{"id":3901,"date":"2026-07-21T17:41:06","date_gmt":"2026-07-21T17:41:06","guid":{"rendered":"https:\/\/crosscountrymovingteams.com\/?p=3901"},"modified":"2026-07-21T17:41:06","modified_gmt":"2026-07-21T17:41:06","slug":"mathematicians-grapple-with-a-very-rapid-and-very-unsettling-change-as-ai-cracks-yet-another-century-old-problem","status":"publish","type":"post","link":"https:\/\/crosscountrymovingteams.com\/?p=3901","title":{"rendered":"Mathematicians grapple with a \u2018very rapid and very unsettling change\u2019 as AI cracks yet another century-old problem"},"content":{"rendered":"
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By the time Kevin Buzzard woke up in London the next morning, the result had been verified. By lunch, it was all his peers at the Imperial College London\u2019s pure mathematics department could talk about; at the time of writing, Anthropic employee Levant Alp\u00f6ge\u2019s post announcing the result has drawn more than 20 million views on X.<\/p>\n

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\u201cIt is a big day,\u201d Buzzard told Fortune<\/em>. \u201cI think it\u2019s a great time to be alive, personally.\u201d<\/p>\n

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It was the latest in a series of AI-driven mathematical breakthroughs. AI\u2019s progress (or assault) on unsolved mathematics has compounded rapidly since mid-2025, when models first solved five of six problems at the\u00a0International Mathematical Olympiad. From there, the list of fallen problems grew fast: OpenAI\u2019s model disproved an 80-year-old Erd\u0151s conjecture on combinatorial geometry in May, and in June, 16 researchers from 15 universities published the\u00a0Leiden Declaration on Artificial Intelligence and Mathematics, urging the profession to set guardrails around transparency, attribution, and peer review before AI reshapes what mathematical knowledge even means. <\/p>\n

Mathematicians, relegated to the role of shepherd, are left to watch AI close these questions one-by-one, reaching places where the human mind can\u2019t follow. Their reaction is a now familiar mixture of dread and amazement.\u00a0<\/p>\n

The problem is called the Jacobian conjecture and since 1939, it has rested on the work of German mathematician Ott-Heinrich Keller. Fundamentally, the problem is about what mathematicians call \u201cmaps,\u201d and the conditions under which, given a set of outputs, you can determine the input. This being math, it was based on yet another German\u2019s work a century earlier: Carl Gustav Jacob Jacobi\u2019s Jacobian determinant. The main issue for modern practitioners is that they were unable to prove Keller\u2019s conjecture true, or find a reason that it was false\u2014until now.\u00a0<\/p>\n

On Sunday. Alp\u00f6ge\u2019s result met the Jacobian determinant at every point in space\u2014the determinant holds steady at \u22122 everywhere\u2014yet sends three different starting points to the same destination. Meaning, it didn\u2019t pass the test.\u00a0<\/p>\n

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It\u2019s a \u201cvery exciting\u201d result, Buzzard said, one that demonstrates the potential of language models to eventually reach the \u201csupermathematician\u201d Google Deep Learning scientist Christian Szegedy warned about half a decade ago.\u00a0<\/p>\n

But it also leaves mathematicians wanting. The trouble with getting current AI models to solve pure math is that you get the \u201chow\u201d without the \u201cwhy,\u201d explained Akhil Mathew, the University of Chicago mathematician who Alp\u00f6ge credits with suggesting the problem to him. \u201cOne can check out that it\u2019s correct,\u201d Mathew told Fortune<\/em>, \u201cbut it would be nice to be able to tell a story.\u201d\u00a0<\/p>\n

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Alp\u00f6ge didn\u2019t respond to Fortune\u2019s<\/em> request for comment.<\/p>\n

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Mathematicians have faced down automation before. Most people with high-school level math see the job as calculation, which computers conquered decades ago. \u00a0 \u201cThen you go to college, and if you do some advanced math classes, you learn that actually math is all about reasoning,\u201d Buzzard said.<\/p>\n

A calculator multiplies four-digit numbers faster than any human. What a mathematician adds is the reason: told that 131 times 137 is four million, Buzzard doesn\u2019t need to reach for a calculator\u2014he knows two odd numbers can\u2019t make an even one. To understand something, he said, is to \u201cmake it fit in your brain,\u201d so well that you could regenerate the result yourself from the idea.\u00a0<\/p>\n

