Li Jianshu and Wang Jian on AI and Mathematics: From an Excess of Answers to Two-Way Empowerment

In recent years, AI's capabilities in mathematics have advanced at an accelerating pace. It is no longer confined to assisting with computation and theorem proving; it has begun to be applied to research-grade mathematics, participating in conjecture exploration and proof construction, and even tackling mathematical problems that humans had left unsolved for decades. In May of this year, a Google DeepMind AI agent solved 9 previously unsolved Erdős problems and simultaneously cracked 44 open mathematical conjectures. Recently, OpenAI published 722 mathematical manuscripts generated by its internal AI models all at once on GitHub, covering number theory, algebraic geometry, theoretical computer science and other frontier fields, sparking heated discussion about AI's impact on mathematical research.

The mathematics community is not taking this lying down. Terence Tao, Deng Yu and 25 other Fields Medalists jointly published an open letter warning of a "serious misalignment" emerging between AI and mathematics; the Human Mathematics Association, for its part, called on mathematicians worldwide to stop collaborating with OpenAI.

On one side are "results" produced in bulk; on the other, a mathematics community saying "no." This "conflict" forces one to ask: what does mathematics truly care about—the answer or the process? Does a proof that passes verification but that no one can explain the reasoning behind count as a gain for mathematics? As AI breaks into mathematics, is the relationship between the two one of replacement, superposition, or mutual fulfillment? In the entanglement between AI and mathematics, what roles should mathematicians and AI engineers play? Around these questions, the reporter interviewed Li Jianshu, an academician of the Chinese Academy of Sciences and director of the Institute for Advanced Study in Mathematics at Zhejiang University, and Wang Jian, an academician of the Chinese Academy of Engineering and director of Zhijiang Laboratory.

AI is bringing science into an era of "answer surplus." In fields such as materials, drugs and the life sciences, generative models can throw out candidate structures and hypotheses on the order of a million at a time, while the pace of experimental verification has barely moved—some scholars call this gap the "verification scissors gap." Generation is getting cheaper and cheaper, while verification is getting more and more expensive, and the center of gravity of scientific discovery is shifting from "proposing hypotheses" to "judgment and verification." Mathematics faces the same problem in this upheaval: AI can "solve" mathematical problems and even judge whether a conclusion is correct, but it cannot explain clearly why it is correct.

Li Jianshu: Different people may have different views on AI's impact on mathematical research. For an individual mathematician, if a mathematical problem he has spent 10 years researching is suddenly solved by AI, a sense of loss is quite normal. But looking at the future of mathematics as a whole, not only would I not feel a sense of loss—I would be extremely excited. Because it means an exciting new era of mathematics is about to arrive.

Take the invention of calculus in the history of mathematics as an example. Before calculus appeared, mathematicians' work calculating curve lengths, surface areas and volumes of geometric solids was enough to fill research papers. After calculus was invented, this work became undergraduate homework. But mathematics and mathematicians did not disappear as a result; instead they were "empowered," and this gave rise to modern mathematical directions such as differential geometry, harmonic analysis, analytic number theory and differential equations—the entire landscape of mathematics was changed.

Li Jianshu: In traditional mathematical research, when a mathematician claims to have proved something, that in itself proves nothing; only after verification can it be acknowledged that he has indeed proved it. For example, since my university days I have received countless proofs of Goldbach's conjecture, but one certainly cannot believe that he has proved it just because he claims to have done so. However, I believe that among those difficult problems, AI may indeed have completed part of the proof for at least some of them—it is just that we still need to understand and check its proof process.

Wang Jian: Indeed, mathematicians are the group that earliest emphasized the importance of "asking questions," especially "asking original questions." AI's intervention has suddenly given so many difficult mathematical problems "answers." Setting aside for the moment whether these "answers" can pass verification, I believe that solving these problems will in fact spur humanity to pose more original questions. "Questions" will never run dry, and humanity may thereby have the opportunity to discover more valuable questions.

Science history has repeatedly staged the same script: a discipline builds a tool, and the tool in turn reshapes the discipline. The telescope turned astronomy from naked-eye recording into precise measurement, and also forced optics and precision manufacturing to advance together. Today it is the turn of AI and mathematics—except that this time, engineering has run ahead of theory: why scaling laws, generalization and long-chain reasoning in models hold is still lacking a rigorous explanation; in some high-risk scenarios, a model may "get the answer right by luck while taking the wrong path." What is more worth discussing is that at present AI's participation in scientific research is mainly prediction, but what science truly needs is not only prediction but attribution. Moving from correlation to causality cannot be solved by piling up data; it must rely on the reconstruction of mathematics and other disciplinary frameworks. In this process, what can AI and mathematics do for each other?

Reporter: AI has brought enormous impact to mathematical research. To evaluate this impact, it may be necessary for us to trace back to the roots of mathematics. What exactly is the purpose of studying mathematics? Will the emergence of AI change the paradigm of mathematical research, or merely speed up the existing pace?

Li Jianshu: Mathematics has many difficult problems and conjectures, like one mountain peak after another. Conquering a difficult problem or conjecture is like climbing to the summit, and this process itself is a great achievement. But the purpose of mathematical research is not only to conquer difficult problems and climb to the summit; more importantly, it is to see more beautiful scenery after reaching the summit and to discover more mathematics. The paradigm of mathematical research may change because of this. The emergence of AI makes this possibility greater.

