language and Information at Stanford University. He is the author of many books and articles that popularize mathematics and is the "Math Guy" for National Public Radio. He is the author of The Unfinished Game (9780465009107) and The Math Instinct (978-1560258391), among many others.

The long experience of both authors can be clearly seen in the way they describe a number of problems … they succeeded in exactly the right balance between mathematical depth and accessibility for a wide audience. The result is an easily digestible book full of humor for anyone with an affinity for mathematics …—Dan Roozemond, Nieuw Archief voor WiskundeThe sleuth-like style and lucid writing certainly make this book an enjoyable read. Many explanations are framed by relevant historical context and tales of mathematicians whose use of experimental mathematics helped them gain insights into difficult problems. . . . I thoroughly enjoyed reading this short introduction to experimental mathematics. It will no doubt appeal to a broad mathematical audience, both professional and amateur alike.—Mitch Wheat, Gazette of the Australian Mathematical Society, July 2009It is a pleasant and readable book for any working mathematician who wants to know something more about the use of computers for generating hypotheses on relations among known and less known special numbers.—Newsletter of the European Mathematical Society, June 2009... allows [the reader] to take a look at some interesting problems and solve [them] using [a] computer. The authors are showing how a mathematician can use a computer as a tool. ... The book covers a variety of topics and examples in order to give the reader a good sense of the current state of play in the rapidly growing new field of experimental mathematics. ... The writing is clear and the explanations are enhanced by relevant historical facts and stories of mathematicians and their encounters with the field over time. The book will be of interest to any reader who would like to taste the solving of mathematical problems with a computer. No matter if readers may not have much mathematical knowledge: they can catch the essentials with the book, and have fun exploring some questions.—Valentina Dagiene, Zentralblatt MATH, September 2009... a pleasant and readable book for any working mathematician who wants to know something more about the use of computers for generating hypotheses on relations among known and less known special numbers.—EMS Newsletter, June 2009... a lovely little book which builds a strong case for experimental mathematics. Any practicing mathematician or serious amateur should consider checking out this introduction to a topic that will no doubt transform mathematics.—Antonio Cangiano, Math-Blog.com, July 2010

• Preface, 1 What Is Experimental Mathematics?, 2 What Is the Quadrillionth Decimal Place of p?, 3 What Is That Number?, 4 The Most Important Function in Mathematics, 5 Evaluate the Following Integral, 6 Serendipity, 7 Calculating p, 8 The Computer Knows More Math Than You Do, 9 Take It to the Limit, 10 Danger! Always Exercise Caution When Using the Computer, 11 Stuff We Left Out (Until Now), Answers and Reflections, Final Thought, Additional Reading and References