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The demonstration of your knowledge,in formal mathematics, is a \u201cproof,\u201d a chain of logical steps, each following from the last, that ends at the claim you\u2019re making. Proofs are both how mathematicians build and how they\u2019re measured. A great proof can run hundreds of pages and take months of explaining to experts to trust.<\/p>\n

So far, AI doesn\u2019t yet have the capabilities to create such a proof, Buzzard said. Creating a delicate 150-page proof requires hundreds of steps, and language models have a habit of bridging gaps with plausible-sounding filler. because unlike a human colleague, the model risks no reputation by being wrong.<\/p>\n

If and when that bottleneck cracks, it\u2019ll be Buzzard\u2019s own doing, though. His career project is Lean, a popular computer language in which proofs are checked by machine rather than by exhausted PhDs. He said the proof was already checked in Lean by the time he woke up. The moment proof-writing models meet his proof-checking machine, one of human\u2019s last advantages in mathematics disappears.\u00a0\u00a0<\/p>\n

Mathew was more tempered in his excitement, calling this moment \u201ca very rapid and very unsettling change\u2026 especially for junior mathematicians.\u201d <\/p>\n

Michael Harris, a professor of mathematics at Columbia, wrote in a June essay in Boston Review<\/em> that the AI industry treats reasoning, or understanding, as commercially worthless, and human mathematicians as a \u201cbeta version of intelligence.\u201d\u00a0 Yet mathematics, he argued, is one of the last examples of unalienated labor, a field that people enter, in the words of Abel Prize winner Pierre Deligne, because one can earn a living \u201cby playing\u201d \u2014\u00a0what Mathew calls \u201ctelling a story.\u201d Even when Deep Blue \u201csolved\u201d chess by beating Garry Kasparov in 1997, people didn\u2019t stop playing chess; they learned from it.\u00a0<\/p>\n

But perhaps it sounds uninspiring for the public to subsidize mathematicians to play. Even before AI threatened their work, federal funding for mathematics research has fallen roughly 72% under the Trump administration\u2019s cuts to the National Science Foundation. PhD admissions at top research universities are down 15% this fall, the second consecutive year of contraction; George Washington University\u2019s math doctorate will admit no funded students at all.<\/p>\n

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Some think that the death of mathematical professionalization is good, that the machines democratize the whole enterprise, the \u201cplaying.\u201d Garry Tan, president of Y Combinator, reacted to the news on X by hailing the return of the age of the \u201cgentleman scientist\u201d\u2014 rich savants \u00e0 la Benjamin Franklin, funding their own curiosity. But Alp\u00f6ge is no hobbyist; he is a Harvard valedictorian who has spent a decade using algorithms to calculate exactly this kind of problem.\u00a0<\/p>\n

And that might be the trick to keeping humans in the mathematical loop, Buzzard said. Beyond calculating, beyond even logical reasoning, \u201cunderstanding,\u201d at the bottom, is knowing what to ask, what Silicon Valley has taken to calling \u201ctaste.\u201d<\/p>\n

\u201cPeople have tried to get machines to ask questions, and they\u2019re abysmal,\u201d he said. \u201cAll the questions they ask are either boring or obviously true or obviously false.\u201d The monuments of the field\u2014the Riemann hypothesis or Keller\u2019s Jacobian\u2014are named for the people who posed them, not the people who settled them, Buzzard pointed out. \u201cIt\u2019s not a coincidence. You have to be a brilliant mathematician to come up with the right question.\u201d<\/p>\n

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Anthropic’s Levant Alp\u00f6ge, a former Harvard valedictorian, used Claude’s Fable 5 to find something that mathematicians have failed to since 1939.<\/p>\n","protected":false},"author":1,"featured_media":3900,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[158],"tags":[],"class_list":["post-3901","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-science"],"yoast_head":"\nMathematicians grapple with a \u2018very rapid and very unsettling change\u2019 as AI cracks yet another century-old problem - Cross Country Moving Team<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/crosscountrymovingteams.com\/?p=3901\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Mathematicians grapple with a \u2018very rapid and very unsettling change\u2019 as AI cracks yet another century-old problem - 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