Will AI kill mathematics?
On July 23, the 2026 Fields Medal winners were announced. While domestic media focused their attention on the two Chinese mathematicians Wang Hong and Deng Yu who won this year's awards, another laureate — Canadian mathematician Jacob Tsimerman — quietly dominated the headlines of foreign tech media. At the press conference after the award ceremony, Tsimerman solemnly announced that he would join OpenAI in August and shift his research focus from pure mathematics to AI safety research. On the day the highest honor in the mathematics community was awarded, a young mathematician at the peak of his career unexpectedly decided to "switch careers" to AI, which was absolutely explosive news.
Speaking of Tsimerman, he is a total maverick in the mathematics circle. He has extremely high talent and is very good at re-"building bridges" between different mathematical fields to achieve dimensionality reduction strikes. For example, he once transformed the o-minimality method, which originally had strong logical characteristics, into a powerful tool in arithmetic geometry and complex algebraic geometry, and used it to solve a series of mathematical puzzles including the André-Oort conjecture. However, such a mathematician with outstanding achievements has been bearish on mathematics since the advent of ChatGPT in 2022, believing that AI will replace most of the work of mathematicians within a few years. Based on this belief, he has refused to supervise graduate students since 2023. Even in his own research, he no longer conducts proofs personally, but only puts forward some grand ideas and then hands over the remaining details to AI to complete. In 2025, he published the paper *A Taxonomy of Possible AI Existential Catastrophe Scenarios*, which systematically sorted out multiple paths that AI could lead to human extinction, thus officially stepping into the field of AI safety. From this perspective, his career switch announcement at the Fields Medal award ceremony is actually no more than an official public announcement of his career path change.
It is worth noting that in the mathematics community, Tsimerman is not the only one who believes that the development of AI may pose a "threat" to mathematics. For example, Terence Tao, the 2006 Fields Medalist, believes that the arrival of AI is pushing mathematics into a turbulent period, where its values and practical foundations will be challenged. William Timothy Gowers, the 1998 Fields Medalist, also believes that large language models will not only surpass humans in all aspects of mathematical problem-solving soon, but also may raise problems, construct theories and formulate definitions on their own.
From a practical point of view, the achievements AI has made in the mathematical field in the past year or so seem to confirm their views: In October 2025, mathematicians from UCLA used GPT to conquer the Nesterov conjecture, a puzzle in the optimization field that had been shelved for 42 years; In January 2026, DeepMind's AlphaEvolve model discovered the high-dimensional hypercube structure that had not been found for 50 years in permutation groups, thus solving an open problem in combinatorial group theory; On May 20, 2026, OpenAI's general reasoning model independently falsified the Erdős distinct distances conjecture that had been suspended for 80 years, and the results were verified by 9 top mathematicians; The next day (May 21), DeepMind released AlphaProof Nexus, which completely proved 9 open problems proposed by Erdős at one time, and simultaneously proved 44 OEIS integer sequence conjectures; On July 20, 2026, Anthropic Fable 5 assisted mathematicians in finding a concise counterexample to the Jacobian conjecture, overthrowing a century-old unsolved case at the core of algebraic geometry... Describing AI's performance in the mathematical field as "completely dominant" is not an exaggeration at all.
Then why can AI achieve such eye-catching performance in the mathematical field? In addition to helping people solve more mathematical puzzles, what other changes will AI bring to mathematics? Will it eventually kill mathematics? What kind of impact will this have on the way humans understand the world? Let's talk about all the above slowly.
01
AI: More Than Just "Faster Calculation"
When it comes to the advantages of AI in the mathematical field, many people's first reaction is that it can "calculate fast and remember a lot". This view is not wrong, but it greatly underestimates the capabilities of AI. Just as the steam engine is not just a faster horse, the Internet is not just a post office that transmits information faster, AI is not just a calculator that can calculate faster. The reason why it can make such significant achievements in mathematics is largely because it has an intelligence different from that of humans.
First, AI's ability to call interdisciplinary knowledge at the same time is far higher than that of humans. Modern mathematics is already a highly specialized discipline, and the barriers between its internal branches are very clear. A top mathematician may be proficient in a certain branch of number theory, but only have a general understanding of random matrices, dynamical systems or computational complexity. In contrast, AI has no sense of boundary like human scholars. It not only has encyclopedic memory, but also can call in knowledge of number theory, geometry, combinatorics, probability, optimization and computer science in one search, and carry out large-scale reorganization of this knowledge. In this way, AI turns the cross-domain connection that human scholars can only establish through accidental conversations or communications into a daily search method, which can easily find inspiration across boundaries.
Second, AI has a parallel exploration ability that is difficult for humans to match. When studying a difficult problem, mathematicians often walk alone in a maze — they may keep several alternate routes in their minds, but usually only one or two can be deeply advanced. If they follow a route for half a year and find it is a dead end, what they lose is not only time, but also attention and confidence. But AI is different. It can send out hundreds of "avatars" at the same time to try different routes respectively. In this way, not only the probability of finding the correct path is greatly increased, but also the failed routes will not be wasted in vain, and can be entered into the database to tell subsequent models which paths are already impassable.
