Wen/Chen Yongwei

On July 23rd, the Fields Medal for 2026 was announced. While domestic media is focusing on the two Chinese mathematicians Wang Hong and Deng Yu who won awards this year, another winner - Canadian mathematician Jacob Zimmerman - has quietly captured the headlines of foreign technology media. At the press conference after the award ceremony, Zimmerman solemnly announced that he would join OpenAI in August and shift his research focus from pure mathematics to AI security research. On the day of the highest award in the field of mathematics, a young mathematician at the peak of his career has decided to switch careers to AI, which is truly explosive news.

Speaking of Zimmerman, he is also a complete outlier in the field of mathematics. He has extremely high talent and is very good at "bridging" between different mathematical fields to achieve dimensionality reduction. For example, he once transformed the highly logical o-minimization method into powerful tools in arithmetic geometry and complex algebraic geometry, and used them to solve a series of mathematical problems including the Andr é - Olt conjecture. However, it is such a mathematician with outstanding achievements who has been singing the praises of mathematics since the emergence of ChatGPT in 2022, believing that within a few years, AI will replace most of the work of mathematicians. With this belief in mind, he has refused to guide graduate students since 2023. Even in his own research, he no longer personally proves it, but is only responsible for proposing some big ideas and then handing them over to AI to complete the remaining details. In 2025, he published a paper titled 'A Taxonomy of Possible AI Existential Catastrophe Scenarios', which systematically sorted out the various paths that AI could lead to human extinction, thus officially entering the field of AI security. From this perspective, his career transition statement at the Philippine Awards ceremony is actually just an official announcement of his career path transition.

It is worth noting that in the field of mathematics, Zimmerman is not the only one who believes that the development of AI may pose a "threat" to mathematics. For example, in 2006, Fields Medal winner Tao Zhexuan believed that the arrival of AI is ushering mathematics into a turbulent period, and its values and practical foundations will be challenged. In 1998, Fields Medal winner William Timothy Gowers also believed that large language models would not only soon surpass humans in all aspects of mathematical problem solving, but could also independently propose problems, construct theories, and formulate definitions.

From a practical perspective, the achievements of AI in the field of mathematics over the past year seem to confirm their viewpoint: in October 2025, UCLA mathematicians used GPT to overcome the long-standing optimization problem of the Nesterov conjecture; In January 2026, DeepMind's AlphaEvolve model discovered high-dimensional hypercube structures in permutation groups that had not been found for 50 years, thus solving open problems in combinatorial group theory; On May 20, 2026, OpenAI's universal inference model independently falsified the Erd ö sh plane unit distance conjecture that had been suspended for 80 years, and the results were verified by 9 top mathematicians; The next day (May 21st), DeepMind released AlphaProof Nexus, which fully proved 9 open questions proposed by Eldesh and simultaneously proved 44 conjectures about OEIS integer sequences; On July 20, 2026, Anthropic Fable 5 assisted mathematicians in finding a concise counterexample to the Jacobian Conjecture, overturning the century old unsolved core of algebraic geometry... It should not be an exaggeration to describe AI's performance in the field of mathematics as "insane".

So, why can AI achieve such impressive performance in the field of mathematics? Besides helping people solve more mathematical problems, what changes will AI bring to mathematics? Will it really kill mathematics? What impact will this have on the way humans understand the world? Let's talk about all of the above slowly.

1、 AI: Not just 'faster calculation'

When it comes to the advantages of AI in the field of mathematics, many people's first reaction is that it can "calculate quickly and remember more". Although this view cannot be miscalculated, it greatly underestimates the capabilities of AI. Just as the steam engine is not just a faster horse, the Internet is not just a faster post office, and AI is not just a faster calculator. The reason why it can achieve such significant achievements in mathematics is largely because it possesses an intelligence different from that of humans.

