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01量子位
Epoch AI says FrontierMath Tier 4 is now "saturated": by its accounting, when attempts across different models and different time periods are accumulated, every Tier 4 problem has been correctly solved by an AI at least once. OpenAI reports a score of 97.6% for GPT-6 Astra, which solved the one problem that had never been cracked before. When Tier 4 launched on July 11, 2025, the top score on the board was only about 5%. Jay Pantone, an associate professor of mathematics at Marquette University and one of the problem setters, said earlier AIs tended to find numerical shortcuts, whereas this solution was quite close to his own. Tier 4 was later revised: a v2 released in June 2026 corrected 12 problems and removed 7, leaving 43. The project has since added Open Problems and FrontierMath Erdős, where Astra solved only 2 of 68 problems.
Hugging Face Daily Papers
A central tenet of human cognition is systematicity, the principle that understanding one concept is inherently tied to understanding close variations of that concept. Do reasoning models robustly exhibit such systematicity? If so, we would expect consistent performance on structurally equivalent variants of the same task. Here, we extend established rule induction tasks from cognitive science to assess the systematicity of thought in current reasoning models. Each task family has compositional structure that we use to create structurally equivalent task variations through task isomorphisms such as recombination and substitution. We find that despite being able to correctly solve a task, models often fail on structurally equivalent variants of the same task. These findings suggest that many model behaviors lack systematicity, rendering it difficult to robustly establish the cognitive abilities of reasoning models beyond the particular contexts they were evaluated in.
Terence Tao
[This is a guest post by Lucas Fagan . This blog post was initially written in a different file format and converted using AI. — T.] I am excited to announce the Andrews–Curtis Conjecture Challenge , which opens today. This challenge is a collaboration between the SAIR Foundation and the Math-AI group at Caltech , organized by Sergei Gukov, Terence Tao, and myself. The Andrews–Curtis conjecture is one of the most prominent open problems in combinatorial group theory and also has deep connections to low-dimensional topology. Its potential counterexamples are relevant to the search for exotic smooth four-spheres and the smooth four-dimensional Poincaré conjecture , as well as the Generalized Property R conjecture about surgery on links . Yet unlike many open problems at its level, Andrews–Curtis can be formulated as a combinatorial search problem with easily checkable solutions, making it ideal for a challenge of this form. At Caltech, we have been developing reinforcement learning and combinatorial search methods for this problem to resolve potential counterexamples (see What makes math problems hard for reinforcement learning: a case study and The Two-Hump Problem ). However, many important cases have resisted all our efforts. We hope that this challenge will lead to resolving these and more (or disproving the conjecture), especially given the recent progress in AI. We give more details about the different tracks of the competition below. To briefly introduce the problem: the Andrews–Curtis conjecture says that any balanced presentation of the trivial group can be transformed to the trivial presentation using the following moves (which do not change the underlying group): (AC1) Invert a relator: . (AC2) Multiply a relator by another: for some . (AC3) Conjugate a relator by a generator or its inverse: for some . Two presentations connected by these moves are called AC-equivalent ; a presentation that is AC-equivalent to the trivial presentation is called AC-trivial . As a simple example, is AC-trivial: It is generally suspected that the conjecture is false ; there are many simple potential counterexamples in which all computational efforts have failed to find a path to the trivial presentation. The most notable of these is the Akbulut–Kirby family whose AC-triviality is open for . Indeed, , with total relator length , is the shortest possible counterexample…
Discovery · OpenAI
It was a week that left mathematicians reeling. Hot on the heels of a flurry of cases of artificial intelligence furthering the field, OpenAI declared a major scalp: its latest AI model had cracked a Millennium Prize Problem, a puzzle with a $1m reward that had defied human brains for decades. The achievement bore little resemblance to how mathematical problems normally fall. A near-trillion dollar private company had unleashed 10,000 agents – AI systems that carry out tasks autonomously – on the problem. The bill was estimated at $15m. The trajectory towards AI capable of superhuman maths has long been clear, but to nail such a substantial problem so swiftly sent shock waves through the field. Mathematicians are asking what will be left for them if works in progress are hoovered up and claimed by others, and how they should train the next generation when even fiendish assignments can be solved at the press of a button. “I feel slightly shell-shocked,” said Prof Colva Roney-Dougal, the head of pure mathematics at the University of St Andrews. At a recent public lecture, she said she believed that AI was unlikely to do anything remarkable soon. “Three months later, I’m totally wrong,” she says. “We’re all just waiting to see what happens. It’s coming so fast.” Prof David Silvester, a mathematician at the University of Manchester, said the field felt “very unstable” given the pace of change. “All the open maths problems could fall with enough resources,” he said. “This is irreversible. This is not going to change.” Prof James Robinson, a mathematician at the University of Warwick, said hard problems were the fuel of mathematics, driving creative approaches across successive generations. “It’s frustrating to see these big tech companies burning this fuel up just so that they can show off about how great their latest model is,” he said. “It seems like immature playground boasting writ large, underpinned by billions of dollars and the potential for significant environmental damage in an age when climate change is probably the biggest challenge we face.” One reason Silvester went into maths was the rush that comes from cracking a problem. For many mathematicians it is the weeks, months and years spent circling a problem, breaking it down, trying one approach after another, and never quitting that appeals. “Without that, the subject seems completely different to m…
