I’ve been thinking a lot lately about books. About all the books I’ve read, all the books I want to read. And the ever-lengthening list of books that have been recommended to me. But even though I suspect I will never get through all the books on this lift, I am always grateful for a well-thought-out recommendation.
In that spirit, today I want to recommend three books to anyone who has enjoyed any post on this site. Each of them is full of information about the history of mathematics, brain-strengthening math content, and most importantly to us deep insights into the Zen of mathematics. I assure you that none of these books is about apples.
Today’s Recommendations (alph. by author)
- Prime Obsession, by John Derbyshire
- Journey Through Genius: the great theorems of mathematics, by William Dunham
- An Imaginary Tale: The Story of , by Paul Nahin.
I have a copy of Prime Obsession on the shelf in my office in Ann Arbor, and it is surprising how often I show it to a student to make one point or another. People often ask me what I do, or what mathematicians do, or what there can possibly be left to study in mathematics that isn’t already figured out. This book deals with the Riemann Hypothesis, the proof or disproof of which is widely considered the hottest open problem in mathematics today. If you want to know why, read the book. The format of the book is extremely helpful — the chapters deal alternately with mathematical history and with mathematics directly. Readers with very specific interests can easily read just the appropriate chapters and have a self-contained experience. Reading the whole book gives the full picture.
It so happens that I included Journey Through Genius on today’s list, I suppose because it is the first book I read by this author, but the truth is any of his books belongs on this list and deserves a mention. Dunham is an outstanding expositor of mathematics ideas to a very wide audience.
I confess that I have not yet finished reading An Imaginary Tale–I’m a bit more than half of the way through and enchanted. This Tale turns out to deal with deeper themes of pure and applied mathematics, of computations and problem-solving, of confusion and controversy, and of the role of “meaning” in mathematics.