If nightmares had titles, that would be the title of a recurring nightmare that plagues more than a few colleagues: that our funding will be at the mercy of the meat cleaver if the word ever gets out that mathematicians pursue our vocation because it brings us pleasure. I am certainly not going to complain about Jim Holt’s exceedingly generous review in the New York Review of Books, but it was to be expected that some of my more complex arguments would not survive the process of compression to fit the review’s (also generous) word limit. Thus, after reporting my suspicion that mathematicians use the word beauty to describe our goal because it sounds more respectable than pleasure, Holt goes on to frame a quotation from MWA:
Why should society pay for a small group of people to exercise their creative powers on something they enjoy?
“If a government minister asked me that question,” Harris writes, I could claim that mathematicians, like other academics, are needed in the universities to teach a specific population of students the skills needed for the development of a technological society and to keep a somewhat broader population of students occupied with courses that serve to crush the dreams of superfluous applicants to particularly desirable professions (as freshman calculus used to be a formal requirement to enter medical school in the United States).
That first step down the slippery slope of compression leads inevitably to talk of angry taxpayers. Hence, this online comment by Richard Fateman, a retired computer scientist from Berkeley, who read the review but not the book, and observes:
one cannot be surprised when (US) taxpayers object to what they see as wasted money. My own institution, the University of California, used to be “state supported”. The state dropped its funding to 11% (2011-2012). (may be slightly higher in this next year). Outside of academia, taxpayers apparently object to paying for the repair of bridges and roads. (etc. etc.)
How then can one drum up government (or private!) support for studies in pure mathematics when they are portrayed as having no utility except to give pleasure to a small group of mathematicians?
How indeed? My advice is to begin by examining what one has been programmed to think and to say, and how this programming — or operant conditioning, the habit of repeating what we hear — diverts us from the path of analysis and inquiry. The word taxpayer already conjures up a different conception of society than the word citizen. The latter participates in a social contract, the former is an agent of rational choice who views society as an opportunity to choose an investment strategy. I personally don’t believe that the “taxpayer” exists as an autonomous political force. Since the notorious “taxpayer’s revolt” of 1978 — one of whose consequences was the transformation of the UC system from a nearly tuition-free institution into one that is practically inaccessible to students from modest backgrounds — the image of the “taxpayer” has been manipulated by well-financed political movements (Howard Jarvis’s Taxpayer Association, pictured above, in the case of California’s Proposition 13) as a bugaboo to frighten elected officials into enacting their agenda of tax cuts compensated by reduction of socially-provided services. Before we can begin to address the question Who should pay for mathematics — described here as an ethical problem, meaning among other things that I don’t pretend to know the answer — we have to address the disease of which use of the word taxpayer is a symptom, the disease that might be called the advanced state of degeneration of American democracy (not that things are much better elsewhere). Perhaps this is a disease that one can begin to cure by understanding just this kind of symptom.
Holt writes society rather than taxpayers, which is much better, but the effect of his paragraph is still one of compression. If you look on pp. 69-70 of MWA you’ll see that I have inserted the better part of a long paragraph between question 1:
we have not yet explained why we should be paid for the time we spend working on mathematics. If it’s so enjoyable, wouldn’t we do it for free?
and question 2, the one that introduces the passage Holt quotes:
why is it a matter of general interest, independently of the uncertain prospects of short- or long-term benefits to human welfare, to have a small group of people working at the limit of their creative powers on something they enjoy?
A matter of general interest — no taxpayers in that sentence (which actually applied to philosophers as well as mathematicians). The passage starting “I could claim” ends with deliberate absurdity to amplify the hint that I could, but I don’t repeat this familiar justification for mathematics. Instead the passage continues by invoking the Golden Goose argument — which is rejected elsewhere in the book because it is inconsistent with the real motivations of pure mathematicians — and ends with a riddle:
if the notion of “general [or public] interest” means anything at all, it should be a matter of general interest that work be a source of pleasure for as many people as possible.
A riddle is the only legitimate way to address the ethical problem at stake in question 2, which could be formulated by compression as question 1 — Who should pay for mathematics — but which in most of MWA is framed as the why question, without reference to any material interest of the hypothetical taxpayer’s angry fingers. In fact, I don’t pretend to answer question 1 because the standard answers are not convincing and I don’t have a better answer.
