Compared to him we are all math-challenged

kw: book reviews, nonfiction, mathematics, mathematicians, memoirs, short biographies

The Weil Conjectures: On Math and the Pursuit of the Unknown, by Karen Olsson, is part biography (of André Weil and his sister Simone), part memoir, part rumination. The one thing it is not, is a description of the Weil Conjectures. Let's see why, beginning with this statement, not from the book, but from the Online Encyclopedia Britannica:

"Weil believed that many fundamental theorems in number theory and algebra had analogous formulations in algebraic geometry and topology. Collectively known as the Weil conjectures, they became the basis for both these disciplines."

The four (not two) disciplines mentioned are utter mysteries to everyone but a literal handful (really!, like four or five) of mathematicians who have a sufficient grasp of all of them for the quote above to make sense. Ms Olsson is not one of those few, but if she were, she might find describing these things to a popular audience (including me, an accomplished mathematician, but not in this league) a task similar to that shunted aside in 1965 by Dr. Robert Feynman; when asked after the Nobel Prize ceremony in which he was awarded the Prize, "Can you tell us briefly what it was that you did?", he replied, "Buddy, if I could tell you that in one minute, it wouldn't be worth a Nobel Prize."

In nearly every page the book switches gears, between a mini-biography of Simone Weil, one of André Weil, the author's memories of mathematical study (which she dropped after receiving her degree at Harvard), her more recent attempt to rekindle her early love of math, and vignettes about historical mathematicians whose work underlay that which André Weil labored upon.

The word "mathematics" literally means "learnings", emphasizing plurality. The power of the Weil Conjectures lies in making connections between and among areas that have been treated as separate, to show that they are all one. With that in mind, I find a multi-threaded book like this to be just the vehicle needed, to induce in someone like me at least a bit of the feeling that must have inhabited Weil as he considered his conjectures and the way the disciplines so treated reflected from one another to show mathematics as a conceptual whole. The satisfaction of finishing this book lies not in comprehending Weil's work, but in seeing that whole, though from afar.