Fields Medalist Yu Deng: Human Researchers Must Remain at the Centre of Mathematics in the Age of AI
As artificial intelligence advances at an unprecedented pace, the mathematical community is facing an unprecedented period of uncertainty and debate. On 25 October 2026, Fields Medalist and Professor in the Department of Mathematics at the University of Chicago, Yu Deng, delivered an online keynote address at a forum jointly organised by The Intellectual and Science Salon. In his speech, he presented a comprehensive perspective on the future of mathematical research in the age of AI.
In Professor Deng's view, AI can help mathematicians explore ideas and handle technical details, but it cannot replace independent human thinking. Commenting on the large number of mathematical proofs recently announced by an AI company, he argued that the development of AI should be guided by academic standards. Researchers should retain control over how their data are used, and transparent mechanisms should be established to trace and attribute individual contributions.
Looking ahead, Professor Deng believes that AI could strengthen connections between different branches of mathematics and help mathematical research address real-world problems more effectively. However powerful AI may become, he emphasised that human researchers must always remain at the centre of mathematical inquiry.
The following is the full text of Professor Deng's speech. Some editorial revisions and abridgements have been made for readability.
Professor Yu Deng's Speech: Mathematics and Research in the Age of AI
Hello, everyone. It is a great pleasure to be invited to this forum on AI and mathematics organised by The Intellectual.
The mathematical community has experienced quite a turbulent period recently. There are many different opinions about the future of mathematical research and the role of mathematicians in the age of AI. I would like to take this opportunity to share some of my personal views and thoughts about what lies ahead.
My talk today has two main parts.
Part I: AI, Mathematical Research and Academic Standards
The Recent Wave of AI-Generated Mathematical Results
First, I would like to discuss the announcement made by an AI company on 6 October, involving more than 300 mathematical problems and over 700 papers.
About a month earlier, the same company had also announced a proof concerning a bubble construction for the forced Navier–Stokes equations, a problem related to one of the Millennium Prize Problems. These developments have had a significant impact on the mathematical community and have arguably triggered the recent widespread debate about mathematical research and the role of mathematicians.
I have looked through several of these papers. From my understanding, a considerable proportion of the work represents significant mathematical progress.
Most of these results build on deep existing human understanding and established mathematical techniques. AI has either combined techniques from different areas and fields in clever ways, or developed new techniques and approaches based on existing human ideas and lines of reasoning. In this way, it has helped solve problems that were previously difficult to tackle.
Some of the work, however, appears to follow existing human approaches quite directly. More than one mathematician has pointed out that ideas and approaches they had previously provided to AI models appeared, sometimes just a few weeks later, in the company's latest releases in remarkably similar forms, including very similar proof strategies.
This brings us to two major advantages that AI has over individual human researchers.
The first is its breadth of knowledge. Human researchers have limited time and energy. No individual can develop a deep understanding of every field and technique in modern mathematics. AI, however, can learn from or distil the vast body of mathematical literature available online, potentially gaining access to knowledge across a much wider range of mathematical disciplines.
The second advantage is the extremely low cost of experimentation and trial and error. When a mathematician pursues an approach for several months only to discover that it does not work, that time and effort cannot easily be recovered. AI systems, by contrast, can deploy thousands or even tens of thousands of agents to explore different approaches and test possibilities efficiently. If humans try to compete with AI purely in terms of speed, there is little chance of winning.
However, there is one principle we must uphold: in mathematical research, as in every other endeavour, human beings must remain the principal actors. AI is a tool that we use to conduct research.
This is the fundamental premise for everything I will discuss next. We must remain human-centred and use AI as a tool to advance our own research and pursue the questions that genuinely interest us.
Under this premise, humans are responsible for setting the direction. We can use AI to conduct numerous experiments and explore different possibilities.
For example, once we have an initial idea, we need to turn it into a concrete roadmap. Every step along that roadmap requires extensive consideration of technical details. If the approach does not work, certain steps or intermediate stages may need to be adjusted. AI can help with all of this, including the technical details.
Another important aspect is that AI can generate new ideas by combining approaches and techniques from different fields. We can, of course, learn from these ideas as well.
In the short term, I believe we will see a process of mutual development between humans and AI. Based on human understanding of a problem, AI may develop new techniques and new ways of approaching it, thereby solving further problems. We can then study AI-generated proofs and develop new ideas and approaches of our own. We can feed these ideas back into AI systems, learn from their subsequent developments, and continue this cycle.
