The Weil Conjectures by Karen Olsson

Author:Karen Olsson
Language: eng
Format: epub, pdf
ISBN: 9781526607553
Publisher: Bloomsbury Publishing
Published: 2019-05-30T08:12:45+00:00

Have you ever worked in your sleep or have you found in dreams the answers to problems? Or, when you waken in the morning, do solutions which you had vainly sought the night before, or even days before, or quite unexpected discoveries, present themselves ready-made to your mind?

André dreams of a bucket of candied fruit, one that he bought in actual waking life from a factory that was selling off its seconds, just before his family crossed the Atlantic. On the voyage they devoured those sticky scraps of pear and citron in the evenings, before all the passengers crowded into single-sex rooms to sleep in bunk beds, lumped together like litters of kittens. In the dream he puts his hand straight into the syrup, as others press around him, holding out plates or palms, touching his jacket, and though he would like to save all the sweets for Eveline and Alain, he can’t turn these people down, no, in spite of himself he distributes shiny gobs of second-rate fruit to these mewling strangers.

Mathematical discoveries do not occur in dreams, Hadamard claims, or if they do, they are probably absurd. Yet Hadamard can’t resist including a strange exception to the rule, reported by an American mathematician named Leonard Eugene Dickson, who had heard the story from his mother. When she was a girl, she and her sister had been keen on geometry, both competing against and collaborating with each other. They once “spent a long and futile evening over a certain problem,” only to give up and go to bed, but during the night, in their shared bedroom, Dickson’s mother dreamed of the problem and stated the solution, while asleep, in a loud and clear voice. Her sister heard her, got out of bed, and took notes. At school the next day, the sister gave this (correct) solution to the problem, which Dickson’s mother, though she had dictated it in a dream, had no recollection of knowing.

In general, though, new ideas are far more likely to present themselves to a person who is just waking up, Hadamard notes, adding that he was once jolted out of sleep by a loud noise, and “a solution long searched for appeared to me at once without the slightest instant of reflection.”

During the lull between waking and willing, the haphazard miracles of the liminal mind.

I can remember a dream I had in college—oddly enough, since I don’t usually remember dreams the next day, much less years later—which was about matrices, rectangular arrays of numbers. The matrices of my dream were life-size, with detachable rows and columns that would hover over a person and act upon him or her in some inscrutable way.

In the introduction to an article published in 1990, the mathematician Robert Thomason explains that a dream ushered him toward the work he was presenting, and because of it he chose to include as his coauthor a friend and colleague who’d committed suicide the year before. “The first author must state that his coauthor

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