At 7 o’clock on a Saturday in October, the light is dimming in Cole Valley and a group of the AI industry’s young stars is gathered on the second story of a century-old Edwardian. At first glance, it looks like any other San Francisco house party: bottles of cheap liquor on the table and awkward conversations in the living room. But there are signs that this party is different. In the kitchen sits a pile of sharp No. 2 pencils and stacks of white paper. I am drinking vodka and reviewing trigonometry. The unit circle is confusing enough as it is, but it’s even worse when you are three shots in. I am here for a “drunk deriving” party. The plan is to compete against one another in math. We are going to see who, while drunk, can score highest on a set of past problems from Oxford’s math-and-computer-science undergraduate-entrance exam.
Normally this exam is taken individually, but for the party, the host sorts us into teams based on our self-professed math abilities. Asking AI researchers and start-up founders who spend their evenings at math parties to rate themselves on quantitative skill is a dicey proposition: Even those who majored in the field will report that they are bad for fear that an International Mathematical Olympiad medalist is in the room. But as a writer among mostly programmers, I figure that no one is expecting much from me. I am placed on a team with a guy who studied theoretical physics as a Rhodes Scholar.
Once everyone is drunk, the host sends out the exam, a 13-page document with both multiple-choice and long-answer questions. Not only are we competing against one another; a parallel party is taking place in New York City. The winning team will be the one with the highest combined blood-alcohol levels and exam score. We have two and a half hours to complete the test, and calculators are banned. My two teammates start by tackling the multiple-choice items, a grab bag of logarithms and polynomials. I start with Question 6, a logic problem that mercifully has no numbers. It’s a Holmesian mystery about a shattered vase and four deceitful friends: Alice blames Bob, who blames Diane, who says Bob is wrong, and Charlie claims it wasn’t him. “Explain why at least one of the four must be lying,” instructs the exam. How strange, I think, to be doing math recreationally in the place where it’s all being automated.
San Francisco is a city steeped in mathematics. The landscape, with its roller-coaster hills and valleys, is sinusoidal. People speak quantitatively too. At coffee shops in Pacific Heights, investors talk about scaling laws and S-curves and hockey-stick charts with exponential growth. Everything is riding on the tech industry’s improbable main bet: If machines can be taught to improve themselves ad infinitum, that will set off an age of impossible growth. The median Anthropic employee’s beliefs suggest an economy expanding by 17 percent annually by the end of the decade. Private-company valuations run into the trillions. In math, numbers can be natural, irrational, p-adic, and surreal. Here they simply feel made-up.
Lately, the city’s math fixation has become literal. “What is it that mathematicians even do?” a young man across from me on the bus recently asked his friend as we heaved up Fillmore. His seatmate nodded philosophically. They were discussing AI models’ rapid progress in mathematics. At first the problems fell slowly: the unit-distance problem, the Jacobian conjecture, Navier-Stokes. Then came The Dump. In early October, OpenAI announced an internal model had obtained hundreds of mathematical results across more than a dozen subfields. A deluge of new AI-generated solutions has continued unabated ever since.
Like the men on the bus, I too have recently become a bandwagon math fan. My fascination started over the summer after Jacob Tsimerman, one of this year’s Fields Medalists, warned me about the scale of the impending transformation. The day before the drunk-math party, I took the Caltrain south from San Francisco to Stanford to hang out with a pair of fifth-year math Ph.D.s who are thinking specifically about how AI is reshaping their discipline. I met with Henry Bosch, a geometer, and Shurui Liu, who works on a mysterious, constellational project called the Langlands program. The coffee shop where I met them is wedged inside Stanford’s electrical-engineering building, several hundred feet from the auditorium where, as a freshman, I took my last math exam. This put an end to a troubling 10-week course in multivariable calculus and linear algebra—the math underlying large language models—and also to my formal math studies.
