Looking Out To Sea

Let this be a salutary lesson on the dangers of impulse buying. If you don’t spend a few minutes reading reviews on Amazon you might accidentally buy Amir Aczel’s The Artist and the Mathematician, the “story of Nicolas Bourbaki, the genius mathematician who never existed”. And that would be a mistake.

Nicolas Bourbaki was the pseudonym of a group of French mathematicians who attempted to formalise mathematical thinking in the early to mid-twentieth century. In the author’s opinion Bourbaki’s publications had important influences on the structuralist movement that would spread from linguistics and anthropology to many disparate areas of science.

Well, I wouldn’t know about that; and I still feel like I don’t know about it. The book is filled with tedious and trivial details where it should provide only impressions — and sketchy and vague where it should be exact and clear. In fact it exemplifies everything the Bourbaki group were pushing against. Aczel takes whole chapters to explain the minute detail surrounding the early life of one mathematician (including the life of his parents when they were young…) though this has no real relevance to the work he did. In fact, now I think on it I can’t even remember which mathematician gets all the boring backstory.

Whatever: the point is that the writer doesn’t bother telling you why any of this matters. He name-drops mathematical ideas without context or explanation. They have no more relevance to the reader than the endless litanies of people and parents’ occupations and meetings and so on. Amir Aczel insists that Bourbaki was incredibly influential in whatever it was they did, without bothering to reveal whatever it was they did. And that many other fields borrowed these ideas to do whatever it was that they did, again without explanation or detail. And then eventually we find that Bourbaki became less relevant — though again, without explanation.

It’s quite satisfying to say that an author who talks about abstract algebras and category theory is “over-generalising”. If only the book were as satisfying. Instead, I can heartily recommend Mario Livio’s The Equation That Couldn’t Be Solved — a proper tribute to genius mathematics.