The behind-the-scenes processes by which things get made — laws, journalism, sausages — are usually said to be so chaotically unhygienic that seeing them in action will put you off the thing itself for good. There are exceptions, though, and in the last few days, mathematics has earned a spot on that second list, at least as far as uninitiated lay people are concerned.
Last week, a young mathematician at HP Labs, Vinay Deolalikar, began circulating a paper that claimed to solve what’s known as the P=NP problem. This is one of the biggest unsettled issues in math and computer science; in fact, the terms “P” and “NP” appear in the titles of computer science research papers more than just about any others. While proposed solutions to P=NP have been common over the years, they are typically offered by amateurs and crackpots. To have a credentialed researcher at a top-flight institution step forward and claim the laurel is rare indeed. In some circles, Deolalikar quickly became even better known than his former boss, Mark Hurd, who was forced out as HP CEO last week after a bizarre non-sex non-scandal.
...In a post yesterday about the Deolalikar paper, I remarked on how civil the online discussion about it seemed, certainly in contrast to most other Internet debates. One correspondent chided me for being too naïve, and reminded me that mathematicians are as capable of catty bitchfests as anyone. A prominent example involves the issue of credit for another math problem, the Poincare conjecture. The controversy was written up in the New Yorker by the author of “A Beautiful Mind.”
I plead guilty to being a slavish math fanboy. But at least I am not alone. As another blog commenter put said about the current discussionThis member of the community at large can’t understand a word you say, but is nevertheless fascinated by every new post and comment. Seeing the review process unfold in public has rekindled my long-dormant interest in mathematics…Thank you.- Lee Gomes, "A Beautiful Sausage"
Like Gomes, I know nothing about the mathematical details behind this recent attempt at a P!=NP proof. I fled precalculus with extreme abandon in eleventh grade, and since then I have had no exposure to any mathematical concept more complicated than the middle-school-level problems on the GRE. When I read even layman's terms summaries of such concepts, my mind instantly abandons any attempt at coherent reasoning and starts thinking about dinner instead. Does this make me a bad historian of science/technology/mathematics? On a certain level, yes--to the extent that we, even more than scientists themselves, are expected to render the development and evolution of concepts from the hard sciences intelligible to people from other fields. I don't think I'll ever be able to do that well without relying on handwaves that camouflage my own ignorance.
Of course, the fact that I don't understand something is not much of a topic for a blog post. I am interested in something more, well, interesting: the contrast between the mathematical sociability captured in Gomes's post and the scientific mode of self-presentation I described last month. Here's the paradox. By and large, the general public, even the public of educated people, is just as ignorant of mathematics as I am (despite probably having gotten to calculus). So why is there so much interest in the big stories that have shaken the mathematics world recently--Deolalikar's attempt to prove P!=NP and Grigory Perelman's apparently successful proof of the Poincaré Conjecture? These stories are not blips, either: consider the popularity of Pi and A Beautiful Mind and that one documentary about Andrew Wiles. The New Yorker-reading section of the public, it is safe to say, loves math drama.
Contrast this with the reception of similar developments in the hard sciences. Although almost everyone knows something about science, we are generally neither exposed to nor allowed to glimpse the catty infighting and intrigue that surrounds them. The best we generally get is a bare "Scientists have found," whose content, from the point of view of public access to the scientific process, is only slightly above that of an ancient report on the entrails of the latest sacrificial goat. As a result, the public focuses on the findings--which may be interesting and even awe-inspiring--but learns little about their context or significance, and gains little trust in scientists themselves. Science journalism is reviled, and reviled deservedly, because it remains wedded to this model of publication. (Where would science journalists be without press releases?)
The other paradox, which is perhaps even more significant, is that this kind of access to mathematical drama has not lowered the prestige and intellectual authority of mathematicians. Quite the contrary: I would say that not since Albert Einstein have mathematicians inspired so much unmixed admiration. I suspect that the explanation is not too distant from the one I suggested a month ago. When you demonstrate to people that you are not a conspiratorial gang of power addicts and control freaks in league to manipulate the public--and even when you expose, as Grigory Perlman did, the petty plagiarism and priority squabbles that characterize your profession--it instantly becomes easier to comprehend what you are trying to accomplish. Mathematicians have been locked in a self-enclosed world for so long that they have not made serious or visible efforts to construct a public face for their profession; this has left them, paradoxically, better placed than scientists to take advantage of the great reserves of sympathy and interest that characterize our new economy of attention. Let's hope the lesson is heeded.