Problems for Journey Through Genius: The Great Theorems of Mathematics

Editor’s note: William Dunham’s enduring classic, Journey Through Genius: The Great Theorems of Mathematics, has enjoyed popularity among readers who want to learn more about mathematics and its history ever since its initial publication in 1990 (John Wiley & Sons; Penguin Paperbacks, 1991). Still in print after 25 years, it has been translated into Spanish, Italian, Japanese, Korean, and Chinese. Its finely crafted chapters, each featuring a “great theorem” of mathematics; its compelling and entertaining biography and history; and its substantial but accessible mathematics have made it a popular text for history of mathematics courses, despite its not having the exercise sets that usually follow each chapter of a mathematics textbook. Many of its adopters have written their own exercises, and some have enjoyed using the hitherto unpublished set of 162 exercises developed by Dunham himself during the early 1990s.

On the 25th anniversary of the publication of Journey Through Genius, Convergence is pleased to make available to our readers William Dunham’s own problem sets to accompany the book. The 162 problems are divided into 12 problem sets, one for each chapter of the text. In his Preface to Journey Through Genius, Dunham described the "great theorems" and proofs presented in each chapter as “genuine classics—the Mona Lisas or Hamlets of mathematics” (p. vii). He set out to provide both history and biography, he said, but to make his main focus “the creativity evident in these ‘mathematical masterpieces’” (p. vi). His “Problems for Great Theorems” are primarily mathematical problems, some of them quite challenging, that explore and extend the mathematics – and often the history – presented in Journey Through Genius.

Download PROBLEMS for Great Theorems (1.6MB pdf file).

Acknowledgments

Along with his wife Penny Dunham (now professor emeritus of mathematics at Muhlenberg College), William Dunham directed summer workshops titled “The Great Theorems of Mathematics in Historical Context” from 1988 to 1996. Perhaps fittingly, these workshops were funded not by NSF, but by the National Endowment for the Humanities (NEH). It was during the 1990s workshops, held at The Ohio State University, that Dunham, assisted by his workshop participants, developed the problems in the exercise sets presented here. During this time, Dunham sent copies of typewritten problems with hand-drawn diagrams to anyone who requested them. By 1996, the problems had been retyped in Word and, a bit later, the diagrams re-drawn. If you are responsible for the improved diagrams, please email the editor, Janet Beery, and let her know!

About the Author

William Dunham has taught mathematics as a professor at Hanover College in Hanover, Indiana; as Truman Koehler Professor at Muhlenberg College, in Allentown, Pennsylvania (where he is now emeritus); and as a visiting professor at Harvard University, Princeton University, and the University of Pennsylvania. He is a 2014-2016 MAA Pólya Lecturer; the instructor for the 24-lecture video course, “Great Thinkers, Great Theorems,” produced by The Learning Company for its Great Courses series; and the author or editor of five books on the history of mathematics, including Journey Through Genius. Presently, he is a Research Associate in Mathematics at Bryn Mawr College.

- Janet Beery, Editor, MAA Convergence