Saturday, February 17, 2007

Tao on "Good Mathematics"

Early this week, Terence Tao posted an essay entitled What is Good Mathematics? on the arXiv. I thoroughly enjoyed reading this beautifully written article, commissioned to the author by the Bulletin of the AMS. Even though the description of the technical developments in the story of Szemeredi's theorem (see also here), which Tao uses as an example of good mathematics, passed me by (not surprisingly, alas), there is so much warmth and thoughtfulness in that essay to serve as an example of essay writing to all of us.

The final lines of the piece will serve as an appetizer.

Thus I believe that good mathematics is more than simply the process of solving problems, building theories, and making arguments shorter, stronger, clearer, more elegant, or more rigorous, though these are of course all admirable goals; while achieving all of these tasks (and debating which ones should have higher priority within any given field), we should also be aware of any possible larger context that one’s results could be placed in, as this may well lead to the greatest long-term benefit for the result, for the field, and for mathematics as a whole.

Well said indeed!

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