With Hilbert as a landmark, the great mathematicians before the early 20th century were often polymaths versed in knowledge across all fields of mathematics. But after the early 20th century, the disciplinary system of mathematics grew ever more vast, to the point that no single mathematician could master every direction and branch of mathematics. And the greatest strength of AI is its ability to integrate interdisciplinary knowledge; with this ability, the mathematics community may be able to carry out a new integration and simplification of the vast and fragmented discipline of mathematics, thereby deepening the understanding of and insight into mathematical problems. As the great mathematician Hua Luogeng said, in reading one should go from the thin to the thick, and then from the thick to the thin; the more thoroughly one understands, the more one has a sense of thinness. Based on a renewed understanding of mathematical problems, can the mathematics community develop new mathematics? This idea is especially exciting.

Wang Jian: I do not specialize in mathematical research. In my understanding, algebra and geometry are two completely different specialties, but with the Cartesian coordinate system as a "bridge," they became thoroughly integrated. In recent years, AI has not only become more powerful; it has also undergone a profound transformation itself, namely that the methodology of large models has achieved unification. In other words, AI now has its own "Cartesian coordinate system," which gives AI the ability to break down disciplinary boundaries and integrate knowledge from different fields. Therefore, the deep integration of AI and mathematics may indeed change the paradigm of mathematical research.

Wang Jian: The reasoning ability that AI models can learn directly from text is very limited; today's reasoning ability comes mainly from the contribution of code. Today's AI looks powerful, but the reasoning ability that large models gain from code is not ultimate. Why? Because code, as a key data source, differs qualitatively from the data sources of the entire field of mathematics in the support it can provide for stronger models. We can imagine that when AI learns deeper reasoning abilities from data in the field of mathematics, it will not only greatly benefit AI's own development but also further expand its impact on other scientific fields.

Li Jianshu: People often talk about "AI for Science," but rarely mention "Science for AI" or "Math for AI." At present, the development of AI relies mainly on engineering practice and old mathematical theories. What exactly is the underlying mechanism of AI? Are there more efficient algorithms to optimize it? What new fundamental mathematical research could bring revolutionary change to AI? This is a major task facing the mathematics community. To be realistic, mathematics has done far from enough for AI. I believe that in the future more world-class mathematicians will care about and study AI. If the mathematical foundations of AI can be supported by new theories, then the improvement of AI capabilities will rely not only on computing power and electricity but also on the sustained investment of "brainpower."

From two-way empowerment to open cooperation, what can we do?

Mathematics is the foundation of all science and technology and plays a unique role. Today, people expect AI to also become such a foundational force, driving changes in the research paradigm and accelerating the process of scientific discovery. For AI to truly become part of the infrastructure of science, technology alone is not enough; an open and trustworthy order is also needed. But order is never generated automatically by technology; it is established by people and guarded by people—who should participate in this reshaping of order? How can countless individuals from different institutions and different disciplines be organized? Once order is truly established, how will it affect the people within it?

Reporter: In the face of a completely new era, how should we respond?

Li Jianshu: We need to create a fully open innovation and cooperation mechanism and establish an "AI + Mathematics" innovation community, so that research institutions focused on AI innovation, professional mathematics research institutions and teams, private enterprises full of innovative vitality and practical capability, and individuals who love mathematics and AI can all participate and jointly explore new paths for the deep integration of mathematical research and AI, promoting basic research and the development of the scientific frontier.

This also brings up another level of thinking: what kind of mathematicians will be needed in the future? I believe that the kind of work that improves on the research of predecessors can be handed over to AI. Mathematicians should, with the help of AI, carry out higher-level mathematical thinking and give play to their individual original value. From this perspective, the demand for first-class mathematicians will greatly increase in the future. Correspondingly, mathematics teaching and the growth of mathematicians will also undergo fundamental changes—curriculum design, teaching paradigms, training programs... far too much work needs to be completed by our generation.

Wang Jian: In fact, AI does not cooperate with a particular discipline; it cooperates with scientists and ultimately solves practical problems for humanity. Therefore, there should not only be "AI for Science" but also "AI for Scientist," and ultimately "AI for Humanity" and "Science for Humanity." Objectively, this requires an open mechanism that does not belong to any one person, so that AI and mathematics can better serve all disciplines and all people.

Li Jianshu: This may be a proposition that requires continuous exploration. At present, the Institute for Advanced Study in Mathematics of Zhejiang University and Zhijiang Laboratory have jointly launched the "Future Mathematics Program," taking the first step of a "long march of ten thousand li."

The program will focus on the two-way empowerment of AI and mathematics and carry out open innovation in four key areas: first, develop foundational mathematical models, enabling models to integrate knowledge from various branches of mathematics while promoting mathematical reasoning ability as an underlying capability of foundational scientific models; second, conduct research on formal verification, making AI-generated mathematical content verifiable, accumulable, and reusable, providing support for reliable mathematical reasoning and exploration of frontier problems; third, study the mathematical mechanisms behind AI, exploring how to explain from first principles key issues such as learning, generalization, and long-chain reasoning in AI models, and using new theories to drive the development of the AI frontier; fourth, promote the empowerment of other disciplines by foundational mathematical capabilities, exploring how to better integrate mathematical theory into interdisciplinary scientific research and provide support for the entire basic disciplinary system.

Wang Jian: The "Future Mathematics Program" aims to build a mutually reinforcing research system: on the one hand, using AI to expand the capabilities of mathematical research; on the other hand, probing from a mathematical perspective the boundaries of AI's capabilities and its theoretical foundations, and promoting scientific research to improve its ability to solve problems from the source and at the fundamental level.

(Reporters Zhang Xiaohua and Lu Jian of our newspaper)