"The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought."

"The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be ‘voluntarily’ reproduced and combined."

Said Albert Einstein, quoted in "The Weil Conjectures: On Math and the Pursuit of the Unknown" by Karen Olsson.

Einstein — participating in a study of the working methods of mathemeticians — was responding to the prompt: "It would be very helpful for the purpose of psychological investigation to know what internal or mental images, what kind of 'internal world' mathematicians make use of..."

Olsson writes more generally, not just of mathematicians: "If only we had more access to the untranslated thoughts, to the mystery of how the mind churns."

"... and while she endures their pranks and shares meals with them, she invents a secret friend. This friend is, curiously, distant and hidden..."

"... a friend who she hopes will be revealed to her one day. She has made up a friend who won’t keep her company."

Imagine being snubbed by your friends, creating an imaginary friend, and being snubbed by your imaginary friend! (Or is that easy to imagine: It's religion.)

I'm reading "The Weil Conjectures" by Karen Olsson.

I noticed that book because of "Two Brilliant Siblings and the Curious Consolations of Math," a review in the NYT. Excerpt:

The precocity of the Weil siblings is the stuff of legend. At 9 years old, André was tinkering with doctoral-level math. By 12, he had taught himself Sanskrit, become a proficient violinist and taken his younger sister’s education in hand. The pair spoke to each other in rhyming couplets and Ancient Greek....

“The Weil Conjectures” takes its title from a series of propositions written by André that led to the development of modern algebraic geometry. “The word ‘conjecture’ derives from a root notion of throwing or casting things together,” Olsson writes. To the story of the Weil siblings, she adds her own infatuation with mathematics, which she studied briefly in college before turning to fiction...

The book advances in fragments, historical divagations that drift by, smoothly as clouds: Hippasus of Metapontum supposedly flung off a ship for his discovery of irrational numbers, or the unearthing of the Rhind papyrus of 1700 B.C., one of the oldest mathematical documents, with an insuperable opening line: “Directions for Attaining the Knowledge of All Dark Things.” Olsson is drawn to anecdotes that emphasize the role of beauty and chance. Why do we represent the unknown with x? Credit René Descartes’s printer, who was running out of letters while producing copies of the treatise “La Géométrie.” X, y and z remained, and the printer settled on x, the least used letter in French....

For all of Olsson’s skill at untangling knotty mathematics, she is baffled by Simone.... The issue of Weil’s mental state has long preoccupied and divided her biographers. She died at 34, from tuberculosis, aggravated, it is said, by prolonged malnutrition from restricting herself to children’s wartime rations....