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A Mathematician Used Claude Fable to Disprove the 87-Year-Old Jacobian Conjecture in a Few Hours
Levent Alpöge, a number theorist at Anthropic, announced on X that he had found a counterexample to one of algebraic geometry's most notorious problems, crediting Fable as his collaborator.
A New Declaration Warns AI Could Threaten the Foundations of Mathematics
AI is reshaping math—and how mathematicians work. That's fine, but experts want some clear standards.
Richard Tapia, Mathematician Who Pushed to Diversify His Field, Dies at 88
A math whiz as a young man, he later blazed trails, both with his theoretical advances and his advocacy for minority students.
A mathematician used Fable 5 to disprove a major math problem
The Jacobian conjecture has bedeviled math experts for nearly 90 years.
The Mathematician Crushed Between OpenAI and Anthropic Over a Math Problem
Tristan Buckmaster was on the path toward an important proof when one of the A.I. giants used its staggering resources to get there first.
These Russian Mathematicians Taught AI Models How to Talk to Each Other Without Using Words
A startup called Mostik has a wild new approach to combining the capabilities of AI models.
The Four-Color Theorem Gets a Rare New Proof
By revisiting the famous problem — which was controversially solved in the 1970s with the help of computers — mathematicians have gained important new insights into the nature of graphs.
Can researchers trust that AI models won’t leak their ideas?
Research funders are asking how they can stop confidential scientific ideas in grant proposals from leaking out through large language models (LLMs), for example if reviewers use AI to help them judge applications. Last week, a row erupted in mathematics after OpenAI announced it had solved a notoriously difficult problem, only for another mathematician to demand answers over whether the company had used ideas he had fed into its models. The spat, and the broader issue of idea leakage through AI models, was discussed by funders at an R&D policy conference held in Paris on September 14. At worst, it threatens to undermine the correct attribution of breakthroughs, one of the foundations of modern science. The mathematics dispute around OpenAI is “certainly something we're looking at” Jason Gallo, head of the newly established Office of Metascience at the US National Science Foundation (NSF), told the Blue Sky Forum, hosted by the Organisation for Economic Co-operation and Development. The controversy started on September 8, when OpenAI announced it had cracked a mathematical problem that had gone unsolved for 90 years. Using a swarm of AI agents, millions of dollars’ worth of computing power and a new internal model, the company said it had finally proved that a long-used formula for modelling fluid dynamics breaks down under certain conditions. However, Tristan Buckmaster, a New York University mathematician who had been independently working with collaborators on the same problem using OpenAI’s Codex tool, hit back with a statement questioning whether the company had snooped on his Codex sessions to gain an advantage. OpenAI has always denied it looked up the “specific user data” of Buckmaster and colleagues. However, the company initially admitted that “while unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models,” although its proofs “differ significantly” from Buckmaster’s. The firm later said that, following an investigation, it concluded that Buckmaster’s Codex prompts “could not have influenced the [OpenAI] system in any way, including through training.”Funder concernYet OpenAI’s initial admission that its model might have ingested Buckmaster’s ideas, then spat them out to its own mathematicians, has scientistsworriedthat their work could leak out if shared with AI. Some AI tools give users an opt-out option to stop their sessions from training the model. If such guarantees can be trusted, this gives scientists some confidence they can use an LLM to develop an idea without the risk of it leaking out.But there’s a bigger potential vulnerability. To win money to investigate ideas, scientists have to share them with funding bodies. These grant proposals are normally kept strictly confidential, to prevent other scientists from scooping them, or to protect commercially valuable intellectual property. To preserve this confidentiality, when the NSF uses AI models, “we have to be sure that it's not making server calls out to an external party, leaking that data,” said Gallo to delegates in Paris. Leaks through reviewersHowever, funders normally use external academic reviewers to assess proposals. And there are growing worries that these reviewers are feeding grant ideas into AI models to help them make a judgement. Research funders have noticed that peer review reports and funding recommendations have “suddenly become much longer, more detailed and complex,” said Diogo Machado, head of the data science unit at Technopolis, a science and technology-focused consultancy. “The sense is that reviewers are increasingly using generative AI in their review work, even where guidelines sometimes forbid it,” he told Science|Business. “This is very difficult for funders to control or prove.” Happening at scaleThis sharing of confidential proposals with AI models is “happening at scale already,” said James Wilson, executive director of the Research on Research Institute, based at University College London, during the debate in Paris. In response, Gallo said the NSF had “strict guidance” around the uploading of proposals to AI models. But he added the NSF was mulling new types of assessment to make sure applicants were truly the originators of their ideas, such as following a short-form proposal with an oral presentation, which would allow the foundation to “really interrogate the investigator on their intellectual contribution.” Related articlesHow can Europe cope with a flood of AI-assisted research grant proposals?The risks and benefits of AI in screening research grant proposals Viewpoint: AI could make scientific overload worse“For us as funders, a lot of the ways to ensure that the application remains the applicant's own intellectual contribution, those ways are quite regressive,” Peter Clifford, head of strategy at Research Ireland, told delegates. “They're maybe ten or 15 or 20 years old, and they don't scale particularly well.” Disputes over the origin of ideas are as old as modern science. Isaac Newton and Gottfried Wilhelm Leibniz spent more than a decade arguing over who invented calculus, for example. And long before LLMs emerged, academics would agonise over how much of their early work to reveal at conferences, in case their colleagues scooped them, Jack Leahy, a senior metascience advisor to the UK government, told delegates. But AI was “accelerating” the “problems of the system,” he said.
