Several reviews were published while I was in Peru. All but one were highly flattering (in one case inadvertently), and a few of them actually taught me things about the book, and about its author, that I would not have been able to figure out on my own. Brendan Larvor’s review in the London Mathematical Society Newsletter begins by informing the reader that
Michael Harris is more than a mathematician; he is a Parisian intellectual.
This calls for a bit of background. During my first extended stay in Paris, for the spring semester of 1985, physicist Paul Kessler invited me to sign a letter to Israeli Prime Minister Shimon Peres that was published in Le Monde on July 24. You can read the letter here (and try to imagine how controversial it may have been at the time). What matters for our present purposes is that the Le Monde article was entitled “Protest of about fifty French intellectuals.” Several of my colleagues who heard about this persisted in calling me “the French intellectual” until I actually moved to France in 1994, at which point the question became moot.
Larvor is right to suppose that I might “resist that title” of French intellectual, and not only because of the Le Monde experience; but his diagnosis of the condition is both perceptive and informative.
he makes good jokes about Lacan, explores philosophical themes through literary analysis, treats popular culture as seriously as he does high culture, fills his book with references and allusions, argues by telling stories, reflects on the narrative conventions of those stories and is deeply suspicious of high-falutin’ talk.
I have to plead guilty on all counts, and if that means I walk, talk, and quack like a Parisian intellectual, then I have no choice but to accept Larvor’s diagnosis.
Although Larvor’s review is excessively flattering, it’s clear to me that he understands the point of the book as well as anyone, probably better than the author. In one sense this is not surprising. Not only is Larvor a philosopher and therefore professionally equipped to understand points; he also helped the author define his purpose by inviting him to the Two Streams in the Philosophy of Mathematics conference that he co-organized with David Corfield at his home University of Hertsfordshire in 2009, and again to the third of the series of conferences in London on Mathematical Cultures, just last year. The review also draws a subtle line between two tendencies in writing about mathematics that run roughly parallel to the two streams:
[MWA] resembles Weber’s lecture on the values that animate scientists and the place of those values in the wider culture rather more than it resembles insider-reports such as Cédric Villani’s Birth of a Theorem.
The stream with which I do not identify is the mainstream, by a long way, and most readers are probably not even aware that the second stream (the mavericks, in Reuben Hersh’s terminology — click on the tab Description if you don’t see it) even exists. This suggests that some of the negative writing about the book that has surfaced on the web, and in a few of the reviews, may be a reaction to the mistaken assumption that it represents a failed attempt to define the mainstream.
I do have a second-order disagreement with Larvor’s use of the word “bogus” to characterize how I analyze utility, truth, and beauty as justifications for mathematics. He’s certainly right that MWA argues that these are inadequate justifications, but because they are part of the mainstream discourse about mathematics, they are performative: they can’t be ignored precisely because so many people believe them to be adequate. But that just sounds like some Parisian intellectual trying to speak the language of J. L. Austin, and I don’t make the point consistently in the book, so I’ll leave it at that.
I have been waiting eagerly for a good, genuinely insightful, negative review of MWA. The few negative reviews that have appeared so far have been either intellectually disappointing or based on a severe misunderstanding of the book’s objectives. So I have decided to write my own negative review, highlighting the book’s genuine flaws. Look for it in this space next month.