The main topic of this post has absolutely nothing to do with mathematics, except insofar as the well-known analogies between mathematics and music are concerned, but the recent article “Pearls before breakfast” in the Washington Post makes for fascinating reading. They conduct a very interesting experiment regarding the relationship between quality and context: what would happen if one took one of the finest and most renowned violinists in the world, and made him give a concert-quality performance, while busking incognito at a busy subway station? The results… well, I won’t spoil them, but suffice to say that the article is well worth the read.
One wonders whether one could conduct a similar experiment in mathematics. The main new difficulty, of course, is that good music can (in principle) be appreciated by any attentive and interested listener, but the same is much less true of good mathematics. But perhaps there is a substitute experiment which would also be revealing. For instance, in Feynman’s well-known book (in the chapter “Alfred Nobel’s other mistake”), one reads that, to avoid crowds of curiosity-seekers, the Nobel prize-winning physicist would sometimes give public lectures unannounced, as a last minute substitute for the announced (and fictional) lecturer; but the published title and abstract (e.g. “On the structure of the proton”) would be absolutely accurate, and thus only draw in people who were interested in the subject matter and not in the lecturer himself. Indeed, the crowds were much reduced as a consequence.
[Update, April 25, 2008: The above article won the 2008 Pulitzer Prize for Feature Writing.]