The word conjecture derives from a root notion of throwing or casting things together, and over the centuries it has referred to prophecies as well as to reasoned judgments, tentative conclusions, whole-cloth inventions, and wild guesses. “Since I have mingled celestial physics with astronomy in this work, no one should be surprised at a certain amount of conjecture,” wrote Johannes Kepler in his Astronomia Nova of 1609. “This is the nature of physics, of medicine, and of all the sciences which make use of other axioms besides the most certain evidence of the eyes.” Here conjecture allows him to press past the visible, to sacrifice the certainty of witnessing for the depth and predictive power of theory. There’s another old definition of conjecture that means something inferred from signs or omens (for example, from a Renaissance work on occult philosophy: “Whence did Melampus, the Augur, conjecture at the slaughter of the Greeks by the flight of little birds . . .”).
Elsewhere it’s hokum, claptrap, bull: “Conjecture, which is only a feeble supposition, counterfeits faith; as a flatterer counterfeits a friend, and the wolf the dog,” wrote one early Christian theologian. So it’s a word with contradictory meanings, since at times conjecture carries the weight of reasoning behind it, and at other times it’s a wild statement, an unfounded claim. Good thinking or bad, clever speculation or a reckless mental leap.
In contemporary mathematics, conjectures present blueprints for theorems, ideas that have taken on weight but haven’t been proved. Couched in the conditional, they establish a provisional communication between what can be firmly established and what might turn out to be the case. More than a guess, conjecture in this sense is a reasoned wager about what’s true.
A rough draft. A trial balloon. It seems to me laced with optimism, a bullishness about what could, in the future, come more fully to light.
André now a professor at the University of Strasbourg, travels back to Paris and convenes a meeting of young mathematicians at the Café A. Capoulade. They all teach similar undergraduate courses in analysis—higher-level calculus—and they are dissatisfied with the existing textbooks, so they’ve decided to form what they call the Committee for Writing a Treatise on Analysis.
This rather dry mission soon takes a strange turn. The Committee for Writing a Treatise on Analysis will evolve into a semisecret society, a sort of wry mathematical mystery cult.
My math fever dream lasted for two and a half years, which were spent messing around on the lower rungs of a tall ladder that stretched into the clouds, that led to a cloud land of tantalizing abstract structures, curves and surfaces and fields and vector spaces, accessible only to those who learn the elaborate cloud language, a vehicle for truths that cannot be expressed in any other tongue.
Then I stepped off the ladder and walked away. It’s not often that I experience even a passing wish to go back, and even in those moments the allure of math is much fainter than it was in college, since now I have no illusions that I would ever make it very far up—I’m left to imagine that land, and what I wish for now is less the specific math knowledge than a certain constellation of feelings that came with it.
Simone goes to work in a factory because she wants to investigate directly what she hasn’t been able to figure out theoretically, namely: How can an industrial society be organized in a way that its workers are not oppressed? And then there’s that self-mortifying impulse, the fact that she has wanted to do hard physical labor since she was a teenager. She tells her friend Simone Pétrement (who will later become her biographer) that although she’s scared—she is notoriously clumsy, not good with her hands—she is determined to kill herself if she can’t manage the work.
She is twenty-five. Her confidence, Pétrement would write, “was quite terrifying, especially when one knew her almost inhuman energy and her lack of self-pity.”
Into a den of machines. A woman regularly overcome by headaches assigns herself to the factory floor with its stamping press, the fly press, the iron crank, the compressed-air hose, the screws, the blades, the mallets. The screech and whine and hammer and hiss. She is assigned to fit copper plates into magnetic circuits and must take care not to ruin the pieces in the process.
The days are short, and when the windows go dark the wan lamplight hardly compensates. She can barely see. It’s loud and it’s dark and she can’t keep up with what the foremen demand, the required rate of work. Holding a flashlight in one hand and adjusting newly assembled parts with the other. “Manual labor,” she’ll write later. “Time entering into the body.”
Wednesday, she doesn’t make the rate. Thursday, she doesn’t make the rate.
She imagines that the others pity her, but then she sees how they side with the foreman when another woman is fired. The fired woman was tubercular, her husband unemployed—but she botched a job and hundreds of pieces had to be done over. She ought to have known better, the others comment. “You’ve got to be more conscientious when you have to make a living,” they say. Even on the night shift, even in the near darkness.