Firstly, AI has a much higher ability to simultaneously apply interdisciplinary knowledge than humans. Modern mathematics has become a highly specialized discipline, with clear barriers between its various branches. A top mathematician may be proficient in a branch of number theory, but only maintain a general understanding of random matrices, dynamical systems, or computational complexity. In contrast, AI does not have the same sense of boundaries as anthropologists.It not only has encyclopedic memory, but also can simultaneously import knowledge of number theory, geometry, combinatorics, probability, optimization, and computer science in a single search, and perform large-scale reorganization of these knowledge. In this way, AI has turned the cross disciplinary connections that anthropologists can only establish through occasional conversations and communications into a daily search method, making it easy to "cross boundaries" to find inspiration.

Secondly, AI possesses parallel exploration capabilities that are unmatched by humans. Mathematicians, when studying a difficult problem, often feel like walking alone in a maze - they may keep a few backup routes in their minds, but usually only one or two can truly delve deeper. If he walks along a route for half a year only to realize that it is a dead end, then for him, the loss is not only time, but also attention and confidence. But AI is different. It can simultaneously send out hundreds or even thousands of 'clones' to try different routes. In this way, not only does the probability of finding the correct path increase significantly, but the failed routes will not be wasted, and can be entered into the database to inform subsequent models which paths are no longer feasible.

Thirdly, AI has a much higher tolerance for boredom and ugliness than anthropologists. In popular science literature, the discovery of mathematics is often described as a product of mathematicians' sudden inspiration, but in reality, it is more of an artistic beautification. In the daily process of mathematical research, it is mostly dry repetition and "ugly" formula derivation. Indeed, mathematicians' aesthetics have driven many great discoveries, but such aesthetics may also form biases. People prefer concise, symmetrical, and familiar objects, which often leads to the deliberate neglect of routes that require excessive classification discussions, lengthy calculations, or a temporary inability to see beautiful structures. But AI is different. It will not lose patience because a proof is not elegant enough, nor will it worry about a study not meeting mainstream tastes, but will honestly continue to search in high-dimensional space, extreme parameters, and rare objects.

Fourthly, AI has a stronger ability to compress different research processes into closed loops than anthropologists. In traditional research, searching for literature, performing calculations, proposing hypotheses, finding counterexamples, and writing proofs are often scattered across different tools and time periods. AI can complete multiple rounds of loops in a short amount of time: first find relevant theorems from the paper library, and then write programs to check finite cases. Once an anomaly is detected, modify the hypothesis. Subsequently, the formal proof system is called to verify the key steps. If it fails, it can still go back to the previous stage and reorganize the problem.

Fifthly, AI has excellent replicability. Once an AI model learns a proof strategy, it can be replicated in countless instances; And if an AI discovers a new route on a certain project, or finds that a certain route is not working, it can immediately synchronize this information with other AI, making this information the common experience of the entire system. In this way, mathematical research can transform from a job with constant or even decreasing returns to scale to a job with increasing returns to scale.

From the above analysis, we can see that AI's ability is not just to increase the speed of a mathematician by tens of times. In a sense, it is more like compressing libraries, computing centers, discussion classes, opposing review and formal verification institutions into a continuously operating research organization. It can be said that human mathematicians are extremely powerful minds, while mature mathematical artificial intelligence (AI for Math) may become an artificial research institute composed of countless minds.

2、 Will AI activate empirical mathematics?

If AI only helps mathematicians prove theorems faster, then the changes still mainly belong to the productivity level. But its potential probably goes beyond that. Perhaps its other ability is giving mathematics a capability that was not fully possessed in the past, thus driving a comprehensive shift in mathematical paradigms. This ability is to observe the mathematical world on a large scale.

