Saying that AI has ruined mathematics might still be underestimating AI.
Just now, OpenAI trained VPLiam Fedus in response to mathematicians such as Terence Tao, who argued that AI should not only pursue problem-solving but also advance mathematical understanding.
He agrees with Terence Tao’s emphasis on conceptual understanding, but also believes that today’s AI capabilities should not be used to limit future possibilities.
In Liam’s view, future AI will not only solve problems but also generate valuable insights and establish new conceptual frameworks for mathematicians to build upon.
In other words, if the AI’s training goal extends beyond merely “getting the right answer” to also explaining why, distilling methods, and helping humans understand, it could ultimately become a mathematical research partner that not only provides answers but also generates new insights.
This optimism shares both consensus and disagreement with the initial statement signed by 25 Fields Medalists, including Terence Tao.
Both parties agree that mathematics cannot be reduced to just the answer.
The difference is that mathematicians are more concerned that the current approach of AI companies chasing problem-solving benchmarks may harm the accumulation and transmission of mathematical knowledge; while Liam, within the AI industry, is more optimistic that as AI capabilities continue to improve, future AI systems themselves will be able to contribute to creating this knowledge.
This contrast between cold and hot also reminded netizens of Go in the past.
Although AlphaGo cannot explain its moves, human players still learned from studying its moves and win rates.
Liam also agrees with this analogy and cites Noam Brown’s previous observation: after AlphaGo, human chess players’ skills significantly improved, and a similar shift may occur in mathematics.
Is today's mathematics undergoing the same struggles that Go once experienced?
Has AI ruined mathematics?
On September 11, Terence Tao published "The Misalignment of Artificial Intelligence in Mathematics" on his personal blog.
This statement is co-signed by 25 Fields Medalists, spanning nearly half a century from Pierre Deligne, a 1978 Fields Medalist, to Yu Deng, a 2026 Fields Medalist, encompassing nearly all of the most distinguished scholars in modern mathematics.
The statement argues that current AI companies treat "solving famous mathematical problems" as a key metric for evaluating model capabilities, which represents a significant deviation from the mathematical community's goals of conceptual understanding, methodological refinement, and knowledge transmission—and may even harm the development of mathematics itself.
Specifically, they emphasized five key points:
Solving difficult problems is only one part of mathematical research. A more important goal of mathematics is to understand the underlying structures and to develop new concepts and methods that can be applied to other problems.
2. An answer must be understood before it can become shared knowledge. A discovery must also be discussed, simplified, and systematically organized before it can be included in textbooks and learned and used by future generations.
3. AI may rush to release results, potentially overlooking prior contributions. The lack of comprehensive论证, methodological clarification, and proper citations can lead to issues regarding attribution and plagiarism.
4. The process of cultivating students cannot be replaced by the final answer. Research training is not only about obtaining results, but also about teaching individuals how to understand problems, pose questions, and develop their own ideas.
5. AI has the potential to advance mathematics, but how it is used is crucial. The mathematics community must adapt to these changes, and AI companies must adjust their focus to ensure technological progress truly serves understanding and exploration.
These concerns have erupted today precisely because AI's ability to perform mathematics has begun to cross a new threshold.
In 2024, AI's representative breakthroughs in mathematics were still primarily focused on competition math, such as the IMO, gradually advancing from silver medal level toward gold medal level.
By 2025 to 2026, models began rapidly tackling genuine open mathematical problems, progressively taking on long-standing unsolved challenges such as the Erdős series, geometric conjectures, and the Millennium Problems.
In May of this year, an internal OpenAI model refuted the Erdős unit distance conjecture, which has stood for nearly 80 years. This problem in discrete geometry investigates: given n points in the plane, what is the maximum number of pairs of points that can be exactly distance 1 apart.
The model not only constructed infinitely many counterexamples but also introduced tools from algebraic number theory in its proof. The related results, after being reviewed by external mathematicians, have been called a "milestone in AI mathematics" by Fields Medalist Tim Gowers and others.
Furthermore, in early September, OpenAI announced that it had used approximately 10,000 autonomous AI agents in conjunction with internal advanced models to find a proof of singularities in the three-dimensional Navier–Stokes equations within about 88 hours, and verified it formally using Lean.
If this result is ultimately confirmed by the mathematical community, then AI will no longer be tackling merely “human-designed exam questions,” but will instead begin to enter the very frontiers of research that have puzzled mathematicians for decades—some even classified as Millennium Prize Problems.
But as AI becomes increasingly like a true "mathematical researcher," new questions arise.
Who should be credited for the results? Who should be listed as an author? And how did the model learn about this research direction?
In early September, New York University mathematics professor Tristan Buckmaster and Anthropic mathematician Levent Alpöge publicly presented a study on singularities in fluid equations, and OpenAI announced nearly simultaneously that its internal model had also completed the corresponding proof with the collaboration of approximately 10,000 AI agents.
Controversy quickly erupted. Buckmaster suspected that OpenAI began working on the problem only after learning about their unpublished research directions, leading to disputes between the two parties over authorship, priority, and whether the model might have accessed relevant user data.
At this point, the issue circles back to where Liam initially responded to Terence Tao.
Liam believes that as the boundaries of AI capabilities continue to expand, "solving a problem" and "providing humans with new ways of thinking" will ultimately not be contradictory.
Future AI could very well be responsible not only for finding answers but also for establishing a conceptual framework that humans can understand, reuse, and further develop.
However, the issue is that even if AI has the ability to generate insights in the future, it cannot automatically answer how research should be organized today to ensure those insights are understood and utilized.
When AI begins to genuinely participate in knowledge creation, how should this knowledge be generated, attributed, understood, and integrated into humanity’s existing academic community?
The answer is far from settled. However, recent statements from several major mathematical institutions have begun to address these issues individually.
The American Mathematical Society (AMS) emphasizes that this latest progress on the singularity problem of the Navier–Stokes equations was not an isolated breakthrough achieved by AI alone; it builds on decades of cumulative work by generations of mathematicians including Navier, Stokes, Leray, and more recently Córdoba, Martínez-Zoroa, Buckmaster, and Alpöge.
AMS also clearly stated: The purpose of mathematics is human understanding.
The London Mathematical Society (LMS) further clarified the position of AI.
The London Mathematical Society (LMS) positions AI as a powerful new tool: it can accelerate exploration and discovery, but posing questions, creating new concepts, and forming genuine mathematical understanding remain human endeavors.
The Clay Mathematics Institute (CMI), which is actually responsible for awarding the Millennium Prize, responded to a more practical issue:
How can the results provided by AI be formally incorporated into the body of mathematical knowledge?
Regarding the new proof of the Navier–Stokes equations, the Clay Mathematics Institute has not directly confirmed its validity, maintaining a highly cautious stance: the result still requires public scrutiny, peer review, and long-term validation.
At the same time, CMI also reiterates that the value of major mathematical problems has never been limited to the final answer alone, but also includes the new ideas, methods, and theoretical tools developed during the problem-solving process.
So, the real question worth exploring in the future is not “Did AI destroy mathematics?” but rather, how the human mathematical community can ensure that newly generated knowledge produced by machines is understood, verified, and truly integrated into mathematics once AI begins participating in knowledge creation.
Liam's answer addressed the future, but what may be more important is the present.
Reference link
[1]https://x.com/LiamFedus/status/2099123244640989213
This article is from the WeChat public account "Quantum Bit," authored by: Focused on Frontier Technologies