“What I went through there marked me in so lasting a manner that still today when any human being . . . speaks to me without brutality, I cannot help having the impression that there must be a mistake,” Simone will recall. She is assigned to a small workshop, separate from the rest of the factory, and instructed to insert copper bobbins into a furnace and then take them back out again. She burns her hands and her arms, comes out blistered and scarred. Yet it’s her favorite part of the factory, because the workers there are decent to one another.
The young mathematicians hold their first conference in the summer of 1935, near Lac Pavin, a volcanic crater collared by pine forest in central France. Seven months after forming the Committee for Writing a Treatise on Analysis, they’ve advanced well beyond their original intention to improve undergraduate math education. This has been supplanted by a much grander goal, no less than laying a formal, consistent, and comprehensive foundation for all of modern mathematics—or at least all of it that they find interesting.
Taking a break from a stalled discussion of analytic functions, several members of the group flee to Lac Pavin and dive naked into the water, yelling out a Greek name: Bourbaki! Bourbaki! Bourbaki! Over and over again, their shouts echoing across the surface of the lake: Bourbaki! Bourbaki! Bourbaki! Bourbaki!
One seed of this happy outburst was planted in 1923, back when André and many of the others at the conference were studying at the École Normale. A third-year student named Raoul Husson played a prank on the first-years by posing as one Professor Holmgren. Wearing a false beard and speaking in an indefinite foreign accent, he gave a lecture on a series of made-up results, which culminated in the presentation of “Bourbaki’s theorem.”
And, when he was living in India, André had advised a young mathematician friend by the name of Kosambi, who was caught up in an academic rivalry with another man, to flummox his competitor by publishing an article about an imaginary Russian mathematician with a Greek name. Kosambi did just that; his (spoof) paper “On a Generalization of the Second Theorem of Bourbaki” appeared in the Bulletin of the Academy of Sciences of the United Provinces of Agra and Oudh.
The group at the summer conference adopts the name Bourbaki, a mischievous pseudonym that also serves a purpose, in that they’ll avoid having to sign every single one of their names to publications. In the fall, André will submit to the journal Comptes Rendus a perfectly serious article concerning the theory of integration, yet he’ll report that it was passed on to him by a man named Bourbaki. “I’m sure you’ll recall that Mr. Bourbaki is the former professor of the Royal University of Besse-en-Poldévie whom I met some time ago at a café where he spends most of his day and even the night, having lost both his job and most of his fortune amid the troubles that caused the unfortunate Poldévian nation to disappear from Europe,” André will write to the journal editor, a fellow mathematician who is in on the joke. “Now he earns his living at the café by giving lessons in belote, the card game he plays so brilliantly.”
There was, by the way, an actual Charles Bourbaki, a nineteenth-century French general of Greek heritage who distinguished himself in battle and as an inspector general of the infantry before he was sent, in 1870, to command a miserable, half-starved French army already losing to the Prussians. After a defeat at Héricourt, in eastern France, he was forced to retreat through Switzerland, where his soldiers’ guns were confiscated and he tried to kill himself. The attempt failed, and he eventually returned to France.
The brief Kafka story “The Top” is about a philosopher who loiters around children because he is fascinated by their tops and hopes to catch one in mid-spin, convinced that a spinning top could lead him to enlightenment—that “the understanding of any detail, that of a spinning top for instance, was sufficient for the understanding of all things.”
As a top spins, the philosopher goes “running breathlessly after it,” full of hope, but upon catching it he is disappointed, for “when he held the silly piece of wood in his hand he felt nauseated.” It’s the pursuit, the running after knowledge, that takes his breath away.
Commenting on this story in the preface to her book Eros the Bittersweet, Anne Carson doubts that the desire to gain knowledge is what really motivates Kafka’s philosopher. “Rather,” she writes, “he has become a philosopher (that is, one whose profession is to delight in understanding) in order to furnish himself with pretexts for running after tops.”
Running breathlessly after tops, in that heightened state that comes of being deprived not only of the thing you’re chasing but of the air you need to chase it. Sometimes I think of writing in this light, too: as running after tops.
Excerpted from The Weil Conjectures: On Math and the Pursuit of the Unknown by Karen Olsson. Published by Farrar, Straus and Giroux, July 16th 2019. Copyright © 2019 by Karen Olsson. All rights reserved.
