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A tweet claims that the AI model Claude Fable produced a counterexample to the Jacobian Conjecture, providing an explicit polynomial map that is not injective despite having constant nonzero Jacobian determinant.
AI systems have made breakthroughs in mathematics, helping to overturn Erdős's long-standing conjecture about unit distances in the plane. But an essay warns: the stronger the automation, the more important human ability to understand and audit machine reasoning becomes, while the U.S. mathematics talent pipeline is degrading due to budget cuts.
This paper argues that as AI systems achieve breakthroughs in mathematics, the United States is neglecting the human mathematical infrastructure needed to understand, verify, and direct these systems, posing a strategic risk.
Starting with the story of Galois group theory, the article delves into the boundaries of AI's capabilities in mathematics, distinguishing between two types of progress: "connecting lightning" (cross-domain connections) and "building mountains" (creating new frameworks). It analyzes the limitations of the RLVR training method and introduces the concept of "grindability" to explain AI's rapid advancements in mathematics and coding.
This paper applies the VGPT-RSI AI system to produce formally verified partial results related to the Riemann Hypothesis, including boundary certificates and finite Lagarias inequalities, while explicitly identifying remaining mathematical obstructions.
This paper trains a small one-layer encoder-decoder transformer on the zeta map bijection for Dyck paths and uses mechanistic interpretability to extract a new explicit algorithm called the scaffolding map, demonstrating an AI-assisted approach to mathematical discovery.
Aleph Prover has formalized OpenAI's disproof of Paul Erdős' planar unit problem in Lean 4 and released it as open source for independent validation, demonstrating AI's role in accelerating mathematical research with verifiable proof data.
Over the weekend, Mythos was tested on the Erdos unit distance problem (Problem #90) and successfully solved it.
Terry Tao remarks on AI enabling mass-produced mathematics at scale, turning proof-writing into a searchable problem that generates thousands of mini-lemmas and filters them with cheap checkers.
An OpenAI model autonomously disproved a central conjecture in discrete geometry known as the unit distance problem, marking the first time an AI has solved a prominent open problem in mathematics.
DeepMind researchers discovered new families of unstable singularities in fundamental fluid dynamics equations using AI techniques, potentially advancing understanding of century-old mathematical problems like the Navier-Stokes equations. The work collaborates with Brown, NYU, and Stanford, revealing patterns in blow-up behavior with unprecedented computational accuracy.
A mathematician used Codex 5.6 to successfully disprove an algebraic surface conjecture that had taken him three years to try to prove. The model can automatically spawn sub-agents to handle heavy computations, allowing him to focus on difficult problems and life.