It is a process of mutual learning and mutual advancement.
In this sense, the emergence of these papers is itself a significant contribution to mathematical research. They demonstrate the value of AI and its potential to benefit human researchers. Clearly, there is no reason for us to reject such tools when they can help advance our research.
However, tools must be used properly and responsibly.
1. If AI Is Treated as a Researcher, It Should Follow Academic Standards
This brings me back to the problems and papers announced on 6 October.
I believe these developments have the potential to advance mathematics considerably. However, two separate questions need to be considered: What role did the AI company play in the process, and were its actions appropriate? Could it have made better choices?
I believe these two questions should be evaluated independently.
Let us consider an analogy.
Many people regard an AI model as a virtual researcher. It learns from academic literature available online, develops ideas about mathematical problems, conducts original research and produces results.
If we evaluate AI according to this model, then we should also apply the standards of the academic community. If we treat an AI system as a researcher publishing research results, it should be subject to the same academic expectations.
There are several important standards to consider.
First, when a researcher obtains a significant result, the mathematical community will invite them to give presentations at different levels of detail. The main purpose is to explain how the proof was developed and what ideas and reasoning lie behind it.
An AI system may not be able to give a presentation in the same way as a human researcher, but it can provide explanations. In this context, the reasoning process behind an AI-generated proof is represented by its chain of thought.
If an AI system proves a major mathematical result, it is reasonable to ask the company to disclose the AI's chain of thought. Yet this particular company has been unwilling to do so. Among all the proofs it released, only a very small number included the actual chain of thought. In most cases, the company refused to disclose the reasoning process and related information, citing concerns about distillation.
I think this is a straightforward issue. For a human researcher, one of the first questions people would ask is: How did you arrive at this idea? What approaches did you try along the way?
The company's refusal to disclose this information clearly departs from established academic practices.
As for the concern about model distillation, many people have already made this point: an AI company cannot freely distil the entire body of human knowledge and academic literature from the internet, but then refuse to share its own reasoning because it assumes others might use that information to distil its model.
People are not necessarily trying to distil the model. They simply want to understand its reasoning process.
I do not think this is a particularly reasonable justification.
Second, human researchers have a responsibility to acknowledge the ideas and contributions of others. If a researcher has used another person's approach, especially if an entire proof closely follows someone else's reasoning, they should clearly state this and explain the extent to which their work builds on or depends on that person's ideas.
Even when only certain parts of another researcher's approach are used, proper acknowledgement is necessary.
Similarly, in many of the papers released by this AI company, I did not see sufficient acknowledgement of previous human contributions. In some cases, existing human approaches appeared to have been followed directly without appropriate attribution.
Finally, human researchers are expected to verify the correctness of their proofs before publication.
For an AI company, formal verification could be used to check the correctness of mathematical proofs before releasing them. Yet this was not done consistently. Instead, the company published the results without providing any guarantee of correctness. Subsequent reviews revealed errors in multiple papers, and some were eventually withdrawn.
Taken together, these issues suggest that the company's conduct in the specific 6 October announcement raises legitimate questions from the perspective of academic standards.
2. From a Commercial Perspective, What Do Mathematicians Gain?
Some may argue that the company is a commercial business and therefore does not necessarily have to follow academic conventions.
But looking at the situation from a commercial perspective raises another interesting question.
A commercial company provides a product, and mathematicians are its customers. We pay to use your product and input our ideas and research approaches into it. You then use the ideas we provide to train your next-generation products, which go on to solve open mathematical problems and receive all the recognition.
As users, what do we get in return?
Nothing.
If we receive nothing, why should we pay so much for your product?
I believe this arrangement raises questions from a commercial standpoint as well.
3. How Should Mathematicians Use AI Responsibly?
My position is that we should certainly not reject AI in mathematical research. Instead, we should make use of these tools, but only in appropriate ways.
What, then, constitutes appropriate use? I would like to highlight several principles.
First, AI should be used as a tool by mathematicians. In fact, users do not necessarily have to be professional mathematicians; even mathematics enthusiasts can use these tools. The essential point is that users should be the ones using the tools. AI companies, as providers of these tools, should not step in and conduct the research themselves on behalf of users.
Second, users should have the ability to choose, or at least be able to make that choice easily: whether the data and ideas they input into an AI system can be used for model training. I believe this choice should belong to the users.
Third, we need traceability.
For example, suppose Researcher A provides an AI system with certain ideas and approaches. The AI learns from these contributions. Later, when Researcher B asks the AI a question, the system uses those ideas to develop a proof.
