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An AI model named Fable discovered a counterexample to the Jacobian conjecture, a long-standing open problem in mathematics, by finding a polynomial function that meets the special conditions but is not invertible.
Loopie is a new looped Transformer model that achieves gold-medal performance at the 2025 IMO and IPhO without external tools, using a novel post-training pipeline. It outperforms vanilla Transformers trained with the same compute budget.
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.
TheoremGraph is a unified statement-level dependency graph that spans both informal mathematics (arXiv papers) and formal mathematics (Lean projects), using semantic embeddings to bridge the gap between them. The authors provide datasets, extractors, and APIs to support mathematical search and retrieval.