In Journey through Genius, author William Dunham strikes an extraordinary balance between the historical and technical. He devotes each chapter to a principal result of mathematics, such as the solution of the cubic series and the divergence of the harmonic series. Not only does this book tell the stories of the people behind the math, but it also includes discussions and rigorous proofs of the relevant mathematical results.
In the Preface, the author comments that it is common practice to teach appreciation for art through a study of the great masterpieces. Art history students study not only the great works, but also the lives of the great artists, and it is hard to imagine how one could learn the subject any other way. Why then do we neglect to teach the Great Theorems of mathematics, and the lives of their creators? Dunham sets out to do just this, and succeeds beyond all expectations.
Each chapter consists of a biography of the main character interwoven with an exposition of one of the Great Theorems. Also included are enough additional theorems and proofs to support each of the main topics so that Dunham essentially moves from the origins of mathematical proof to modern axiomatic set theory with no prerequisites.
Admittedly it will help if the reader has taken a couple of high school algebra classes, but if not, it should not be a barrier to appreciating the book. Each chapter concludes with an epilogue that traces the evolution of the central ideas forward in time through the history of mathematics, placing each theorem in context.
In chapters 2 and 3 we get a healthy dose of Euclid. Dunham briefly covers all 13 books of “The Elements”, discussing the general contents and importance of each. He selects several propositions directly from Euclid and proves them in full using Euclid’s arguments paraphrased in modern language.
The diagrams are excellent, and very helpful in understanding the proofs. If you’ve ever tried to read Euclid in a direct translation, you should truly appreciate Dunham’s exposition: the mathematics is at once elementary, intricate, and beautiful, but Dunham is vastly easier to read than Euclid. The Great Theorems of these chapters are Euclid’s proof of the Pythagorean theorem and The Infinitude of Primes, which rests at the heart of modern number theory. Dunham obviously loves Euclid, and his enthusiasm is infectious. After reading this, it is easy to see why “The Elements” is the second most analyzed text in history (after The Bible).
In brief, “Journey Through Genius” might almost be considered a genius work of mathematical exposition.
Related Books:
- The Princeton Companion to Mathematics: Timothy Gowers,June Barrow-Green,Imre Leader
- The Language of Mathematics: Making the Invisible Visible – Keith Devlin
- The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics : Clifford A. Pickover
- Team of Rivals: The Political Genius of Abraham Lincoln – By Doris Kearns Goodwin
- Basic Teachings of the Great Philosophers : S.E. Frost
- Elementary and Middle School Mathmatics: Teaching Developmentally (Paperback)- By John A. Van De Walle
- Algebra and Trigonometry : By Michael Sullivan
- A Journey: My Political Life – Tony Blair