Third, AI's tolerance for tedious and "ugly" work is far higher than that of human scholars. In popular science readings, mathematical discoveries are often described as the product of a mathematician's sudden inspiration, but in fact, this is more of an artistic beautification. In the daily process of mathematical research, most of the content is tedious repetition and "ugly" formula derivation. Admittedly, the aesthetic of mathematicians has indeed promoted many great discoveries, but such aesthetic may also form prejudice. People like simple, symmetrical and familiar objects, so those routes that require excessive classification discussion, lengthy calculation, or no beautiful structure can be seen temporarily are often deliberately ignored. But AI is different. It will not lose patience because a proof is not elegant enough, nor will it worry that a research does not conform to the mainstream taste, but will honestly continue to search in high-dimensional spaces, extreme parameters and rare objects.
Fourth, AI's ability to compress different research links into a closed loop is stronger than that of human scholars. In traditional research, literature retrieval, calculation, conjecture proposing, counterexample searching and proof writing are often scattered in different tools and different time stages. AI can complete multiple rounds of cycles in a very short time: first find relevant theorems from the paper library, then write programs to check finite cases. Once an abnormality is found, modify the conjecture. Then, call the formal proof system to verify the key steps. If it fails, it can go back to the previous link and reorganize the problem.
Fifth, AI has very good replicability. Once an AI model learns a proof strategy, it can replicate it to countless instances; and if an AI finds a new route in a certain project, or finds that a certain route is impassable, it can immediately synchronize this information to other AIs, making this information the common experience of the entire system. In this way, mathematical research can be transformed from a work with constant or even decreasing returns to scale into a work with increasing returns to scale.
Through the above analysis, we can see that the ability of AI is not just to increase the speed of a mathematician by dozens of times. In a sense, it is more like compressing a library, a computing center, a seminar, a counterparty reviewer and a formal verification institution into a continuously operating research organization. It can be said that a human mathematician is an extremely powerful mind, while a mature mathematics-specific artificial intelligence (AI for Math) may become an artificial research institute composed of countless minds.
02
Will AI Usher in Empirical Mathematics?
If AI only helps mathematicians prove theorems faster, the changes will still mainly belong to the productivity level. But its potential is probably far more than that. Perhaps another of its capabilities is enabling mathematics to gain an ability that it did not fully have in the past, thus promoting a comprehensive transformation of the mathematical paradigm. This capability is: observing the mathematical world on a large scale.
Since Euclid, people have been accustomed to understanding mathematics as a deductive science — mathematicians first give definitions and axioms, and then derive theorems through proofs. It is this point that makes mathematics fundamentally different from natural science in nature: natural science faces the empirical world, so it needs to test theories through observation and experiment; while mathematics faces formal objects, and the truth seems to only come from logic. Although in practice, many mathematicians often guess laws by calculating examples, drawing pictures and other methods, the trial and error and intuition in the process of discovery are often deleted in the formally published results, and what is finally presented to people are only those concise and beautiful proof chains from assumptions to conclusions.
Many mathematicians have challenged this research paradigm. Among them, the most famous one is Gregory Chaitin, the founder of algorithmic information theory. Based on the viewpoint of algorithmic information theory, he put forward a shocking view: a finite formal system contains a limited amount of information, and it is impossible to systematically deduce arbitrarily many facts with higher information complexity than itself. Since there may be a large amount of incompressibility in mathematics, it may not be a transparent building that can be deduced layer by layer from a small number of self-evident principles as depicted by the traditional ideal.
In his book *Metamathematics: The Quest for Omega*, Chaitin discusses this by taking the "halting probability" Ω as an example. On this basis, Chaitin further explains that there are actually a large number of incompressible things like Ω in mathematics, which makes it impossible to deduce all mathematical theories from simple axioms. Based on this understanding, he advocates that we can treat mathematics with a "more empirical" attitude. For example, we have verified the correctness of the Goldbach conjecture on numbers with millions of digits, so we can completely regard this conjecture as an empirical theorem for the time being, and construct further theories on this basis. When a counterexample is found, we can add a patch to it.
Although Chaitin's view is very shocking, for a long time, it was more of a position in the philosophy of mathematics. The reason, apart from the innate resistance of mathematicians, is that human's ability to observe the mathematical world is very limited. This limitation of ability makes it difficult for people to build relevant theories based on conjectures with confidence.
The development of AI is changing this condition. AI can continuously generate millions of graphs, groups, sequences, functions and geometric structures, calculate their various invariants, and find recurring relationships, outliers and phase transitions among them. It does not even need to wait for humans to raise questions first, but can discover that "there seems to be a phenomenon here" first. This is quite similar to the change that telescopes brought to astronomy. Telescopes did not replace physical theories, but expanded the universe that humans can see. AI may also become a mathematical telescope: it will turn the formal space that can only be touched by sporadic examples into an object that can be systematically scanned.
