The Weil Conjectures: On Math and the Pursuit of the Unknown – Karen Olsson

Thoughts: I found The Weil Conjectures odd—a book-length essay, something I’d more have expected to come across in a literary journal than in the mathematics section of the Kitchener Public Library. Drawing on aspects of pop math, historical fiction and personal memoir genres, Karen Olsson’s book is a succession of short paragraphs depicting in turn André Weil, Simone Weil, Olsson while writing the book, Olsson in college, and various mathematicians from throughout the millenia. While I came away from it with a couple of new ideas about math and a better sense of who Simone Weil was, by the end I was left feeling that I had read a pile of notes, musings and personal recollections rather than a book.

(The notes below are not a summary of the book, but rather raw notes - whatever I thought, at the time, might be worth remembering.)

Olsson, Karen. 2019. The Weil Conjectures: On Math and the Pursuit of the Unknown. Farrar, Straus and Giroux.

• 108- : Jacques Hadamard conducted a survey among mathematicians asking about how they worked and how they achieved their insights
  • 112: Hadamard concluded that moments of insight rarely occurred during sleep, but “new ideas are far more likely to present themselves to a person who is just waking up”
    • c.f. Edison’s practice of holding ball bearings while taking naps, which he would drop as he dozed off
  • 114-115: in earlier writing, Poincaré highlighted the importance of deeply engaging with a problem in order to allow insights to present themselves serendipitously: “These sudden inspirations … never happen except after some days of voluntary effort which has appeared absolutely fruitless and whence nothing good seems to have come, when the way taken seems totally astray.”
• 143: the fixed point theorem (there are actually a family of them): for any continuous function in any number of dimensions that maps a point within a finite space to another point within that space, there will exist at least one input for which the output will equal the input (i.e. a fixed point)