Excerpted with permission fromMathematics without Apologies: Portrait of a Problematic Vocation, by Michael Harris. All rights reserved. Copyright © 2015, Princeton University Press.
Hal: [...] Mathematicians are insane. I went to this conference [...] last fall. I’m young, right? I’m in shape. I thought I could hang out with the big boys. Wrong. I’ve never been so exhausted in my life. Forty-eight straight hours of partying, drinking, drugs, papers, lectures...
Catherine: Drugs?
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Hal: Yeah. Amphetamines mostly.[...] Some of the older guys are really hooked. [...] They think math’s a young man’s game. Speed keeps them racing, makes them feel sharp. There’s this fear that your creativity peaks around twenty-three and it’s all downhill from there. Once you hit fifty it’s over, you might as well teach high school.
—Proof, by David Auburn; cited in [Hofmann 2002].
A totally unfounded fantasy, and if you were expecting any serious gossip at this point I'm afraid you're going to be disappointed. On the contrary, there seems to be a growing consensus that, in spite of the persistent public fascination with mathematics, it's not among mathematicians that you'll find the best parties, and that life is more fun in the company of dancers, philosophers (Anglo-American or continental), hedge fund managers, fashion designers, biomedical engineers, theater critics and/or performers, historians, industrialists, Russian Orthodox theologians, or anyone involved with the movies. In the new world of public-private partnerships, leading European research institutions are also encouraged to follow the dark side into its realm of dream and magic. Consorting with the men and women at the summit of the socioeconomic firmament is consistent with the injunction raining down on us from all quarters to tie our work more closely to the needs of production, especially the production of wealth. The culture industry, meanwhile, deals primarily in the production of novelty, and indications are that the added value of mathematics, as a cultural signifier of indeterminate scope, has yet to be exhausted. Darren Aronofsky's Pi, whose plot is driven by Wall Street's search for a (deterministic) formula to predict the future course of stock prices, stands as a reminder that the "forces of evil" will not invest in our work without expecting a substantial return. When a mathematical community still largely faithful to the romantic ideal crosses paths with the masterminds of enlightened materialist ruthlessness, will the result be a second Enlightenment mind-body synthesis, a Faustian bargain signaling a renewed appreciation of one another’s desirability, with the "brilliant women of the court" replaced in the updated version by shapers of taste and prophets of economic competition, and with the reflection on human freedom of a Rousseau or a Condorcet replaced by obsessive attention to the bottom line?
In recent years, mathematics has made its mark on the inexhaustible witches' sabbath that is Paris nightlife. Harvard mathematician Benedict Gross passed through Paris in the fall of 2008 for the opening of his collaborative installation with multimedia artist Ryoji Ikeda at Le Laboratoire, a "[n]ew creative space” near the French Ministry of Culture “dedicated to experimental collaboration between artists and scientists,” directed by the author and biomedical engineer David Edwards. After exchanging messages for a year on "mathematics, infinity, the sublime,"1 Gross and Ikeda settled on an installation of two horizontal monoliths, each covered with more than seven million tiny digits representing in one case a prime number, in the other a "random" number.
Biomedical engineers have the edge on parties, if the opening reception at Le Laboratoire is any indication. Wandering across the dimly lit exhibition space—the two numbers were illuminated from above and their digits could only be inspected with the help of a magnifying glass—the few mathematicians in attendance, Ed Frenkel and I among them, gradually found one another in a crowd of hundreds of the experimental collaboration’s boisterous and exuberantly stylish celebrants. An office door slid open before us and we were ushered in to join the collaborators. While Edwards fiddled with a magnum of VIP champagne, Ikeda dropped to his knees at the feet of Jean-Pierre Serre and announced, "For me you are a rock star!"
Parisian mathematics had no official representation at Le Laboratoire but was in evidence at the March 2010 opening of another Japanese-American collaboration, this time between the late topologist Bill Thurston and Dai Fujiwara, creative director for the Issey Miyake fashion house.
