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
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  and Functions and Graphs . Much later in my
life I met one of the authors of the books, the famous mathemati-