Take Google's FunSearch as an example. It does not start from an existing theorem, but continuously generates runnable structures in the program space, and selects exceptionally excellent ones by evaluating the results. In this way, researchers can first see the structure discovered by the machine, and then ask why it works. As a result, the order of mathematical discovery may be reversed: instead of having a theory first and then finding examples, a surprisingly performing object appears first, and then an explanation is created for it.
With the support of AI, future mathematical research may become more like the model of natural science today. Every mathematician may be like a research director, leading a group of AI agents to carry out research. These agents can work around the clock, while human mathematicians, like research directors, are mainly responsible for putting forward ideas and then waiting for them to report progress.
In this sense, AI may make the quasi-empirical mathematics mentioned by Chaitin obtain a mature technical foundation for the first time. Although mathematical research will not give up the pursuit of necessity because of this, it will gradually have its own telescopes, laboratories and automatic observation systems like an experimental science, and re-examine the mathematical world from an empirical perspective.
03
When Proof No Longer Equals Understanding
In addition to the improvement of research efficiency and the impact on the research paradigm, AI may also reshape people's cognition of mathematics. Several concepts that were often mixed together in the past — truth, credibility, verifiability and understandability — may thus be forced to be distinguished.
In the traditional imagination, when a theorem is proved, it of course means that mathematicians know why it holds. However, the reality is certainly not so simple. As early as the era of computer-aided proof, there have been cases where humans could not read all the situations one by one, which challenged the cognition that proof equals understanding. In the AI era, this contradiction will be pushed to a whole new level. Just imagine, if an AI model generates a formal proof containing millions of steps, which is verified by an AI proof assistant to be correct, but no mathematician can grasp the overall structure of the proof, is this result considered to be understood by humans?
From the perspective of truth value, it has of course been strictly certified. However, from the cognitive perspective, people may only know that "the machine has not found errors", but cannot explain the mechanism that really works. In the future, this situation may be very common, and mathematical knowledge will be jointly guaranteed by a huge technical system, but every mathematician will find it difficult to understand the whole picture.
When AI can produce more and more various mathematical conclusions, the value of mathematical theorems and mathematicians themselves may face a comprehensive re-evaluation. In the future, the cheapest thing may be truth, and the most expensive thing 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. And whether one can master this judgment may become a new standard for judging whether a mathematician is excellent.
Furthermore, future mathematics may even divide into two interrelated worlds. One side is "machine mathematics", which is large in scale, strict in proof, and amazing in search speed, but not necessarily suitable for human reading; the other side is "human mathematics", which pursues concepts, simplicity, intuition and meaning. In this case, the work of connecting the two will become extremely important. Future mathematicians may not have to complete every detail of the proof personally, but will spend a lot of time translating machine discoveries into new definitions, lemmas and theoretical languages.
From this perspective, AI will not make proof lose its value, but let us see that proof has different functions. Proof can certify that a proposition is true, help discover new conclusions, and explain why a structure is necessarily so. AI may take over the first function first, and gradually enter the second function, but the third function — transforming correctness into understandable order — is still difficult for it to handle for the time being, and this area may become the frontier of human-machine co-competition and co-operation.
Through the above analysis, we can see that with the large-scale application of AI, mathematics will face profound changes no matter in the research methods, research content, or its own meaning. From this perspective, what Tsimerman said that AI is "killing" the current mathematics is not far from the truth. However, from an optimistic point of view, this kind of "killing" may not be a bad thing for the development of mathematics. With the deepening of human-machine co-creation, it may bring human's cognition of mathematics to a higher level.
04
Not Just Mathematics
It needs to be pointed out that the changes AI brings to the way of cognition and discovery will not stay in the mathematical field. On the contrary, compared with mathematics, AI has a more far-reaching impact on natural sciences such as physics, chemistry, biology and materials science. Mathematics faces the formal world composed of axioms and definitions, and whether a proposition is valid can in principle be judged by proof and formal verification; while natural science faces a more chaotic real world: observations are noisy, variables are entangled with each other, experiments are time-consuming and expensive, and many key processes span different time and space scales. This series of features give AI more room to play, and its impact on research is more significant.
First, AI is changing the way scientists "see things". The development of modern science is to a large extent a history of continuously expanding human senses — telescopes extend the view to the depths of the universe, microscopes open up the world of cells and microorganisms, and particle accelerators allow humans to indirectly observe elementary particles that cannot be captured by the naked eye. Today, the difficulty of scientific research is no longer the lack of data, but that people can no longer independently digest the massive data generated by instruments. In this case, AI exactly plays the role of a cognitive filter: it can find structures that have not been named by humans from countless background signals, and discover which phenomena are worthy of further observation. Scientific discovery may thus no longer always start from a clear theoretical problem, but from an anomaly, a set of clusters or an unexpected association identified by the machine.
Second, AI is changing the way scientists "conduct experiments". Traditional experiments usually rely heavily on the experience of researchers. Scientists need to select variables and design experiments based on experience,