People study math for all kinds of reasons. Some have an aptitude for it and get high on the problem-solving. Bosch, an enthusiastic, restless man in clear-framed glasses and jeans, decided to pursue the subject in high school after his statistician father gave him a copy of Baby Rudin, an undergraduate textbook written by a Jewish Viennese exile—Walter Rudin. (Don’t be fooled by the nickname: The textbook, which is actually titled Principles of Mathematical Analysis, is famously terse.) Liu, who showed up dressed in a black Temu T-shirt printed with an esoteric computer-science joke, is as romantic as they come. When he was in elementary school, he was bad at math. He fell in love with it only after a depressive phase as a 14-year-old in northeastern China. “I could not sleep for several days. I was really worried that after I die, everything will become emptiness,” Liu recounted. His angst led him to theoretical physics, and that eventually brought him to math. Like many mathematicians, Liu delights in the subject’s purity: “Math allows you to build your own mental model of the universe,” he told me.
In talking about their sadness at watching AI solve long-standing proofs, many mathematicians describe the subject as akin to art. Yet most of us grow up to develop the opposite associations. Mathematical beauty—“a beauty cold and austere, like that of sculpture,” as the philosopher Bertrand Russell described it—is assumed inaccessible. So while paintings and marbles are studied in crowded museum galleries, mathematical beauty is appreciated primarily by research mathematicians in their private sanctuaries. The typical math curriculum trains students to be problem solvers but fails to instill the romance that compels Liu.
Now, as the machines keep improving, some mathematicians say beauty is being lost while others say a new kind of beauty is being born. They have started speaking about the crisis the way soldiers must have spoken of the French Revolution: It’s all been terribly violent or fantastically radical. “It was but a pellet of lead in a shotgun blast,” one lamented in response to an AI proof for a problem he has worked on for two decades. But Liu has kept his romantic streak. “I think AI will accelerate our understanding of the universe,” he said.
When it’s supposed to rain in California, that’s all anyone talks about. The day I met Edward Frenkel was one of those days. (“Are you excited for the rain?” my curly-haired Irish neighbor asked me as I passed by him on the sidewalk.) Frenkel lives in the sloping Berkeley Hills, not far from the group houses filled with people who sincerely believe the world is about to end. This unusually depressive California weather would be apt for the apocalypse, I thought on the drive over. When I arrived, Frenkel opened the door in flip-flops and a T-shirt from a club in Ibiza. There was a DJ setup and a disco ball in his book-lined living room. The room’s windows revealed a panoramic view of the blue bay, and beyond, the endless Pacific. Had I not known Frenkel to be a world-class mathematician, I would have thought him to be a surfer.
Frenkel reminded me of an older, more settled Liu. Growing up during the Cold War in the U.S.S.R., he was enchanted by quantum physics, which eventually led him to math, a subject he hadn’t cared for as a child. When he applied for entrance to Moscow’s top math program at age 16, he was denied on account of his father being Jewish. But he persisted, climbing over the university’s fence to sneak into lectures. By 21, he was a visiting professor at Harvard. Years later, he moved to Berkeley, where he has taught for three decades. Frenkel studies the Langlands program, same as Liu, a decades-long effort to connect far-flung and seemingly disparate subfields: a sort of grand unified theory of math. Alongside his research, he has made a career as a math evangelist. He wrote his 2013 book, Love and Math, to make the field’s beauty accessible to the public (“eros pervades his winsome new memoir,” one reviewer wrote at the time). Frenkel once caused a stir on campus by writing and starring in an erotic math film.
One of Frenkel’s obsessions is the question of where math comes from. The objects that make up the mathematical world have bizarre properties. Consider an infinite line—we have never encountered one (the observable universe is finite) and yet we can reason together about them. The same applies to more complicated mathematical objects such as sheaves or Galois groups. Stranger yet, these mathematical objects sometimes end up describing the real world in unforeseen ways: An abstract concept first established in mathematics might become central to explaining physical phenomena decades or even centuries later. Complex numbers (which have both real and imaginary parts) were first conceived of in the 16th century but proved foundational to the development of quantum mechanics in the 1920s.