In such a situation, it should be possible to trace the origin of the contribution. If Researcher B publishes a paper based on the proof, the underlying ideas should be traceable to the original input provided by Researcher A.
I believe this would not only help prevent disputes over research priority, but also make it possible to distinguish precisely which contributions came from AI, which came from human researchers, and which came from particular individuals.
This is especially important in the short term, during the transitional period when the mathematical community is beginning to adopt AI widely.
I understand that several groups are already working to address these issues, including through the development of open-source mathematical models.
I believe open-source models could help ensure that the mathematical community has access to models of its own, rather than having to depend entirely on commercial AI companies. Their use could also follow academic standards, including rules governing data usage, disclosure of reasoning processes and traceability.
Of course, current open-source models still lag considerably behind the most powerful commercial models in mathematical capabilities. We can work to narrow this gap through further training and development.
For the mathematical community as a whole, however, there is no need to insist on having access to the very latest tools at all times. Would it make a substantial difference if we obtained a tool with a certain level of capability six months earlier or later? I am not convinced that it would.
After all, I believe that humans will remain at the centre of mathematical research, and that human researchers will continue to play an irreplaceable role. In many cases, the difference lies not only in the tools available, but also in the people using them.
That concludes the first part of my talk.
Part II: The Future of Mathematical Research in the Age of AI
Humans Will Continue to Set the Direction of Mathematical Research
The second part concerns the future of mathematical research.
AI's mathematical capabilities are continuing to improve at a remarkable pace, and we can expect rapid changes in the short term.
Looking further ahead, suppose AI becomes so powerful that it can independently solve extremely difficult mathematical problems. What will mathematical research look like then? What role will mathematicians play?
First and foremost, one point is crucial: mathematical research must always remain human-centred.
AI may be able to solve problems, but humans can at least formulate the questions and guide AI towards the directions and applications that matter. We can provide the direction.
Of course, some people may argue that AI can also formulate its own questions and decide which directions to pursue.
That may be true. But let us return to the fundamental question.
AI is like a car. We drive the car, set its destination and determine the direction in which it should travel. The car may be capable of autonomous driving and could travel a very long distance on its own. But if we are not in the car, what does that journey mean to us?
AI may be able to generate its own questions, but I see no reason to assume that the questions it independently generates will necessarily be the ones that interest us as human beings.
AI may develop many things autonomously, but that does not automatically make them relevant to us. What we want to understand and discover are the questions that matter to us.
In this sense, human initiative and agency remain essential.
We can guide AI by formulating questions, proposing approaches and contributing ideas. AI can then help us carry out extensive experimentation, explore different possibilities and handle technical details. We can use the results as a foundation for further exploration.
Throughout this process, the role of human researchers is unquestionably irreplaceable.
How Strong AI Could Bring Different Branches of Mathematics Closer Together
If we broaden this perspective from individual research problems to the mathematical community as a whole, I believe the development of powerful AI will have two major positive effects.
At present, mathematics faces several objective challenges. Two of the most significant are the growing distance between different branches of mathematics and the increasing disconnect between mathematics and the real world.
First, different branches of mathematics are becoming increasingly specialised and isolated from one another.
Number theorists may find it difficult to understand the work of analysts, while analysts may struggle to follow the technical details of algebraic research. When attending a talk outside their own fields, mathematicians may be able to grasp the general idea but find it very difficult to understand the specific techniques involved.
Second, mathematics sometimes appears to be becoming increasingly distant from real-world problems.
Research into real-world problems is often extremely complex and may exceed the technical capabilities currently available to mathematicians. As a result, researchers frequently focus on mathematical models. Once they begin working on a particular model, however, they may become so specialised in the model itself that they lose sight of its original real-world context, whether in physics, engineering or other fields.
Some people may attribute these issues to the mathematical community, as though mathematicians have done something wrong. I think this is entirely unfair.
Mathematics expanded enormously and developed rapidly throughout the 20th century. Science also experienced tremendous growth during the same period.
It is somewhat like the expansion of the universe: as the universe expands, the distance between two fixed points increases. Mathematics has undergone a similar process.
As different areas of mathematics advance towards increasingly specialised frontiers, no individual can reasonably be expected to understand the details of every field. At most, one can develop a broad, general understanding of other areas.
This is an objective reality, not a failure of the mathematical community.
