LONDON (Realist English). 2026 has become a turning point for mathematics: artificial intelligence has ceased to be a tool for routine calculations and has begun independently solving problems that had remained open for decades. However, the triumph of machines has turned into a verification crisis — humanity physically cannot keep up with checking and comprehending what AI produces.
OpenAI: 719 papers in one night
On the night of October 6, OpenAI published 722 mathematical papers on GitHub containing full or partial solutions to 372 open problems across 17 fields — from number theory to operator algebras. The model, whose name has not been disclosed, received a catalog of approximately 4,000 problems and selected the most convincing results. Average time per problem — about three hours of computation at the ChatGPT Pro level.
Among the claimed results are a proof of the “quasi-Riemann hypothesis” (a weakened version of the Riemann hypothesis, one of the seven Millennium Problems), a solution to the unique games conjecture, the irrationality of Catalan’s constant, and an improvement to the complexity estimate for matrix multiplication. Mathematician Alex Kontorovich stated that for such a result “they immediately award the Fields Medal, no questions asked.”
However, the very next day OpenAI withdrew three papers concerning the Hodge conjecture due to a sign error: in a key argument, the operation symbol was written as +1 instead of −1, causing a sum that should have cancelled out to become non-zero, and the entire construction lost its foundation. Another 14 papers were edited.
DeepMind: 9 Erdős problems
Unlike OpenAI, Google DeepMind chose the path of academic publication. On October 8, the journal Science published an article on the AlphaProof Nexus system, which autonomously solved 9 of 353 unsolved Erdős problems translated into the formal Lean language. Two of them — including a problem formulated by Erdős and Szekeres in 1970 — had remained open for 56 years.
The system operated on the principle of “model writes — compiler verifies”: Gemini 3.1 Pro generated a proof in Lean, the compiler checked every line, and errors were returned to the model for correction.
Additionally, an “evolutionary” mechanism with sub-agents competing by Elo rating was used, along with a specialized AlphaProof solver for complex subproblems. Cost — several hundred dollars per problem.
The system’s efficiency is about 2.5% (9 out of 353), which corresponds to earlier estimates by Terence Tao regarding the probability of AI success in solving Erdős problems.
China: the Gehring hypothesis
On October 15, it became known that a team led by Professor Xu Dishan from the Greater Bay Area University, using the Chinese Intern-S2 model, proved the three-dimensional Gehring hypothesis formulated in 1995. This is the first case of Chinese scientists using a domestic model to solve a world-class problem.
The process was iterative: the model produced about 400 pages of initial reasoning, some of which was a dead end; researchers selected promising directions and returned them to the model for refinement.
Ultimately, Intern-S2 performed 7 rounds of sequential inference, expanding the problem graph from 15 to 389 nodes, and the total volume of the proof reached a thousand pages. Formal verification was carried out by a team from Peking University using the SHEAF framework.
“Proof indigestion”
Fields Medalist Terence Tao, back in the summer of 2026 at the International Congress of Mathematicians, described the situation with the term “proof indigestion”: the generation and verification of proofs are accelerated by AI, but “digestion” — understanding and assimilation — remains human and cannot keep up with the machine.
Brynja Kraa, a professor at Northwestern University, stated that OpenAI’s results are “stunning,” but “the way they are written makes them impossible to understand,” and tens of thousands of pages require verification, while “peer review is absent.” Scott Aaronson of the University of Texas at Austin noted that “no human, it seems, has yet understood any of these proofs.”
The community’s reaction was sharp: 25 Fields Medalists signed a statement on the “serious dislocation of AI in mathematics,” and Terence Tao initiated the creation of the Human Mathematics Association with a call to suspend cooperation with OpenAI. Mathematicians emphasize: they are not against AI in mathematics, but against the fact that no one understands how AI does it.
The three events — OpenAI’s papers, DeepMind’s article in Science, and China’s Gehring hypothesis — represent different models of interaction between AI and mathematics. DeepMind chose the path of formal verification and academic publication, where every proof is checked by a compiler and reviewers.
The Chinese team used AI as an amplifier of human intuition, leaving researchers the right to select and direct. OpenAI chose mass generation without preliminary verification, which provoked the conflict.
The key problem is not whether AI can solve mathematical problems — it already can. The problem is that mathematics as a discipline rests not only on results but also on understanding.
A proof that no one can read does not expand human knowledge but merely increases the volume of unverified information. If this trend continues, mathematics risks splitting into two streams: a machine one, producing results for other machines, and a human one, trying to preserve understanding. The question is whether a bridge will remain between them.
