The Artist and the Mathematician: The Story of Nicolas Bourbaki, the Genius Mathematician Who Never Existed (review)

Aczel takes the vagaries of Bourbaki as an emblem for those of structuralism as a whole. A group of French mathematicians set out in the 1930s to produce a final synthesis of all of mathematics based on set theoretical foundations-all to be published under the collective pseudonym of N. Bourbaki. The group did issue impressive work, but it now appears in retrospect like a dead end. Bourbaki was founded, and then judged, on the false criterion of finality. If you aim for a theory of everything, so as to end all theory, you will fail and put in question the quest itself. But is that quite fair? It is not that theories of everything do not exist, any more than Bourbaki does not exist. What they are is nonunique. There are plenty of such theories. We should not expect any particular theory of everything to be the last one: the infinite richness of the mathematical universe demands not one theory of mathematical everything, but many. The same, of course, is true for the infinite richness of humanity. We should therefore have many theories of human everything: many structuralisms.

Works of popular science must decide on a balance between intellectual weight and accessibility. Aczel chose accessibility, to the point where one no longer can tell just what it was that was meant to become accessible. The name-dropping of terms like cohomology and algebraical geometry resonates and titillates, leaving no knowledge in its wake. What remains are mostly biographical vignettes . . . which brings to mind a paradox. Why are the biographies of modern academics so boring, while the genre of the academic novel is so full of charm? It appears that the modern research university has constructed the most predictably boring form of life. It sets up the perfect setting for the comedy of bourgeois boredom-while academic biographies remain as interesting as the CVs on which they are patterned.