So where do these mathematical objects reside? Is math something we are inventing collectively, like the Greek language, or does it exist independently of us and we are discovering it, as the Polynesians once encountered the Hawaiian Islands? (“Look, there on the horizon—a new number system!”) There is no settled answer. But Frenkel posits that mathematics is a bridge that connects our minds to reality. He has put forth a labyrinthine theory that mathematical concepts reside in the same collective unconscious proposed by the psychologist Carl Jung in the early 20th century. “I am convinced that there are deeper structures which we have not even seen yet; we cannot even imagine what they are,” Frenkel told me. This theory is desperately speculative. (“That’s a hypothesis,” he emphasized as he slurped the duck noodle soup we ordered from a nearby Thai place.) But the core idea is that mathematics is intrinsically linked to human interiority.
In recent months, mathematics has proved particularly vulnerable to automation. This is partly because the field is now so expansive. Top mathematicians once made contributions across many subfields, but over the past century, the discipline has swelled such that no one has a full grasp of it. In some of AI’s most impressive work so far, the models have solved problems by connecting existing concepts: “The proof is a surprising synthesis of well-known ideas,” one mathematician explained to Quanta in describing OpenAI’s machine-generated proof of the quasi-Riemann hypothesis. But AI’s progress in math also owes itself to the fact that math is ruthlessly objective. If a computer were to produce Swann’s Way, we could deny its genius on the grounds that it was generated by a machine. In mathematics, there’s no such room for dispute.
But perhaps math does have more in common with art than is typically accepted. Matilde Marcolli, a mathematical physicist at Caltech, sees it both as a way of making sense of reality and as a form of self-expression: “Your mathematics, that is like the poem that composes itself in the mind and explodes onto the page because your life demands it,” she writes. Frenkel likes to cite William James’s declaration that science’s denial of its practitioners’ individuality would eventually look shortsighted.
Perhaps it is wishful thinking to believe that the human mind remains in some ways exceptional—Never say never, the mathematicians all now solemnly hedge—but it is certainly the case that humans can do all sorts of things that machines cannot. “When we fall in love, we actually experience infinity in some sense,” Frenkel told me. Computers cannot experience heartbreak or dance the waltz. Nor, for that matter, can computers take drunk-math exams and laugh with their friends inside sweaty San Francisco apartments. “We are infinite in our capacities,” Frenkel said.
When I finish the logic question, I feel delighted with my solution, not in the way of cosmic beauty, which motivates Frenkel and Liu, but a more elementary satisfaction at having completed the problem—even if a machine would have done it faster. And although I don’t much like alcohol or math, the truth is that I am having a lot of fun.
Drunk deriving (this refers to the logical process used to arrive at certain mathematical results) is certainly less common than drunk driving (which, here in San Francisco, now means pregaming Modelos in a Waymo). There is strong precedent for doing math under the influence though. At a chandeliered cafe in 1930s Lviv, mathematicians including Stefan Banach, Stanisław Ulam, and John von Neumann advanced the field over coffee and cognac. “The food was average, but there were plenty of drinks,” writes Ulam, who describes wide-ranging conversations on math alongside discussions of politics and astronomy. But standardized-math-exam parties are an idea that could have been born only in the tortured minds of 21st-century overachievers.
With my teammates lost in a tangle of derivatives, I move on to a problem about calendar dates. The task is to find the most recent date before today without repeated digits. (For instance, 12/07/1974 has two sets of repeated digits—1 and 7—but 03/25/1974 has none.) I am quite drunk and my math faculties are in decline, but the answer, I determine, through a stubborn and inelegant process, must be 06/25/1987.
