Experimental Blog #97

Comments on "Infinite Ascent" - A Short History of Mathematics by David Berlinski and "The Artist and the Mathematician" - The Story of Nicolas Bourbaki, the Genius Mathematician Who Never Lived by Amir D. Aczel


The author, David Berlinski, describes mathematics as "a discipline dominated by men who were often hysterical and almost always vain." However, high school and college mathematics classes probably almost always have a few girls and women who are among the top students, but the "original geniuses", both past and present, seem always to be "guys and more guys", but not very "normal"; and they seem to understand each other almost clairvoyantly.

Although it turns out that most of these "original geniuses" often do a very great amount of long trial and error computation to arrive at their final formulas and theorems; but numbers, figures, spaces, collections, and other abstract mathematical objects are probably their passion, or even their obsession.

Amir Aczel, the author of the second book, more or less begins with a discussion of Einstein's Relativity theories in physics, and cubism, and the modern art of Pablo Picasso and Georges Braque. The intellectual life of the 20th century was then violently interrupted by the Bolshevik revolution in Russia, Facism in Italy, and, most of all, by Nazism in Germany. After World War II came the Existentialist philosophers in France, but Amir Aczel says that Existentialism was replaced by the movement of "Structualism" developed by the French anthropologist Claude Levi-Strauss working with the "Nicolas Bourbaki" group of mostly French mathematicians.

This "Bourbaki" group was founded in the 1930s by Andre Weil, and Amir Aczel writes about 19 members of this group in all. He divides them into three "generations", plus one "in-between". He also describes in very great detail the life and work of Alexander Grothendieck, a temporary member of "Nicolas Bourbaki". Alexander Grothendieck is described as "the most visionary mathematician" of the 20th century.