When I mention a book like Journey Through Genius: The Great Theorems of Mathematics by William Dunham, I generally get two types of reactions. The first is something similar to Sheldon Cooper’s reaction to Brian Greene in the Big Bang Theory.
Brian Greene: (about his book The Hidden Reality) “I explore this possibility [of the multiverse] without presuming any knowledge of mathematics or physics on the part of the reader.” Sheldon: “Hysterical!”
The second is something like math book? It’s not for a class? Okay, sounds dry … If I’m honest, this reaction is usually deserved. Authors writing for the general public usually don’t include many equations or somewhat scientifically rigorous explanations and detail. Whereas more rigorous books like What is Mathematics (one of my favorites), can be a bit dense and dry. Journey Through Genius manages to avoid both these problems.
The book aims to treat math as an art form, presenting the great theorems of math the way great paintings or novels are presented in order to appreciate painting and literature. Dunham places the theorems in their historical context; for example, his chapter on the Pythagorean Theorem gives a summary of the state of mathematics until that point and a history of Greece. He also adds things about the great mathematicians who were the “artists” behind these theorems. Would you believe a story involving intriguing, public face offs in which the loser had to give the winner ”thirty lavish banquets,” a man who had lost three fingers in a particulary bad duel due to his hot temper and his antagonism with a man who had his face slashed by an enemy soldier as a child and was thenceforth known as the “stutterer,” and a socially shunned man who regulary saw and interpreted visions with a gambling problem to be about math? Turns out, it’s about the solution of the cubic.
Dunham does a great job with the actual math too. He presents the theorems quite clearly, and is very lucid with the presentation of the proofs. Some of the proofs do require some effort to get through, but to me that puts the book above most books that can be classified as “popular science.” It certainly does a good job of enabling the reader to really appreciate the ingenuity behind the theorems.
There is one problem I have with the book: Dunham barely mentions the contributions of Islamic scholars to math. He says that they didn’t emphasize or leave behind much of the proofs for their work, but I feel that he could at least mention them more in his synopsis of the state of math and general intellectual history at the beginning of each chapter. Afterall, when both algebra and algorithm derive their name from one scholar and his book Al-Khwarizmi, they deserve some more mention in a book about the great theorems of math throughout history. However overall, this book is a gem for people who like math and intellectual history in general and a recommended read for math undergraduates. I highly recommend it.