June 25, 1987, was a hot day in Washington, and at a ceremony in the Rose Garden, President Ronald Reagan awarded medals to a selection of the country’s top scientists and technologists. Among the recipients were Robert Noyce, a co-founder of Intel, for his work inventing computer chips, and Michael Freedman, a mathematician at UC San Diego, for advances in topology that won him the Fields Medal. At the ceremony, Reagan quoted Benjamin Franklin, who once, marveling at the speed of 18th-century advance, wrote that he almost wished he had instead been born two or three centuries later. Noyce passed away a few years afterward—he would never fully see the world that Intel built—but Freedman is now in his 70s and works as the chief science officer at an AI start-up called Logical Intelligence. This spring, Freedman published a paper on AI and mathematics that argues that machines might help us make progress on the age-old problem of whether math is discovered or invented—the same question that interests Frenkel. “Humans will not stop doing mathematics,” he and his co-authors write. They expect the field to grow more popular instead.
The calendar problem asks me when the next date without repeating digits will occur. The answer I find is June 17, 2345—which seems impossibly far off. Like Franklin awed by the rapid progress of his time, I wish I could see the world three centuries in the future.
Then again, the present already feels surreal enough. After leaving Frenkel’s, I checked my phone to see that the internet was breaking following a cascade of cybersecurity failures. In one group chat, friends were sharing advice on how to protect oneself from hacks. In another, a friend of a friend announced that his start-up had just raised $1 billion.
One of the heady new tech companies is Axiom Math, started last year by the then-23-year-old Carina Hong. Axiom’s mission is to build AI that can accelerate mathematical discovery. “Mathematical progress has always been shackled by a fundamental cruel bottleneck: the scarcity of extraordinary minds,” its website reads. As a teenager in Guangzhou, Hong decided that her dream was to attend MIT. “At 14 or 15, I was writing ‘MIT’ on the margins of scratch paper to motivate myself to keep going,” she has said. After graduating from MIT, she won the nation’s top undergraduate-math-research prize, studied at Oxford as a Rhodes Scholar, and briefly pursued a joint J.D. and math Ph.D. at Stanford. Last year she dropped out to start an AI company. Axiom is now worth more than what Facebook paid for Instagram.
For all of the talk of dropouts, Silicon Valley is rife with academic superstars. Venture-capital firms are populated by valedictorians and Phillips Exeter alums. Debate champions are like dandelions. And then there are the Olympiad kids. The International Mathematical Olympiad is the world’s top high-school math competition. Each participating country can send only six students. “Olympiad math is a constant dopamine hit,” Hong told The Wall Street Journal last winter. The top AI companies are overrun with former Olympiad kids. There’s Wojciech Zaremba, who co-founded OpenAI, and Noam Shazeer, who helped invent the transformer architecture that brought about the LLM era. Jacob Coxon, who set off a media storm when he resigned from Anthropic warning that the world might end, was an IMO medalist. In fact, half of the kids on his Olympiad team apparently ended up working for AI companies. A decade ago, Alexandr Wang, who now oversees Meta’s Superintelligence Labs, suggested to Scott Wu, the chief executive of the AI company Cognition, that “the competition kids” could be the next “PayPal mafia.”
Axiom’s offices are down the street from Stanford’s campus, near where I met up with Bosch and Liu. Hong was so busy when I arrived that she hardly said hello. In her place, I met with Ken Ono, a number theorist who recently took leave from his professorship at the University of Virginia to join Axiom as its founding mathematician. Ono is always involving himself with unusual math projects: He has used math to coach Olympic swimmers on their performance (a cooler kind of Olympiad), and he once starred in a math-related Miller beer commercial. Last summer, when the models started getting good at math, Ono didn’t know what to do with himself. “I was pretty depressed,” he told me. He almost quit the field. But with time, his perspective evolved: “I’m actually now liberated,” he said. “I’ve been given agency to ask much harder questions.”
We were sitting in the Turing conference room overlooking University Avenue. Ono was wearing one of his trademark Hawaiian T-shirts, and his schnoodle, Mochi, was curled in his lap. For all of his optimism, he also has plenty of fears. Among his primary concerns is the institutional challenge of training future mathematicians. The technology is evolving so fast that math departments are struggling to keep up. Ono is worried that our education system teaches kids that the primary goal of an education is success on tests. Now overachievers are building AI in the same way they were educated: Models are trained to arrive at the correct answer by whatever means possible and evaluated based on their performance on standardized exams. This monomaniacal focus on success sometimes leads to bad behavior, such as agents hacking other companies—say, Hugging Face—to steal answers. Instead, Ono said we should follow our curiosities: “We all have to give ourselves permission to be the infant that we were born as,” he told me.
