Today an interview with me was posted at “The Browser,” a British website devoted mostly to book reviews. Before I talk about the interview, let me just say how much I love their concept. The centerpiece of the website is called “Five Books,” a series where they ask notable people (usually authors, sometimes other experts or celebrities) to pick a theme and talk about their five favorite books relating to that theme.
I picked the theme “The Beauty and Fun of Mathematics.” The five books I chose were:
- Induction and Analogy in Mathematics by George Polya;
- Magical Mathematics by Persi Diaconis and Ron Graham;
- Indra’s Pearls, by David Mumford, Caroline Series, and David Wright;
- Penrose Tiles to Trapdoor Ciphers by Martin Gardner;
- The Dot and the Line: A Romance in Lower Mathematics by Norton Juster.
The very first question that the interviewer asked me, actually more of a comment, was a doozy:
You have picked five books that describe the fun and beauty of mathematics – two words which many of us may not usually associate with the subject.
Mathematicians are constantly reminded of the fact that there are lots of people out there who don’t enjoy the subject, and who don’t consider it fun or beautiful. That’s not true of all readers, by the way; there are plenty of readers who completely “get” mathematics. Nevertheless, I am glad to be reminded of the mixed feelings of the reading public, because it reinforces the importance of my message. If I can help just one person “get” it, then I have done something more important than preaching to the already converted.
Anyway, here is how I responded to the sort-of question:
I chose this topic partly with the idea in mind that it might be surprising for people. But for me, mathematics has always been something that I have found both fun and beautiful. Three of the books that I will talk about here have strong personal connections. And they are all a lot of fun.
I think that the fun in mathematics comes from interacting and participating with it. You notice something curious – perhaps something very simple – and you want to understand it. For instance, that the decimal for 1/7 repeats every six digits, while the decimal for 1/3 repeats every digit. Why? What determines the length of that cycle? Mathematics has the amazing property of being able to lead you through a maze of interacting concepts. The phenomenon I just mentioned will lead you deep into a subject called number theory, which is still not completely understood. The fun of mathematics is finding out where it is going to take you.
And the beauty of mathematics has a couple of different interpretations. Sometimes it can be pure visual beauty. Mathematics produces some of the most stunning images that you will find anywhere – images that will completely bend your mind. Another aspect of beauty in maths is closely related to the idea of truth. In mathematics you are always trying to work out what is the truth, and very often the best proof is the most beautiful, because it strips away all of the things that aren’t necessary to your problem and takes you to its very core.
For the rest of the interview, and to read my reasons for choosing each of the above books, please click on over to “The Browser.” Let me just say in conclusion that I enjoyed having the opportunity to direct people’s attention to some unique and unforgettable books, including some long-time favorites and some very new favorites.
