THE ARTIST AND THE MATHEMATICIAN

The greatest mathematician of the 20th century was actually a committee.

Science popularizer Aczel (Chance, 2004, etc.) begins with a mystery: the voluntary disappearance in 1991 of Alexandre Grothendieck, a leading French mathematician. The author surveys Grothendieck’s childhood in a concentration camp in Nazi-occupied France, then shifts to the careers of several other French mathematicians active before WWII. The common thread in their lives is Nicolas Bourbaki, a fictional mathematician under whose name the most influential work of the modern era was published. Bourbaki was, in reality, a group that first met in December 1934 in Paris, believing that math needed to be rebuilt from its foundations, starting with the fundamentals of set theory. Although there were always acknowledged leaders, beginning with André Weil, decisions were made collectively. Bourbaki’s members shouted each other down and argued vehemently over every detail of the work in progress. Miraculously, this chaotic methodology produced brilliant results. Bourbaki’s insistence on rigor and its emphasis on structure revolutionized the way math was taught. The “new math” that swept through schools in the 1960s was a Bourbaki creation. Likewise, as Aczel points out at length, the “structural” movement in philosophy, science and the arts derives from the Bourbaki approach, especially as adopted by Claude Lévi-Strauss, to whom Weil taught the mathematics that would underpin his anthropological studies. For four decades, the best young French—and, increasingly, foreign—mathematicians were recruited into the group, and its influence was unmatched. Grothendieck, most brilliant of the latter-day members, eventually took math beyond the reach of set theory, at which point he left Bourbaki, and the group began its decline. But as Aczel shows, it had left an indelible stamp on mathematics and on the world at large.

A fascinating topic, despite the author’s sometimes plodding approach.