The Amalgamated Mathematician

I recently got done reading The Artist and the Mathematician, a book about the fictitious mathematician Nicolas Bourbaki and his influence on 20th century math. Bourbaki was a pseudonym for a group of French mathematicians who were intent on not only revamping the state of math education in France (it having suffered greatly from the two World Wars), but also rewriting the foundations of math in a more rigorous, axiomatic fashion, based in set theory. The book also posits Bourbaki as part of the genesis of the structuralist movement, with wide-ranging impact in fields such as anthropology, economics, and the like.

I found the parts of the book dealing with Bourbaki and the persons behind the pseudonym to be mostly acceptable. The author, Amir Aczel, delivers the story in a somewhat stilted, somewhat meandering fashion, but on the whole the narrative is readable, interesting, and enjoyable. However, I find the thesis of Bourbaki’s influence on the structuralist movement to be poorly supported (with the sources admitting only an ephemeral connection between the parties involved). If there is a connection, I personally believe it to be more indirect than what is implied.

This may be somewhat mean-spirited, but I must say that I feel the author’s sentiment of amazement regarding the birth of structuralism in anthropology to be akin to awe at the sight of watching a caveman bang rocks together. The way the story is told, an encounter with André Weil and a brief introduction to set theory saves the dissertation of Claude Lévi-Strauss (which would be published later as The Elementary Structures of Kinship), who then pioneers a new movement in anthropology. The apparently insurmountable problem that Lévi-Strauss faced, formalizing notions of marriage restrictions in aboriginal society, can be reduced to a set membership problem that I think any intelligent sixth grader could solve. Lévi-Strauss turned this into his meal ticket, trying to find any way he could to deduce “structure” from anthropological data, constructing theories that had no visible means of support. While doing a bit more reading on the topic, I was amused to find this summary of structural anthropology provided by Wikipedia: “…a great weakness of structuralism is that its main propositions were not formulated in a way so that they could be subject to verification or falsification. Lévi-Strauss did not develop a framework that could prove the existence of his concept of the fundamental structures of human thought but simply assumed them to be there, an unfortunate mistake considering that this concept underpinned all of his work.”

The book contains additional howlers on the subject of economics, psychology, and literature. The work of Jacques Lacan on the “mirror experiment” is “analyzed…using the assumption of hidden structure. This led him to results that confirmed the structuralist approach.” (It should surprise no one that assuming a hidden bogeyman exists would lead you to interpret data in such a fashion as to confirm the existence of the bogeyman.) Aczel also somehow seeks to appropriate the supply and demand curve (an idea which was formulated much earlier, and which has remained largely unchanged since the end of the 19th century) as validation for the ideas of structuralism in economics. Having attempted this bizarre feat, the lack of an attempt to concoct some connection between fractals and micro/macroeconomic behavior seems like uncharacteristic restraint. The coup-de-grace is the description of the Oulipo group, a group of “literary” madmen whose work can essentially be described as a combination of Mad Libs and Eliza, wholly worthless.

Overall, I would say that the book was a disappointment. While the topics of Nicolas Bourbaki and the history of French mathematics in the 20th century were interesting, the book’s detours into other realms of study resulted in a pretty spectacular decline in quality. These sections provoked a palpable sense of outrage — while I felt compelled to finish the book, I also felt compelled to point out these problems. The book’s lack of actual mathematical content was just the cherry on top…