Proof

THE ARTIST AND THE MATHEMATICIAN
The Story of Nicolas Bourbaki, the Genius
Mathematician Who Never Existed
By Amir D. Aczel
Thunder's Mouth. 239 pp. $23.95
Nicolas Bourbaki did not exist. He was dreamt up by a playful clique of French math professors in the mid1930s who used the Bourbaki pseudonym to tear mathematics down to its foundations. That collective tried to root out the imprecision that festered underneath the proofs of the day and replace it with more rigorous underpinnings. In so doing, the nonexistent mathematician produced more important and more original work than most reallife scholars. Alas, The Artist and the Mathematician , the new "biography" of Bourbaki by math writer Amir Aczel, is as derivative  dangerously so  as its subject was creative.
This is a shame, because the story of Bourbaki could be rich fodder for a talented writer. From the start, however, Aczel runs into a problem. Though Bourbaki's fictional status is given away in the title of the book, Aczel coyly treats Bourbaki as a real individual for the first few chapters. Perhaps this was because it allows him to assert that Bourbaki "was the greatest mathematician of the twentieth century." Other mathematicians have a stronger claim, at least based upon the profundity of their works. However, to Aczel, there's much more to Bourbaki than proofs and papers. Bourbaki, argues Aczel, was a product of the zeitgeist that gave birth to Cubism and Dada; Bourbaki, in turn, inspired revolutions within anthropology and literature.
In Paris at the turn of the century, painters Pablo Picasso and Georges Braque developed cubism, a movement that, as Aczel describes it, "concentrated on the relationships among the elements of a subject, as space and time related to the speed of light in relativity theory, creating a new art form." The Bourbaki movement, flush with the same spirit, studied the relationships between abstract mathematical objects  the deep underlying structure of math. This, says Aczel, breathed life into a growing movement ("structuralism") in which anthropologists, writers, psychologists and others embraced abstraction in hopes of getting at the girders of their own fields.
Unfortunately, when Aczel strays away from purely mathematical subjects, he seems uncomfortable and unsure of himself. He sticks closely to the writings of others. For example, his passage on Georges Braque closely parallels a biography on the Guggenheim Museum's Web site.
From Aczel's book: "Then he left for Paris to study under a master decorator, and received his craftsman certificate in 1901. From 1902 to 1904, Braque worked as a painter at the Académie Humbert in Paris, and by 1906, his work, which had been associated with impressionism, was no longer in that tradition and he adopted the Fauve style. Braque spent the summer of 1906 in Antwerp with Othon Friesz, and when he returned to Paris at the end of the summer, he exhibited his Fauve paintings at the Salon des Indépendants."
From the Guggenheim: "He left for Paris to study under a master decorator to receive his craftsman certificate in 1901. From 1902 to 1904, he painted at the Académie Humbert in Paris, where he met Marie Laurencin and Francis Picabia. By 1906, Braque's work was no longer Impressionist but Fauve in style; after spending that summer in Antwerp with Othon Friesz, he showed his Fauve work the following year in the Salon des Indépendants in Paris."