Knowledge Collapse

Source: Michael Harris — Boston Review · 2026-06-10

Eleven years ago, the mathematician Stefaan Vaes, upon receiving the prestigious Francqui Prize for young scientists from the hands of Belgium’s Queen Mathilde, took the opportunity to tell Her Majesty why we mathematicians choose such a misunderstood profession. “Omdat wij dit graag doen,” he said—because we like it. A few years before that, another Belgian, Pierre Deligne, on the occasion of his selection for the Abel Prize—often called the mathematician’s Nobel Prize—explained that he decided on a career in mathematical research when he learned that “one could earn one’s living by playing.”

AI has been targeting mathematics, as both a challenge and a trophy, since its beginnings in the 1950s. Three years after the phrase “artificial intelligence” was coined in the run-up to a legendary 1956 conference at Dartmouth, Alan Newell and Herbert Simon predicted that within a decade, digital computers would reach four milestones—matching human capabilities in mathematics, music, chess, and psychotherapy—on the road to a “world in which [human] intellectual power and speed are outstripped by the intelligence of machines.” The deadlines, periodically revived, came and went; finally, in 1997, IBM’s Deep Blue defeated Garry Kasparov. Progress toward the other milestones largely stalled until the deep learning revolution of the 2010s, when the Newell-Simon program took on new life, amplified by the colossal wealth and ambition of Silicon Valley.

With the rise of generative AI, we are now seeing regular predictions that human mathematical power is at last on the verge of being outstripped, whether or not anyone likes it. From the New York Times publishing an article under the title “AI Is Coming for Mathematics, Too,” to serious journals like Science and Nature repeating industry talking points, the general public is repeatedly being told that mathematics will be the next domino to fall on the inevitable march to artificial general intelligence (AGI). Among mathematicians, versions of the following syllogism have been circulating in recent years with increasing urgency:

Therefore, AI will “solve” math.

“Computational Intelligence is the manifest destiny of computer science,” Edward Feigenbaum wrote more than twenty years ago: “the goal, the destination, the final frontier.” Mathematical boomers share Feigenbaum’s romantic vision; in this they are encouraged by funding agencies like the National Science Foundation (NSF), whose new Institute for Computer-Aided Reasoning in Mathematics at Carnegie Mellon aims to “empower mathematicians to take advantage of new technologies for mathematical reasoning,” as well as by established industry labs and startups like Axiom, which promises, “We stand at the threshold of a mathematical renaissance.” The collective market capitalization of such ventures would suffice to fund 200 math PhDs—the number lost this year in the United States due to cuts to graduate programs—every year for the next 500 years.

For their part, the doomers take the syllogism literally: they agree with the New Scientist that AI “is rewriting what it means to be a mathematician,” and while they “are still hopeful there will be a place for them in an increasingly machine-led future,” they anticipate “a world in which AI mathematicians take humans ‘out of the loop’ entirely.” Meanwhile, to the simmering frustration of those keyed in to our profession’s purported manifest destiny, the vast majority of mathematicians go about their routine, and like it, oblivious to the looming boom and/or doom.

The market capitalization of math-related labs and startups would suffice to fund 200 math PhDs—the number lost this year in the United States—every year for the next 500 years.

Understanding is a lively topic for philosophers, but not for the tech industry. In their race to the ultimate prize of AGI, Silicon Valley’s main players instead see the mechanization of reasoning as the main hurdle. For them, mathematics is the supreme AI challenge because it is the purest form of reasoning. Human mathematicians, from their perspective, are saddled with a beta version of intelligence, reliant on vaporous experiences like understanding that are of no commercial value. A machine, by contrast, can function without anyone worrying whether or not it understands what it’s doing, much less whether the machine likes it.

At their most rhapsodic, boomers would have you believe AI companies aim to democratize the creation of knowledge. Back on this planet, these are textbook cases of alienated labor.

When Silicon Valley’s prophets of superhuman mathematics do violence to the values of human mathematics, in particular to the insatiable desire for understanding, they are forgetting that the technology to which they owe their fearful power derives from the history of that very desire. Consider the following fable, largely true, about the intertwined histories of calculus, number theory, and the most implacable symbolic logic.

This conjecture is the most notorious of the unsolved Millennium Prize Problems, and when we mathematicians talk or write or obsess over the prospect of being made obsolete at AI’s invisible hands, the point of no return often takes the form of an AI proof of the Riemann Hypothesis. The AI companies couch their math fantasies in the same terms. As they tell it, their resolution of RH would be a sign that some epistemic pendulum has swung definitively in their favor. Many mathematicians narrate this same story as a nightmare: a million-line proof that no less definitively marks the defeat of human understanding.

The tokens of mathematical understanding can take many forms—proofs, diagrams, definitions—but their common feature is that they have to be able to be freely available, ready to be shared.

But why, then, does it matter so much to Silicon Valley whether the primes are distributed randomly? Why does Surge AI—which counts Harvard, Oxford, NASA, and the Olympics, Goldman Sachs and Navy SEALs among its clients—promise on its home page to hire “the world’s greatest minds” to “train AI to explore the Riemann Hypothesis and beyond”? Since prime numbers are the basis of the encryption systems used to guarantee security on the internet, some claim a proof of RH may have practical implications. I find this totally unconvincing. Computer calculations have confirmed RH with far more accuracy than any of the physical theories that underlie contemporary technology, without going to the bother of paving northern Virginia or the surface of Mars with data centers and building nuclear reactors to power them. Such confirmation is as good as a mathematical proof for all commercial purposes.

In late January, a message from something called Handshake AI appeared in inboxes in my department:

I hope this email finds you well. I’m reaching out from Handshake AI with an invitation to a selective, paid research project involving expert evaluation of AI systems. We’re assembling a small group of senior researchers with expertise in Analysis, Number Theory, Topology, Algebra/Geometry to help train an AI model to read, interpret, and summarize peer-reviewed scientific literature.

Project details:

It’s not one of those nine-figure signing bonuses we read about, and the decades I’ve spent acquiring expertise in number theory hardly amount to the right kind of background and experience, but an extra $1,850 to $4,000 per week sounds pretty good, right?

At their most rhapsodic, AI boomers would have you believe that such projects aim to democratize the creation and production of knowledge, to bring into being a kind of epistemic communism that, to update a famous passage from Marx’s German Ideology, makes it possible for me to do one thing today and another tomorrow, to hunt in the morning, fish in the afternoon, rear cattle in the evening, mathematize after dinner . . . without ever becoming hunter, fisherman, herdsman, or mathematician.

Back on this planet, the Handshake AI offer is a textbook case of alienated labor. The results of the work belong unequivocally to the firm that commissioned the project, whose identity presumably is never shared with the “experts.” In other words, Handshake’s email was an invitation to claim a spot on a spectrum of “ghost work” or “microwork,” not unlike tagging images or filtering videos, as one of the “human robots” who are “almost indistinguishable from software units,” in the words of sociologist Antonio Casilli. Human robots with few credentials, like Amazon’s Mechanical Turk, have been paid less than $2 an hour; “senior researchers with expertise,” Handshake tells us, can earn a hundred to two hundred times as much. The relation to the finished product is the same in both cases: “the degradation of men into commodities,” to quote Arendt; or as Jeff Bezos put it, “this is basically people-as-a-service.”