Book Review: The Artist And The Mathematician

The Artist And The Mathematician:  The Story Of Nicolas Bourbaki, The Genius Mathematician Who Never Existed, by Amir D. Aczel

It takes this book a while to get to its point.  As a fond reader of matters mathematical [1] and historical, and as someone with a somewhat downbeat view of the goodness of humanity as a whole, I expected that when I read the book I would read about a fraudulent attempt on the part of someone to pretend to be a genius mathematician that gullible people happened to believe.  At any rate, I expected that the author would begin talking about Nicolas Bourbaki fairly quickly, given the fact that his name appeared as part of the title of the book, and certainly as part of the hook to draw the reader’s interest.  What, a world-famous and genius mathematician never existed?  Say what?  However, the author, himself an accomplished and excellent historian of mathematics, most famous for his book on Fermat’s Last Theorem that is on my lengthy list of books that I want to read, decides to delay the reveal of who Nicolas Bourbaki is and why he never technically existed, and why that matters.  Although the payoff is delayed, it is a worthwhile one, and so those readers who are as puzzled as I was upon starting this book should be encouraged that it will all make sense eventually, even if the book is definitely a slow starter.

The contents of this book definitely cross over the border from ordinary into deeply mysterious, examining aspects of biography, religion and philosophy, military history, linguistics, as well as the history of mathematics.  The book opens with the mysterious of one Alexandre Grothendieck, a Jewish mathematician who grew up in France of foreign ancestry who was said to have worked with Nicolas Bourbaki, before retreating into obscurity and voluntary exile and solitude, going entirely “off the grid” as it were, discussing his personal history as a refugee seeking to escape Hitler’s final solution.  The author then turns to a short biography of another French Jewish mathematician named Andrè Weil, whose attempts to avoid service in the French military ended up leading to jail and nearly execution for desertion in the run-up to World War II.  Then the author examines the flight of another French Jewish mathematician from the German wehrmacht in World War II.  On the 59th page of the roughly 200 page book the author asks the obvious question:  Who was Nicolas Bourbaki?  At this point the author goes back and gives context, discussing the career of General Charles Bourbaki in mid-1800’s France, famous for his loyal service to the French nation and his escape into Switzerland and captivity after the disaster of the Franco-Prussian War.  Then the author looks at art history and the relationship between cubist and surrealist art and the mathematics of the 20th century, showing how a group of French mathematicians formed an anonymous/pseudonymous commune as a way of influencing the course of world mathematics by their approach to structuralism with its dependence on set theory.  At this point the author’s mystery has been revealed and a more straightforward discussion of the rise and fall of structuralist philosophy, from its peak influence in the 1950’s and 1960’s, its influence on the pioneering anthropology work of Levi-Strauss, and its gradual decline after the rise of postmodernism.

Aside from the fact that this book is an intriguing and insightful multidisciplinary history that deals with a wide variety of fields with skill and polish, there is an intriguing and deep irony in this book that students of philosophy will find of great interest. Rather, there is a whole host of ironies.  For one, the author is at pains not to relate the Jewish origin of the mathematicians of the Nicolas Bourbaki collective with their struggles of faith in the aftermath of the Holocaust.  For another, a great part of the decline of this collective came about with the decline of nationalist mathematics as a whole, as well as the aftermath of the Vietnam War and the rise of the radical left, for which several of the mathematicians gave their enthusiastic support.  Additionally, the author speaks often about the contradictions inherent in the set theory that formed the philosophical underpinnings of structuralism, but comparatively little time talking about the fact that the entire philosophy of postmodernism is self-refuting [2].  These ironies demonstrate that mathematics is of great importance in the larger culture even if many people shy away from the strangeness and difficulty of intense and deep study in mathematics.

[1] See, for example:

[2] Although the matter is too lengthy to be discussed in full here, it is worthwhile to note that postmodernism believes there is no absolute truth, although the statement that there is no absolute truth is itself an absolute truth.  Likewise, this worldview comes with the point of view that there is no possibility of conveying what is understood by one person to another, but postmodern philosophers write lengthy and weighty tomes in which it is possible for the reader, albeit only an unusually patient and longsuffering one, to understand what the author is getting at.  The fact that postmodern philosophers claim to be teachers of absolute truth and communicate through lengthy books gives the lie to their claims that there is no truth nor any possibility of communication between human beings.  It would be hard to imagine a philosophical view that was more entirely self-defeating.

About nathanalbright

I'm a person with diverse interests who loves to read. If you want to know something about me, just ask.
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