"[Y]ou did not need a top grade in math to understand the fundamentals of this thought-provoking Issey Miyake show…"2 Fujiwara had contacted Thurston after learning about Thurston's Geometrization Conjecture and its connection with the Poincaré Conjecture. Fashion designer and mathematician, it turned out, both used the peeling of an orange to help their students understand geometry. "We are both trying to grasp the world in three dimensions," Thurston told the AP. "Under the surface, we struggle with the same issue."3
Alerted by a message from IHP director Villani (who starred as himself in the 2013 film Comment j'ai detesté les maths—we've seen his own fashion statements favor a 19th century romanticism), my colleagues and I arrived in time to sample the hors-d'oeuvres (American and topological: doughnuts, pretzels, bagels) and to register the shocked expressions of the insiders, too spontaneous to be concealed, as they witnessed the breaching of a fortress of Parisian fashion by the hopelessly unfashionable. Thurston (the "coolest math whiz on the planet," according to an admirer of his YouTube appearance4 with Fujiwara) modeled an original Miyake blazer created for the occasion at the show and again at the reception. Playing neither the natural man nor the romantic hero ("I can't believe this mathematics guy. He's so... not like what I expected."), Thurston told his interviewer that "Mathematics and design are both expressions of the human creative spirit."5
Like the authors of Rites, Thurston invoked truth and beauty in his essay for the show. "The best mathematics uses the whole mind," he insisted, "embraces human sensibility, and is not at all limited to the small portion of our brains that calculates and manipulates with symbols."Thurston was back in Paris in June 2010 for the ceremony organized by the Clay Mathematics Institute to honor Grigori Perelman for his solution to the Poincaré and Thurston Conjectures. A grandson of Poincaré was on hand, and the pantheon of the last fifty years of geometry, with only a few notable exceptions, had been assembled for the occasion, which was extensively covered by the French media (though not more than the Laboratoire show). One by one, the distinguished senior geometers stood up to praise the absent Perelman, who had not yet decided to refuse the Clay Institute's million dollars. Only Thurston took the opportunity to express sympathy for Perelman’s defense of the romantic ideal against the onslaughts of the good intentions of megaloprepeia:
Perelman's aversion to public spectacle and to riches is mystifying to many. … I want to say I have complete empathy and admiration for his inner strength and clarity, to be able to know and hold true to himself. Our true needs are deeper–yet in our modern society most of us reflexively and relentlessly pursue wealth, consumer goods and admiration. We have learned from Perelman's mathematics. Perhaps we should also pause to reflect on ourselves and learn from Perelman's attitude toward life.6
Most of the spectators at Rites' first screening were artists of some sort, rather than mathematicians, and were apparently drawn from Reine Graves' extensive list of Facebook friends. Once again, it was not hard to identify the mathematicians in the crowd at the post-screening reception, but the contrast was not as jarring as at Thurston's fashion show. On the contrary, the champagne was a democratic vintage and everyone in the Rites audience seemed to share a rejection of the couture mindset, the artists by design, the mathematicians by indifference. Communication across the cultural divide was cryptic but unstrained. One of Graves' three friends speculated that les maths sont là pour exprimer l'essence de la nature (the math is [in the film] to express the essence of nature); another saw une beauté calligraphique (a calligraphic beauty), analogous to the calligraphy at the center of the Noh stage, in the tattooed Frenkel-Losev-Nekrasov formula. Number theorist Loïc Merel, on the other hand, thought the film was an exploration of "how to preserve knowledge", but that the question was not taken seriously; the film's language was that of a conte de fées [fairy tale].
To mark the conclusion of a year spent in Paris as the occupant of the Chaire d'Excellence de la Fondation Sciences Mathématiques de Paris, Frenkel organized a mathematical conference entitled Symmetry, Duality, and Cinema at the Institut Henri Poincaré. Four lectures on mathematical topics of interest to Frenkel were followed by another projection of Rites d'Amour et de Math. At the champagne reception that followed7 I took notes while Gaël Octavia, the Fondation's public relations specialist, asked Graves why she decided to make a film about mathematics.8 Without hesitating, Graves, whose motto is ne jamais avouer ("never confess"), gave the very best possible answer. Mathematics, she began, is un des derniers domaines où il y a une vraie passion [one of the last areas where there is a genuine passion]. Cinema, according to Graves, is dominated by economics; so is contemporary art. Mathematics, like a very few other activities—she mentioned physics and sculpture—is practiced without complacency [sans autosatisfaction]; instead there is a true exigence au travail [demanding work ethic]. Mathematicians seek to percer le mystère. You can see it at once in l'oeil qui brille [the eye that gleams].
Let us gaze back a moment into the gleaming mathematical eye that Graves finds so compelling. Amir Alexander describes a portrait of Abel by the Norwegian painter Johan Gørbitz:
it is the young man's eyes that grab our attention and draw us irresistibly toward them. Dark and intense, … [t]hey burn with a fire that suggests deep passions of the soul and profound insights of the mind. Their gaze shoots out from the painting's surface… focused not on us but on a distant point on the horizon… the portrait is of a man … absorbed by his own inner flame and a vision he perceives far beyond.9
And looking back at us from romanticism's troubled borderlands, the eyes of Pechorin, Lermontov's Hero of Our Time, "shone with a kind of phosphorescent gleam…which was not the reflection of a fervid soul or of a playful fancy, but a glitter like to that of smooth steel, blinding but cold."