1 A Taste of Things to Come This is the opening chapter of the book, and I use it to set the tone of my narrative: I start with some simple mathematical observations and briefly discuss what they possibly say about the inner workings of our minds. Surprisingly, this discussion very naturally involves some non-trivial ideas and results from the frontier of mathemati- cal research. But it is better to see it for yourself. 1.1 Simplest possible example Simplicity, simplicity, simplicity! I say, let your affairs be as two or three, and not a hundred or a thousand instead of a million count half a dozen, and keep your accounts on your thumb-nail. Henry David Thoreau, Walden In my account, I am not afraid to be very personal, almost sen- timental, and have decided to start the discussion of the “simple things” of mathematics by turning to my memories from my school years. Always test a mathematical theory on the simplest possible example—and ex- plore the example to its utmost limits. I had my most formative mathe- matical experiences at the tender age of thirteen, when I still lived in my home village on the shores of Lake Baikal in Siberia. I learned elemen- tary calculus from two thin booklets sent to me from a mathematics corre- spondence school: The Method of Co- ordinates [266] and Functions and Graphs [267]. Much later in my life I met one of the authors of the books, the famous mathemati- 3 http://dx.doi.org/10.1090/mbk/071/01
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