But Richard Fateman and other readers and non-readers alike suffer from the recurrent nightmare of the title and therefore assume that my book’s premise must include an answer to question 1. The most dispiriting example is undoubtedly this passage from Mark Hunacek’s review in the American Mathematical Monthly.
My concern is that books like this, with their self-congratulatory tone, may diminish rather than enhance people’s regard for academia in general and mathematics in particular. There are enough people out there with little regard for what university faculty do (witness the fact that a legislator in North Carolina actually proposed a bill that would require faculty in the UNC system, regardless of research expectations, to teach eight classes a year); the last thing we need is to provoke more hostility by suggesting that mathematicians are in the habit of daring the reader to try to understand their enlightened prose.
My concern is that the last thing we need is to concede, as this passage does, that the degeneration of American democracy is inevitable and irreversible. The North Carolina legislator Hunacek mentions is undoubtedly all too real, but the stupid politician (too-stupid-to-understand-the importance-of-mathematics, that is, or of higher education) has been a stock character of common room conversations ever since I applied for my first NSF grant, and functions as the revolting taxpayer‘s evil twin in blocking all rational consideration of the question Who should pay for mathematics as the ethical problem it is.
It’s probably no accident that Hunacek is an applied mathematician, like the readers of Ernest Davis’s (rather more nuanced, but still negative) review in SIAM Reviews (to which the Who should pay for mathematics series was meant as a response); and Fateman (like Davis) is a computer scientist. I’m not claiming that applied mathematicians are immune to pleasure, but it has been documented (in Chapter 3 of MWA, for example)* that they actually do take (legitimate) pleasure in applications. Pure mathematicians, in contrast, see pleasure (including beauty) as the primary virtue of mathematics. It may be a guilty pleasure: as John Conway puts it,
if you or your readers saw what I actually did, they’d be disgusted. They’d say, ‘Good money is being paid out to support these people’.
(And just last month, he told the Guardian (at 24:38) that “I always used to feel guilty about the fact that society pays me for doing this thing that I love.”** )
But elsewhere in Chapter 3 I wrote that
It is not only dishonest but also self-defeating to pretend that research in pure mathematics is motivated by potential applications…
and how could anyone rationally argue otherwise? Indeed, why would anyone deny that the primary motivation of pure mathematicians is to take pleasure in their work? (And if one is not so perverse as to deny this, but still believes that pure mathematics is a social good then it is self-defeating to attempt to attract young people to the vocation by offering them a justification that is manifestly not in line with their deepest motivations. In the Guardian interview quoted above, Conway asserts that his experience as a teacher convinced him students are much more likely to remember something interesting than something they are told is useful.)
The nightmare afflicting certain readers has a basis in reality. Pure researchers in mathematics, as in other academic disciplines, have yet to find an effective way to explain the motivations of their work, the democratic process is severely damaged, and these two factors together have serious consequences for scholarly careers (and not only in the United States). Fateman, Hunacek, and the others do not make it clear whether or not they think these issues will be resolved in the near future — or ever for that matter. In the meantime, for those of us whose work cannot pretend to the kind of utility that would impress the Howard Jarvises of the world, they have no better solution than to counsel despair of the democratic process, dissemblance, hypocrisy. This, they hope, will be the end of their nightmare; it’s where my nightmare begins.
*Table 17 on pp. 278-9 of Bernard Zarca’s sociological study L’univers des mathématiciens lists all the statistics. Among the pure mathematicians in his (large but perhaps not completely random) sample, 91% listed pleasure of doing mathematics as “absolutely important” as a “socioprofessional and psychosocial dimension of the profession ethos,” while the figures were 20% for the fact that one’s research has applications in the other sciences and 8% for the fact that one’s research has applications in the social world. Among applied mathematicians, the figures were 83%, 54%, and 30%, respectively, proving that priorities are different (but that applied mathematicians, in France at least, are no strangers to hedonism). I omit the figures for the thirteen other options.
**Here I should confess that I feel slightly guilty that I write primarily for pleasure, for example my pleasure at finding an excuse for using the word bugaboo a few paragraphs back. On the other hand, I am displeased that one phrase from the ending I had composed while walking to my office had escaped my mind by the time I arrived. If it returns I’ll restore it to its place.