Behold the Manifold, the Concept that Changed How Mathematicians View Space
In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation for modern geometry and physics.
We Finally Know The Name of a Revered Maya Astronomer-Mathematician: Sak Tahn Waax
The 'white-chested fox'.
Leading Chinese mathematicians unite behind use of AI in research
Fields medallist Shing-Tung Yau, who is leading the project, warned that the country is lagging behind the US in using the technology.
‘Immature playground boasting’: Mathematicians uneasy at OpenAI’s latest scalp
As OpenAI model cracks Millennium Prize Problem that puzzled experts for decades, many feel shocked at pace of change
Using AI, Mathematicians Find Hidden Glitches in Fluid Equations
A $1 million prize awaits anyone who can show where the math of fluid flow breaks down. With specially trained AI systems, researchers have found a slew of new candidates in simpler versions of the problem.
Open AI and the million dollar maths problem
In early September, OpenAI announced it had solved a major mathematics problem that has stumped humans for nearly a century. The news left mathematicians reeling, and many expressed concern over what will be left for humans as AI becomes ever more adept at unravelling complex problems. Now 25 recipients of the Fields medal – often called the Nobel prize for maths – have signed an open letter expressing their fears of a ‘severe misalignment’ between AI companies and their field. To find out how AI is likely to upend maths – and how mathematicians might respond – Ian Sample speaks to Colva Roney-Dougal, professor of pure mathematics at the University of St Andrews
Exclusive: OpenAI wants to be a scientific research partner
AI is increasingly being used as a research collaborator for mathematicians and scientists.
The Math Singularity Is Here, and Science May Be Next
OpenAI has released an extraordinary body of mathematical work produced by an unreleased frontier model: 722 manuscripts spanning 372 research families across fields including number theory, complexity theory, and mathematical physics. Each result required, on average, the equivalent of roughly three hours of ChatGPT Pro reasoning. A New Era of Discovery We may be witnessing the beginnings of a “math singularity”: a point at which machine-generated discovery accelerates beyond humanity’s ability to independently reproduce, verify, or fully absorb it. If frontier models can generate hundreds of meaningful results in the time it takes a human researcher to investigate one, the constraint will no longer be producing new mathematics. It will be our capacity to validate, interpret, and integrate it. This does not make mathematicians obsolete. It changes their role. They may increasingly serve as guides, critics, and meaning-makers. Increasingly, they will decide which questions matter, determining which results can be trusted, and explaining why they are important. Mathematical insight may become abundant, while human judgment becomes more valuable than ever. Mathematics May Be Only the Beginning Every scientific discipline could eventually experience a similar acceleration. AI systems could generate and test hypotheses, connect findings across specialized fields, and explore possibilities at a scale no human research community could match. In medicine, imagine models identifying overlooked disease mechanisms, designing drugs and clinical trials, personalizing treatments, or discovering cures in months rather than decades. In materials science, AI could help create better batteries and cleaner industrial processes. In climate science, it could accelerate advances in energy, forecasting, and carbon removal. In biology, it could uncover relationships hidden across enormous genomic and molecular datasets. The result would not simply be faster research. It could expand the frontier of what is scientifically possible. The New Bottleneck Scientific discovery, however, is not the same as scientific progress. A medical breakthrough must still survive laboratory testing, clinical trials, regulatory scrutiny, manufacturing constraints, and real-world deployment. As machine-generated ideas multiply, the bottleneck may shift from producing breakthroughs to validating them safely and translating them into practice. We may soon have more hypotheses than laboratories can test, more drugs than clinical trials can evaluate, and more mathematical results than experts can review. That imbalance will require better systems for automated verification, reproducible research, prioritization, peer review, and collaboration between AI and domain experts. The importance of OpenAI’s work is not merely the number of manuscripts produced. It offers a glimpse of a world in which intelligence can explore thousands of intellectual paths in parallel. If ideas cease to be scarce, humanity’s defining challenge will be deciding which are true, which matter, and how to turn them into progress. The math singularity is not the end of human inquiry. It is the beginning of a new kind—one in which machines expand the frontier of knowledge and humans decide where it should lead. Subscribe Share Leave a comment
Claude Fable 5 AI finds a tiny formula that topples an 87-year-old math conjecture
A mathematician working at Anthropic says he used the AI model Claude Fable 5 to uncover a remarkably simple counterexample to the Jacobian conjecture, a famous problem that has resisted mathematicians for more than a century. The result shows that the conjecture is false in three dimensions and above, although the original two-dimensional version remains unsolved.