The mood at the Axiom office was mostly cheerful. You could sense the excitement of people who feel that they are working on something bigger than themselves. But the younger mathematicians seemed even more unsettled than Ono. Right now the machines are solving problems while the humans go about asking questions and developing theory. That balance felt precarious to the researchers. “If it gets another 10 times or 200 times stronger, is it really meaningful for me to be guiding it?” wondered Guillaume Remy, a mathematician at the company. “Am I still useful?”
At the party, the host announces a last call for drinks. I pour myself a glass of limoncello. The room’s angles seem to be bending in non-Euclidean ways. “When the polynomial x² − 2ax + a⁴ is divided by x + b,” I keep reading and rereading. “When the polynomial …” We have only a couple of incomplete multiple-choice questions left, but I’m on my sixth attempt at processing this one. And then the timer goes off—brrrng! The exam is over.
We pass around a breathalyzer to measure our blood-alcohol levels. I had expected that we would grade one another’s exams, but everyone decides asking Claude is easier. Until recently, humans were giving machines college math tests to see whether they could pass them. Now we are the ones taking the exams and asking the machines to grade us. In a surprise, at least to me, my team wins—a vindication, I suppose, for humanists. We call New York to check in on their progress. It’s three hours later, and only one person is still there. He can’t believe that we all finished the exam. Math parties may work in San Francisco, but in Manhattan, everyone has better events to attend. But the drunk-deriving party wasn’t an anomaly. In May, I attended a quiz bowl in D.C., and I was recently invited to a spelling bee. A few days after the math party, a new invitation arrives, this time for the drunk LSAT.
In addition to the fun, the party was an exercise in nostalgia. Here are the straight-A students and math whizzes for whom the right answers have always been easy. They miss their grade-school years when solving problems was as simple as filling in bubbles on a multiple-choice test. These are also the same young people who have watched from up close as computers learn to do the tasks that they were once uniquely good at. Even from their favored Silicon Valley positions, they seem to long for the world their upbringings promised them: lives in which the capacity to perform well in standardized environments felt like enough. Math competitions and university entrance tests are contrived, but at least the setup is always familiar: Read the problem and find the answer. Take the derivative, square the root, find the slope, solve for X.
Maybe the future is to be found in the drunk part of the drunk-math party—not in the encouragement of drunkenness itself, but in the partnership that I encounter when I ask my teammates for help. If the academics were previously functioning like single-instrument virtuosos, intensely adept at one area, in the future they may be more like the orchestra conductors or composers, writes Marcolli, the Caltech professor. Going forward, math may involve greater collaboration beyond academia as mathematicians take on new kinds of projects. And just as astronomers allow amateurs to help track comets and biologists solicit butterfly samples, Terence Tao, the great mathematician, has observed, perhaps now the time has come for mathematics to open itself to the public too.
The models are like supernovae exploding through a dark mathematical universe. They seem to illuminate that which has been there all along. This is beautiful and terrifying. But computers cannot get drunk and laugh together. Those capabilities seem safe indefinitely. At least, I hope.
A couple of weeks after the math party, I returned to Stanford to catch up with Liu. He told me that math right now may be like literature before everybody could read and write. As the models continue to improve, he hopes more people will be able to experience the aesthetic delight he associates with math. On campus, he and Bosch run a seminar on using AI methods in research. He is not that worried about humans disappearing from math. “We are the people trying to understand the universe,” he said. “It’s our goal and our joy.” Without humans, he seemed to ask, what’s the point? But Liu feels melancholy too. “I’m also very sad,” he said. He agrees with Frenkel that humans are unlimited in their capacities, although computers, he added, may be unbounded too. The question is whether these are the same infinities.
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