Saturday, October 08, 2005

The "right" kind of research

Not Even Wrong points to an essay by Sir Michael Atiyah in the Bulletin of the AMS on mathematical beauty. Reading it (and he writes, and speaks exceedingly well; the interview that he and Isadore Singer gave after wining the Abel prize is a gem to read) reminded me of the constant arguments we have about the "right" kind of theoretical computer science (which the FOCS/STOC/SODA/SoCG brouhaha was really a proxy for).

It reminded me of these arguments because it illustrates how pointless they really are (and I have been as guilty as any in attempting to "define" the right kind of research):
We can identify a long list of desirable qualities: beauty, elegance, importance,
originality, usefulness, depth, breadth, brevity, simplicity, clarity. However,
a single work can hardly embody them all; in fact some are mutually incompatible.
Just as different qualities are appropriate in sonatas, quartets or symphonies, so
mathematical compositions of varying types require different treatment.
He goes on to describe the myriad ways in which mathematical beauty (to him) appears in a work. It's interesting to read it, but what's even more important is the disclaimer:
...what follows are my personal preferences and make no claim to universality. In fact I glory in the diversity of mathematics and the lack of a uniform straightjacket [sic]. This is what makes it live.
At the end of the essay, he briefly dwells on the role of applied work in mathematics (another topic of relevance in theoryCS):
Much of mathematics was either initiated in response to external problems or has subsequently found unexpected applications in the real world. This whole linkage between mathematics and science has an appeal of its own, where the criteria must include both the attractiveness of the mathematical theory and the importance of the applications. [...]. Not only can we mathematicians be useful, but we can create works of art at the same time, partly inspired by the outside world.

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