Things ‘I do not like’ led me to quit US for Hong Kong, top mathematician says
The academic also says he is motivated by his vision to make Asia an intellectual powerhouse for science and learning.
‘I’m on a War Footing’: Terry Tao and the Crisis in Math
The Fields Medalist and celebrated mathematician is on the front lines of a debate about artificial intelligence and the future of his field.
Johns Hopkins cognitive scientist Shari Liu receives Packard Fellowship
The prestigious award recognizes early-career scientists, mathematicians, and engineers who are shaping the future of their fields
Book Review: The Mind-Boggling Science of Enormous Numbers
In "Huge Numbers," mathematician Richard Elwes spotlights some of the largest numbers humans have ever contemplated.
Mathematician Who Waited 50 Years for Proper Credit for Her Work Has Died
At the Los Alamos National Laboratory, Mary Tsingou Menzel’s computer programming helped set the stage for chaos theory and other fields.
The 92-Year-Old Mathematician and the Teenage Apprentice
Joan Birman thought her major discoveries were behind her. Then came an email from a young neighbor — a girl who knew little but wanted to learn.
Unsolved for 90 Years, OpenAI Says AI Cracked Millennium Prize Problem in 88 Hours
OpenAI says one of its AI systems has solved a math problem that has stumped mathematicians for nearly a century. The Navier–Stokes problem is one of seven Millennium Prize Problems, some of the toughest problems in mathematics, with a $1 million prize attached to each one. If OpenAI’s proof holds up, it would be a […]
Mathematicians Build Long-Awaited Graph Sandwich
The proof of a decades-old conjecture has given researchers a new way to understand complex networks.
Four Young Mathematicians Receive Prestigious Fields Medals
The awards are bestowed only once every four years to mathematicians under the age of 40.
Mathematicians prove perfectly fair elections are impossible
Mathematicians have shown that no electoral system can perfectly balance local representation, proportional national results, and a fixed-size parliament once enough parties compete. A newly proposed voting method could soften these unavoidable trade-offs and produce outcomes that are much closer to fair.
The AI Revolution in Math Has Arrived
AI is being used to prove new results at a rapid pace. Mathematicians think this is just the beginning.
Houston Ship Channel bridge honors Dr. Richard Tapia, National Medal of Science recipient
Harris County names Houston Ship Channel bridge after Dr. Richard Tapia, a pioneering mathematician who transformed STEM education nationwide.
Mathematicians Claim Significant Discovery Using ChatGPT
A 23-year-old has apparently found the solution to a famous difficult math conjecture called an Erdős problems by prompting ChatGPT.
OpenAI's big math breakthrough claim sparks drama
The math community is heated over questions about credit and AI training data after a mathematician's allegations against OpenAI went viral.
Mathematician debunks the Parthenon’s famous optical illusions
Some of the 2,500-year-old Greek building's architectural tricks are virtually nonexistent.
Top Mathematician Announces New Institute for A.I. Safety
Jacob Tsimerman, a recent recipient of the Fields Medal, believes that higher mathematics can help curb the dangers of runaway artificial intelligence.
UK mathematician debunks myth around Parthenon’s optical illusions
Study challenges belief that temple’s curves were designed to correct optical illusions that would have ruined its clean lines
Scientists used children’s ‘silly sprinklers’ to solve a physics problem Richard Feynman could not; the reverse version spins 50 times slower
If you’ve ever watched a “silly sprinkler” in action (those bright, looping contraptions that twist and spray water in wild patterns) you’ve probably just seen them as summer fun. But a group of mathematicians have turned these backyard toys into tools for solving a famous physics puzzle that stumped even Nobel Prize–winning physicist Richard Feynman.
After 80 Years, Mathematicians Give Famed ‘Erdős Method’ an Upgrade
Decades ago, Paul Erdős used randomness to illuminate the vast and weird world of networks. Now mathematicians are making his technique even more powerful.
Indian-origin mathematician Nalini Joshi named New South Wales’ Scientist of the Year | - The Times of India
Science News: Indian-origin mathematician Nalini Joshi has been named New South Wales’ Scientist of the Year, becoming the first mathematician to receive the state’.
'This is what happened with Claude and me': AI's failed attempt to crack the Riemann hypothesis led mathematician to a breakthrough
An attempt by Anthropic's Claude failed to prove the Riemann hypothesis, but it did produce something genuinely useful: inspiration.
Science history: Sophie Germain, first woman to win France's prestigious 'Grand Mathematics Prize' is snubbed when tickets to award ceremony are 'lost in the mail'
Sophie Germain was a brilliant, self-taught mathematician who won one of France's most prestigious prizes, yet she declined to attend the award ceremony because the committee members didn't respect her work.
Mathematicians Harness Randomness To Crack a 55-Year-Old Conjecture
After a long hiatus, the problem, which was likely inspired by juggling, has finally been resolved by a group of young mathematicians.