I was reading Ecology, the Ascendent Perspective by Robert Ulanowicz when I came across the following interesting passage which made me think of this thread:
In January 1684 Sir Christopher Wren and Edmund Halley met with Hooke in Oxford during a session of the Royal Society. Wren and Halley were both interested in establishing a rigorous connection between the inverse-square law of attraction and the elliptical shape of planetary orbits. When they inquired of Hooke whether such a connection was possible, Hooke told them he had already completed the demonstration but that he intended to keep the proof secret until others, by failing to solve the problem, had learned to value it (Westfall 1983).
Wren and Halley evidently were dissatisfied with Hooke's coyness, for in August of the same year, when Halley was in Cambridge, he sought out Newton in order to pose the problem to Hooke's rival. Newton told Halley that he too had already solved the problem but had mislaid the proof...Wren decided to call the bluff of the two enemies by publicly offering an antique book worth forty shillings as a prize to the individual who could provide him a proof within two months.
Newton was distraught when Halley told him of Hooke's claim to a proof. Apparently, Newton did not lie when he claimed that he had already proved the connection, for a copy of a proof that antedates Halley's visit has indeed been found among Newton's papers. Being cautious in the company of someone who communicated with Hooke, Newton probably feigned having misplaced the proof. We can only imagine his horror, then, when he looked up his demonstration only to discover that it was deeply flawed. The thought of leaving the field open to Hooke drove Newton to near-panic. He abandoned all other ongoing projects to rush into seclusion and attempt a rigorous exposition. Once thus engaged, the positive rewards of the creative process seem to have drawn him ever deeper into the project. He virtually disappeared from society until the spring of 1686, at which time he emerged, on the brink of mental and physical exhaustion, with three completed volumes of the Principia in hand.
I'm worried about the lack of a citation for the last paragraph, but if this is accurate then it is very interesting.
In my time in the mathematical community I've formed the subjective impression that it's noticeably less common for mathematicians of the highest caliber to engage in status games than members of the general population do. This impression is consistent with the modesty that comes across in the writings of such mathematicians. I record some relevant quotations below and then discuss interpretations of the situation.
Acknowledgment - I learned of the Hironaka interview quoted below from my colleague Laurens Gunnarsen.
Edited 10/12/10 to remove the first portion of the Hironaka quote which didn't capture the phenomenon that I'm trying to get at here.
In a 2005 Interview for the Notices of the AMS, one of the reasons that Fields Medalist Heisuke Hironaka says
(I'll note in passing that the sense of the "genius" that Hironaka is using here is probably different than the sense of "genius" that Gowers uses in Mathematics: A Very Short Introduction.)
In his review of Haruzo Hida’s p-adic automorphic forms on Shimura varieties the originator of the Langlands program Robert Langlands wrote
For context, it's worthwhile to note that Langlands' own work is used in an essential way in Hida's book.
The 2009 Abel Prize Interview with Mikhail Gromov contains the following questions and answers:
In his MathOverflow self-summary, William Thurston wrote
I interpret the above quotations (and many others by similar such people) to point to a markedly lower than usual interest in status. As JoshuaZ points out, one could instead read the quotations as counter-signaling, but such an interpretation feels like a stretch to me. I doubt that in practice such remarks serve as an effective counter-signal. More to the point, there's a compelling alternate explanation for why one would see lower than usual levels of status signaling among mathematicians of the highest caliber. Gromov hints at this in the aforementioned interview:
In Récoltes et Semailles, Alexander Grothendieck offered a more detailed explanation:
The amount of focus on the subject itself which is required to do mathematical research of the highest caliber is very high. It's plausible that the focuses entailed by vanity and ambition are detrimental to subject matter focus. If this is true (as I strongly suspect to be the case based on my own experience, my observations of others, the remarks of colleagues, and the remarks of eminent figures like Gromov and Grothendieck), aspiring mathematicians would do well to work to curb their ambition and vanity and increase their attraction to mathematics for its own sake.