Good books written by great mathematicians

Question

I read many of Richard Fenynman's books and I found them both very entertaining and moving, showing the human side of a brilliant scientific mind. I recently read also a collection of P.A.M. Dirac's writings on the topic of beauty and mathematical truth. I personally find that reading good non-technical books about personal histories, biographies, ways of conceiving the universe written by great scientists is always very enlightening. Feynman and Dirac represent (mostly) a physic's point of view, so I'd be interested in reading some thoughts from great mathematicians.

So my question is: could you please suggest good books of this kind? The constraints are the following:

• the author is a great mathematician (universally acknowledged as such)
• the book/writing is not a paper, i.e. it's not a technical essay on some of the author's research;
• the main topic of the book/writing is the author's world view, philosophical thoughts, considerations about mathematics et similia.

An example of such a book could be Science et Hypothèse by Henri Poincaré.

Answer 1

How to Solve It: A New Aspect of Mathematical Method by George Pólya fits the bill perfectly. Not only is the author a first-rank mathematician, the work is also philosophical, mathematical and above all practical at the same time. A rare combination indeed!

Answer 2

Serge Lang has written a large number of books. The ones satisfying the above requirements contain the following:

• The beauty of doing mathematics (1985)
• Math!: Encounters with high school students (1985)
• Challenges (1997)

There is also a very good book by David Hilbert, "Natur und mathematisches Erkennen" (german title), but I don't know whether there exists a translation into english.

Answer 3

Enigmas of Chance by Mark Kac, perhaps?

Answer 4

Indiscrete Thoughts by Gian-Carlo Rota.

I Want to be a Mathematician: An Automathography by Halmos.

Answer 5

Bertrand Russell was a philosopher in addition to being a mathematician. He wrote a rather famous book, A History of Western Philosophy in which he presents a historical account of Western Philosophy. He won the Nobel Prize in Literature for his lifetime of writings.