Likewise, scientific research made enormous progress during the 20th century. The mathematical problems arising from real-world applications have become increasingly difficult. The development of rigorous mathematical proofs has inevitably lagged behind advances in science, including physics and other disciplines.
I would like to emphasise that the development of AI, particularly powerful AI systems, could help us address these challenges.
AI Could Help Mathematicians Tackle More Complex Real-World Problems
Let me give an example from my own research in partial differential equations (PDEs).
Many PDEs originate from real-world phenomena, but their structures can be so complex that human researchers cannot tackle them directly using conventional approaches.
We often begin by studying simplified models and developing mathematical techniques for them. When we try to extend these approaches to more realistic problems, however, we encounter numerous technical difficulties.
My own work on the derivation of the Boltzmann equation provides an example. The simplest case involves a hard-sphere model. Once we extend the analysis to more realistic models involving interaction potentials, we encounter many additional technical challenges.
With AI, we may be able to delegate some of these technical difficulties to AI systems, allowing us to focus on the global picture and the broader mathematical framework.
For example, once we have established a result for the hard-sphere model, AI might help extend it to more general interaction potentials. Human researchers could then move on to deeper questions, such as how scaling laws compare across different models, or what happens when we study the Landau equation instead of the Boltzmann equation.
By freeing ourselves from tedious technical details, we can devote more attention to deeper mathematical questions, including more complex problems that are closely connected to the real world.
AI Could Strengthen Connections Across Mathematical Disciplines
The second potential benefit concerns the distance between different branches of mathematics.
As individuals, we often cannot master the technical details of every mathematical discipline. With AI, however, we may be able to draw on ideas and methods from other fields without having to understand every technical detail ourselves.
AI is already doing something along these lines: combining approaches and techniques from different disciplines to solve problems.
Naturally, we can learn from this as well.
I believe the emergence of powerful AI will make connections between different branches of mathematics increasingly close. It will also strengthen the relationship between mathematics and real-world applications.
Mathematics Will Retain Its Independence
However, bringing mathematics closer to real-world problems does not mean that mathematics or mathematicians will become subordinate to physics, biology or other disciplines.
Some people even suggest that pure mathematics may disappear and that mathematicians may eventually be absorbed into other academic departments. I think this is entirely unlikely.
Even in the 19th century, many mathematical problems originated directly from research in physics and engineering. Yet mathematicians remained mathematicians. They continued to work on mathematical problems and solve mathematical equations.
Even when mathematics draws inspiration from applications and real-world challenges, it retains its own independence, distinctive ways of thinking and unique perspectives. It cannot simply be absorbed into other disciplines.
Physicists and mathematicians often approach problems differently. Both ways of thinking are valuable and necessary in physics research and mathematical physics.
Mathematics Is an Integrated Whole
What, then, will happen to areas of mathematics that do not have an obvious or direct connection to the real world?
The answer is simple: mathematics is an integrated whole.
As I mentioned earlier, different branches of mathematics are theoretically interconnected. We cannot focus exclusively on the areas that have immediate practical applications while ignoring those that do not appear to have direct uses.
Mathematics is a whole, and we cannot abandon one part of it in order to develop another.
I firmly believe that mathematical research will continue to exist, and mathematicians will continue to pursue it. Human initiative and independent thinking are absolutely indispensable to mathematical research.
Independent Thinking Is What Makes Us Human
Finally, I would like to take an even broader perspective.
From the standpoint of humanity, what is our most distinctive quality as human beings?
I believe it is our ability to think.
There is a famous phrase, which I believe comes from Blaise Pascal: “Man is but a thinking reed.”
The emphasis here is on thinking. What distinguishes human beings from other animals is our ability to think independently, explore ideas and pursue questions through our own initiative.
We may assume that AI will become extremely powerful and capable of answering an enormous range of questions. But AI cannot replace our own capacity for independent thought.
If we give up our ability to think independently simply because AI is available, I believe we will be no different from animals.
Of course, some people may feel that there is nothing wrong with becoming entirely dependent on AI. If that is their position, I have little more to say on the matter.
But if humanity is to preserve its capacity for independent thinking and exploration, then mathematics will remain essential, whether or not AI exists.
Mathematics is one of the key disciplines through which humanity tests and expresses its ability to think independently and explore the unknown. Other sciences, including physics and biology, play important roles too. But in a certain sense, mathematics may be the purest discipline for expressing this uniquely human capacity.
For this reason, I firmly believe that mathematics will not disappear in the age of AI. If it ever did, I think it would represent a profound loss for humanity as a whole.
Thank you very much.