Since Euclid, people have been accustomed to understanding mathematics as deductive science - mathematicians first provide definitions and axioms, and then derive theorems through proofs. It is precisely this that fundamentally distinguishes mathematics from natural sciences in terms of its properties: natural sciences face the empirical world and therefore need to test theories through observation and experimentation; Mathematics, on the other hand, deals with formal objects, and truth seems to only arise from logic. Although in practice, many mathematicians often guess patterns through calculation examples, drawings, and other methods, in formally published results, the trial and error and intuition in the discovery process are often removed, and only the concise and beautiful chain of proof from hypothesis to conclusion is ultimately presented to people.

Many mathematicians have challenged this research paradigm. Among them, the most famous is Gregory Chaitin, the founder of algorithmic information theory. Based on the perspective of algorithmic information theory, he proposed a shocking viewpoint: a finite formal system contains a finite amount of information, and it is impossible to systematically derive the fact that any amount of information complexity is higher than its own.However, due to the potential incompressibility in mathematics, it may not necessarily be a transparent building that can be deduced layer by layer from a small number of self-evident principles, as depicted by traditional ideals.

In his book "Metamathematics: An Exploration of Ω", Chatin discusses this using the example of "outage probability" Ω. On this basis, Chating further explained that in mathematics, there are actually a lot of incompressibility like Ω, which makes it impossible to derive all mathematical theories from simple axioms. Based on this understanding, he advocates viewing mathematics with a more experiential attitude. For example, if we have verified the correctness of the Goldbach Conjecture on millions of digits, we can temporarily consider this conjecture as an empirical theorem and use it as a basis to construct further theories. Wait until a counterexample is discovered, then apply another patch.

Although Chating's viewpoint is very shocking, for a long time, it was more of a mathematical philosophical standpoint. The reason for this is not only the innate resistance of mathematicians, but also the limited ability of humans to observe the mathematical world. The limitation of this ability makes it difficult for people to confidently construct relevant theories based on conjecture.

The development of AI is changing this condition. AI can continuously generate millions of graphs, groups, sequences, functions, and geometric constructions, calculate their various invariants, and search for recurring relationships, outliers, and phase transitions. It doesn't even have to wait for humans to ask questions first, but can discover 'there seems to be a phenomenon here' first. This is quite similar to the changes that telescopes have brought to astronomy. Telescopes do not replace physical theories, but they expand the universe that humans can see. AI may also become a mathematical telescope: it will transform the formal space that could only be touched by sporadic examples into objects that can be systematically scanned.

Taking Google's FunSearch as an example, it does not start from a ready-made theorem, but continuously generates runnable constructs in the program space, and selects exceptionally excellent ones through evaluation results. In this way, researchers can first see a structure discovered by a machine and then ask why it is effective. So, the order of mathematical discoveries may be reversed: it's not about having a theory first and then finding examples, but about having an astonishing object first and then creating an explanation for it.

With the support of AI, future mathematical research may become more like the current model of natural sciences. Every mathematician may be like a research supervisor, leading a group of AI agents to conduct research. These intelligent agents can work day and night, while human mathematicians can act like research supervisors, primarily responsible for proposing ideas and waiting for them to report progress.

In this sense, AI may provide the first mature technological foundation for what Chating called quasi empirical mathematics. Although the study of mathematics will not give up the pursuit of inevitability, it may gradually acquire its own telescopes, laboratories, and automated observation systems like an experimental science, and re-examine the mathematical world from an empirical perspective.

3、 When proof no longer equals understanding

In addition to improving research efficiency and impacting research paradigms, AI may also reshape people's understanding of mathematics. Several concepts that were often mixed together in the past - true, trustworthy, verifiable, and understandable - may be forced to be distinguished as a result.

In traditional imagination, a theorem being proven naturally means that mathematicians know why it holds true. However, reality is certainly not that simple. As early as the era of computer-assisted proof, there were situations where humans were unable to read all situations one by one, which posed a challenge to the understanding that proof equals understanding. In the era of AI, this contradiction will be pushed to a whole new level. Imagine if an AI model generates a formal proof containing millions of steps, which is verified by an AI proof assistant and confirmed to be correct, but no mathematician can grasp the overall structure of the proof, then can this result be considered understood by humans?

