That MWA currently (but temporarily) occupies the top two spots in the Amazon UK ranking in philosophy of mathematics [sic] can be entirely attributed, I believe, to its mention in yesterday’s Guardian column by Simon Jenkins. The journalistic charisma of Jenkins is such that his readers were willing to sail behind him into MWA‘s uncharted waters even though the point of his allusion is by no means clear. Judge for yourselves:
I agree with the great mathematician GH Hardy, who accepted that higher maths was without practical application. It was rather a matter of intellectual stimulus and beauty. A new book by Michael Harris, Mathematics Without Apologies, goes to the extremes of this stimulus, to the categorical ladder, incompleteness theory and the Black-Scholes equation, used to assess financial derivatives. It ends in the “inconsistency nightmare”, that nought might possibly equal one.
I’ve read the sentence with my name in it ten times, not out of vanity but because I still can’t figure out what it means, nor what it has to do with the point Jenkins wants to make: which is that what British pupils really need from school is “crowded out by a political obsession with maths.”
It seems that Jenkins cites MWA as proof of the “extreme” uselessness of mathematics. There is absolutely nothing like that in the book. Nor does the word “nightmare” occur even once (much less “incompleteness theory”) and I have no idea what the “It” is that “ends” in the nightmare equation 0 = 1. The syntactical confusion of this paragraph — which didn’t dissuade a few dozen Amazon UK customers — can be blamed on an overzealous Guardian editor, or perhaps on a Jenkins assistant who was assigned to read (or rather, to “read”) MWA (or perhaps any recent book that alludes to Hardy) and who got muddled in its disorganized snobbery. The article’s motivation, on the other hand, is a recurring theme in Jenkins’s columns. In 2008, he called his study of quadratic equations a “waste of time” and wrote
Maths and science self-justify as economically worthwhile in a way that law or economics or management studies do not dare.
In 2014, he returned to the charge with at least articles, including one entitled For Britain’s pupils, maths is even more pointless than Latin. There have been more diatribes against mathematics and science education over the years, so that Stephen Curry wrote memorably that
Arguing about science with Simon Jenkins is like trying to wrestle with a fart — you can’t miss the odious stink but there’s almost nothing to get hold of.
The malodorous simile didn’t discourage me from trying to cash in on the moment, in my small way, by renaming the link to Princeton University Press “PURCHASE THE BOOK.” Curiously enough, the link in the Jenkins article is to this blog — that’s how I detected the existence of his article — and not to the Guardian bookshop, which reports that my book is in stock and which may be the last place on earth where you can still see the rejected initial cover.
Imagine you had an art class in which they taught you how to paint a fence, but never showed you the great masters. Of course, you would say; ‘I hate art.’ You were bad at painting the fence but you wouldn’t know what else there is to art. Unfortunately, that is exactly what happens with mathematics.
On the evidence of his public disagreement with Andrew Hacker — this tweet seems to be the most recent instance — Frenkel would undoubtedly reject Jenkins’s arguments about the place of mathematics in the curriculum. Frenkel’s fence-painting analogy helps to clarify just what Jenkins got wrong in his (or his assistant’s) reading of MWA. Nowhere is it claimed in MWA that mathematics is useless. Rather, what MWA has to say about the utility of mathematics has two parts. The less important part is that utility, whatever that means, is not a primary motivation for pure mathematicians, nor even a secondary or tertiary motivation. The much more important point is that justification of mathematics on the grounds of utility begs the question of what utility really means, and how the ideology of utility is used by decision-makers (or Powerful Beings) to foreclose reasoned discussion of social priorities, replacing them by invocations of purely technocratic criteria which leave no alternative. The ideology of utility serves in practice to protect the interests of the powerful. Jenkins has certainly not broken with this ideology; he just disagrees with the details of its elaboration.