The recent dramatic effects of AI on mathematics have generated substantial discussion in the mathematical community as well as attracted attention in the public media. I was asked to comment on this topic for two articles in Helsingin Sanomat (9.9.2026 & 26.9.2026), and thereafter to write this blog text.
This text merely aims to collect some recent facts and discussion. Since things are evolving very rapidly, it only reflects the situation at the time of writing (12.10.2026). Moreover, this discussion mainly concerns “pure mathematics” and is more closely related to the mathematical theory of imaging problems studied within the FAME Flagship rather than the applied and experimental parts. AI tools were used for fact checking and for generating hyperlinks in this text.
After the launch of ChatGPT in November 2022, the mathematical abilities of AI tools (especially Large Language Models, LLMs, like ChatGPT and Claude) have developed rapidly:
- In 2024 some models achieved laudatur level performance in the Finnish matriculation examination in mathematics. In International Mathematical Olympiad problems, they reached silver medal performance.
- In 2025 some models reached gold medal level in Olympiad problems. In research level problems the models were still unreliable.
- Over the summer of 2026 the mathematical abilities of AI models improved dramatically. In some areas current frontier models achieve superhuman performance.
Two recent events have made the power of AI tools particularly clear:
- The proposed solution of the Navier-Stokes Millennium problem by OpenAI (8.9.2026).
- Over 700 manuscripts with proposed solutions or progress in open questions in several areas of mathematics released by OpenAI (6.10.2026). Four of these are of direct interest to inverse problems: the anisotropic Calderón problem (scalar and system versions), the static elastic inverse problem, and nonuniqueness for bounded measurable conductivities in three dimensions.
These results were obtained by varying amounts of computation time using unreleased models internal to OpenAI. With the advent of AI tools, it is becoming feasible to produce formal computer verifications for proofs. Some of the above results come with formalizations in the Lean language.
It has been suggested (see for instance Terence Tao, Math 2.0, 10.10.2026) that mathematics, by its nature, is particularly susceptible to the disruption by AI. The special feature of mathematics is that statements can be reliably verified for their correctness. Moreover, a large part of mathematical knowledge can be easily digitized, thus providing large high-quality datasets for training AI models. This has led to the spectacular recent performance of AI models on select mathematical questions.
It seems likely that mathematical research will undergo substantial changes because of AI. There is a very large amount of ongoing debate within the mathematical community on how to deal with this transition. Prominent discussion includes the following:
- An open letter endorsed by Fields medalists (11.9.2026), expressing their concern that the goals of AI companies regarding mathematics are potentially detrimental to the health of the mathematical community.
- Discussion around the Mathathon weekend event announced at Caltech. The event originally intended to produce new solutions to open problems under AI company sponsorship. An open letter initiated by Caltech mathematicians (10.9.2026) criticized such production of quick answers without proper human understanding. Subsequently the event has been restructured with the new title “Mathathon: old problems, new proofs”.
- The resources and procedures behind some of the results publicized by AI companies are not transparent. One attempt for more precise information on the capabilities of current AI models is the First Proof project. There are also initiatives for open source AI models for mathematics, such as SAIR’s Open Models (18.9.2026).
- The publication system for mathematics will be under considerable strain due to the volume and quality of AI-generated work. As a concrete initial measure, arXiv has implemented a quota of two submissions per month per submitter. Journals are beginning to adapt their policies to the new situation, and new repositories such as Hexagon have been founded.
- Supporting junior researchers in this changing situation is particularly important. Some suggestions were given in the PhD Math Education in the Age of AI summit (17.-18.9.2026) at Harvard University and in the text of MIT-based Pavel Etingof and Slava Gerovitch (6.10.2026). There are good reasons to expect that skills obtained in mathematical PhD or postdoc training, such as logical thinking, problem solving, ability to work toward long-term goals, holistic understanding, and critical interpretation of results, are likely to be in high demand also in the future.
AI, when used responsibly, provides powerful new tools that may significantly advance our understanding of mathematics. These tools may also accelerate the process of bringing mathematical methods to new applications and help in collaboration between applied mathematicians and domain experts. For those interested in following the current discussion about AI in the mathematical community, Terence Tao’s blog and the Proofs and Prompts blog are excellent resources.
About the author: Prof. Mikko Salo is a Professor of Mathematics at the University of Jyväskylä and one of the Principal Investigators of the FAME Flagship. In August 2026 the European Research Council, Europe’s premiere funding instrument set up by the European Union to advance the highest quality research, granted its prestigious ERC Advanced Grant funding worth approximately €2 million to support Prof. Salo’s project on foundational mathematical questions in the field of inverse problems.