From a truth perspective, it has certainly been rigorously certified. However, from a cognitive perspective, people may only know that 'the machine did not detect the error', but they may not be able to fully understand the mechanism at work. In the future, this situation may be very common, and mathematical knowledge may be jointly guaranteed by a vast technological system, but every mathematician will find it difficult to understand its entirety.

As AI can increasingly generate various mathematical conclusions, the value of mathematical theorems and mathematicians themselves may undergo a comprehensive reassessment. The cheapest thing in the future may be truth, but the most expensive is explanation. A model can output thousands of new theorems in a day, but which theorems are worth remembering, which proofs contain transferable methods, and which seemingly local results actually point to a new unified theory still require higher-level judgment. Mastering this judgment may become a new standard for judging whether a mathematician is excellent.

Furthermore, future mathematics may even differentiate into two interconnected worlds. On one side is' machine mathematics', which is vast in scale, rigorously proven, and has astonishing search speeds, but may not necessarily be suitable for human reading; On the other side is' human mathematics', which pursues concepts, simplicity, intuition, and meaning. In this situation, the task of connecting the two will become extremely important. Future mathematicians may not have to personally complete every detail of the proof, but they will have to spend a lot of time translating machine discoveries into new definitions, lemmas, and theoretical languages.

From this perspective, AI will not make proofs lose value, but it will show us that proofs have different functions. Proving can verify a proposition as true, help discover new conclusions, and explain why a structure must be like this. AI may take over the first function first and gradually move into the second function, but the third function - transforming correctness into understandable order - is currently difficult for it to handle, and this area may become the forefront of human-machine competition and cooperation.

Through the above analysis, we can see that with the large-scale application of AI, mathematics will face profound changes in research methods, research content, and its own significance. From this perspective, Zimmerman's statement that AI is "killing" current mathematics is neither accurate nor distant. However, from an optimistic perspective, this' killing 'may not be a bad thing for the development of mathematics. With the deepening of human-machine co creation, it may take human understanding of mathematics to a higher level.

4、 Not just mathematics

It should be pointed out that AI's changes in the ways of understanding and discovery will not be limited to the field of mathematics. On the contrary, compared to mathematics, AI has a more profound impact on natural sciences such as physics, chemistry, biology, and materials science. Mathematics faces a formal world composed of axioms and definitions, and the validity of propositions can be determined in principle through proof and formal verification; However, natural sciences are facing a more chaotic reality: observations are noisy, variables are entangled with each other, experiments are time-consuming and expensive, and many key processes span different time and spatial scales. This series of features provides AI with more opportunities for use, and its impact on research is even more significant.

Firstly, AI is changing the way scientists see things. The development of modern science is largely a history of constantly expanding human senses - telescopes extend their gaze into the depths of the universe, microscopes open up the world of cells and microorganisms, and particle accelerators allow humans to indirectly observe fundamental particles that cannot be captured by the naked eye. Today, the difficulty of scientific research is no longer the lack of data, but rather the inability of people to independently digest the massive amounts of data generated by instruments. In this case, AI happens to play the role of a cognitive filter: it can identify unnamed human structures from countless background signals and discover which phenomena are worth further observation. Scientific discoveries may no longer always start from a clear theoretical problem, but from an anomaly, a cluster, or an unexpected association identified by machines.

Secondly, AI is changing the way scientists conduct experiments. Traditional experiments often heavily rely on the researcher's experience. Scientists need to select variables based on experience, design experiments, and then determine the next direction based on the results. But the problem is that many modern scientific problems involve extremely large possible combinations. Relying on manual experience to try one by one can only cover a small part of it. In this case, AI can play a more proactive role here. It not only analyzes completed experiments, but also determines which variables and conditions should be selected and tested for the next experiment based on existing results to minimize uncertainty.

