Thursday, February 03, 2005

Timothy Gowers and the study of mathematics

When I was in high school I used to watch the Carl Sagan series 'Cosmos', and was fascinated by how he used to bring physics to life. I even remember the episode where he describes the physical consequences of the natural constants being closer to real life (suppose the speed of light was 50 mph, etc).

Ever since then, I've looked for expositors who could extract the same kind of beauty out of mathematics and computer science, distilling its essence in a way that might seem obvious to those of us who practice it, but that allows the core concepts to be revealed to a non-technical audience in a way that captures the imagination.

Timothy Gowers, the Fields Medalist, is well known for his expository articles on a variety of topics. He gave a speech in 2000 in Paris at an event sponsored by the Clay Mathematics Institute. The speech was titled 'The Importance of Mathematics', and I highly encourage watching it.

What struck me the most about this lecture was his eloquent defense of mathematics, and how he conveyed a sense of the aesthetic beauty of the field (why mathematicians refer to a theorem as 'beautiful'). With beautiful examples, he systematically laid out the landscape of a mathematical life, not in terms of topics, but in terms of how mathematical work is done.

He firmly dismissed the idea of mathematics needing to be useful (something we have had our own controversies over in theoryCS), and distinguished between the two statements
(1) Mathematics is not a useful subject
(2) A typical mathematician does not try to be useful.
arguing that (1) is false even though (2) is usually true, and that it should be this way.

A simple way of expressing some of the ideas in his lecture would be:
Mathematics is surprisingly useful, because complexity arises from simplicity and beauty reveals itself to be important.
I just bought his book 'Mathematics: A Very Short Introduction', which brings out these ideas in much more detail, and also puts to rest some of the usual canards associated with mathematics (the 30yr old rule, the lack of women, etc).

To some degree, the description of the daily activities of an algorithms researcher are similar to that of a mathematician, but in many ways they are different. We need a similar exposition for theoryCS !

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