Or, as the book puts it, who should be asked to provide the “external goods” that allow the “internal goods” of the mathematical profession to flourish? This fundamental question was raised in this review; although, as I explain here, the reviewer was wrong to think that the book takes a position on the question, it is indeed one of the book’s primary concerns.
In future installments I’ll be exploring this issue at some depth, making use of some of the material that didn’t make it into the book. In the meantime, you might enjoy this essay and this video presentation by Alexandre Borovik of the University of Manchester. Borovik has a lot to say and it’s all thought-provoking and unconventional.
At the conference in London where his presentation was recorded, Borovik reported something he had learned from an older family member when he was growing up in Novosibirsk. One reason the Soviet Union attached so much importance to training mathematicians (in the 1940s and 50s), he claimed, was for the calculation of artillery shell trajectories. In a wartime emergency, it would take too long to teach untrained soldiers the necessary mathematical skills. (I’m writing from memory and certainly I’m leaving out something important; this comment was made during the question and answer sessions, when the cameras were switched off.) I’d guess something similar is behind the NSA’s support for pure mathematical research, but that’s another discussion.