Thirdly, AI is changing the way scientists form theories. The classic narrative of modern science is usually theoretical first: scientists propose a model to explain the world, and then test its validity through experiments. But in fields such as climate systems, cellular networks, turbulence, and complex materials, it is difficult for humans to directly derive all behaviors from a few basic principles.

Now AI provides another path. It can first learn stable patterns from massive data and simulation results, establish models with strong predictive ability, and then be questioned by scientists: what structure does the model capture? Which variables are truly critical? Are there simpler causal mechanisms behind these predictions? Through this method, a complete theory can be gradually mined from empirical data.

This means that the formation of future theories may not always follow the order of "concepts first, then predictions". Sometimes, machines may discover a stable pattern first, and humans may then invent new concepts and theoretical languages to explain this pattern clearly. Scientific understanding will be more manifested as a reciprocating motion: machines discover structures from data, humans transform structures into mechanisms, and new mechanisms guide machines to find more valuable data.

5、 After machines discover more than humans, what else are humans responsible for

When AI demonstrates stronger discovery capabilities than humans in both mathematics and natural sciences, a question arises: what else can humans do in the process of research and discovery? This question is crucial for how we face AI and find the meaning of being human in the AI era. In my opinion, at least for now, humans still need to be responsible for the following things:

Firstly, choose the target. There are infinitely many propositions that can be proven in mathematical space, and there are also infinitely many indicators that can be optimized in the real world. The leap in AI capabilities has given us more opportunities to explore these unknown possibilities, and in this situation, target selection becomes increasingly important. A system can efficiently discover new drugs and design pathogens; You can search for safer materials or harder to intercept weapons. Ultimately, it remains to be decided which research direction to choose.

Next is the significance of judgment. AI can generate a large number of results, but it does not naturally know which results are valuable to human life. Why mathematicians study certain types of symmetries, and why scientists invest resources in climate, disease, or energy issues, involves not only computable benefits but also historical experience, ethical judgments, and public choices. The so-called 'important issues' are never automatically determined by difficulty, they also require human judgment.

Once again, it's about maintaining understanding. Human beings can outsource more and more judgments to machines, but they cannot give up their own cognitive abilities because of this. If doctors only accept the treatment plan provided by the model without understanding the applicable boundaries, and engineers only rely on machine generated designs without being able to determine failure modes, society will become more fragile while enhancing its capabilities. In this sense, although AI can help us discover many new theorems and complete many new proofs, it still requires human translation to transform these theorems and proofs into theories that change reality.

Finally, take responsibility. AI may be able to recommend research directions, but it cannot determine whether to advance them for society; We can calculate risks, but we cannot bear the responsibility that arises when risks become a reality for humanity. As AI becomes a participant in knowledge production, the focus of scientific governance will shift from "how to use a tool" to "how to design a cognitive system" - who has the authority to train and deploy scientific AI, which experiments need to be restricted, how machine generated results should be reviewed, how important knowledge should be shared, and all of this still needs to be decided by human experts.

Zimmerman's shift from pure mathematics to AI safety precisely reflects the weight of this problem. His receipt of the Fields Medal signifies the highest recognition of his human mathematical creativity; He then walked into OpenAI, as if reminding people that this creativity is involved in nurturing an intelligence that may surpass itself. For a mathematician, continuing to solve complex problems naturally holds great appeal. But when a new cognitive force may cross human boundaries in a few years, studying how this force is constrained may become a more urgent mathematical problem.

If we look back at today in the future, people may see Zimmerman's involvement in the AI industry as a turning point. From then on, mathematicians no longer just use machines, but begin to co create mathematics with machines; Scientists are no longer just observing the world through instruments, but are beginning to create new cognitive subjects that can observe, reason, and ask questions. AI may really "kill" mathematics and natural sciences today, but at the same time, a new academic research paradigm may be slowly unfolding towards us.

(Author Observer)