Written: Oct. 21, 2011
In his wonderful iconoclastic , masterpiece, "The Black Swan" the great flâneur Nassim Nicholas Taleb describes (pp. 145-156) the tragedy of the empty suit and the rampant charlatanism in many human "professions". On p. 146, he lists a few exceptions, including astronomers, chess masters, and mathematicians (when they deal with mathematical problems, not empirical ones).
You may be interested to know, my friend Nassim, that even pure mathematics has its share of the empty suit problem. Well, "empty" is a bit too strong. No mathematician, even those at Harvard, Princeton, and Yale, is totally empty, and of course the suits are allegorical, but so many mathematicians are way overrated (and I won't mention any names) because of their fancy "suits", using fashionable buzz-words to impress, dazzle, and intimidate. I agree that Andrew Wiles is a great mathematician, and I also agree that he used modular forms in his proof of FLT, but not everything about modular forms is great mathematics, and not every modular-former is a great mathematician. Conversely there is lots of great mathematics that can be described in plain English. But all things being equal, the chances of a piece of math to be accepted in the PNAS or in "prestigious" journals is far greater when one wears a "fancy suit". Humans will be humans, and while mathematicians are hardly seen wearing real suits, those who wear the metaphorical fancy suits come out "ahead".
Mathematicians also have a hang-up about "truth". For them "truth" means "proved". When a long-standing conjecture by a great mathematician is either proved or disproved it is considered a great event, worthy of publication in a "prestigious" journal. Drew Sills and I have just disproved a forty-years-old conjecture of the great number theorist Hans Rademacher. Alas, our "disproof" was empirical, even though the probability that the conjecture is true is far less than the probability that FLT is false (after all human "proofs" are notoriously unreliable). We tried to interest a distinguished number theorist, member of the NAS, for possible publication in the PNAS, and he politely replied that while the paper is certainly interesting, and should be published in a "good" journal, since we don't have a proven disproof, it is not PNAS material.
That same distinguished member of NAS, a few years ago, approved and endorsed (although it was officially edited and accepted by another member) an article proving "recent unpublished conjectures" about a new function that is "analogous" to famous number-theoretical functions. Its content was far less interesting than our (empirical) disproof of the Rademacher conjecture, but since it was wearing a fancy suit, it was readily accepted.
The truly great mathematics can be described in plain English. But then again, humans will be humans, and while mathematicians are not impressed by actual suits, many of them are suckers for modular forms, Langlands program, Ricci Flow and so on. Conversely, many of them look down on statements, and proofs, (especially empirical ones) that do not require five years of narrow and specialized training in graduate school.