Researchers from New York University in collaboration with Google DeepMind's Rémi Munos have published 'Learning to Discover Interesting Mathematics' (arXiv: 2609.28603). While LLMs excel at proving existing conjectures, autonomous mathematical expansion has been crippled by models spamming trivial or useless lemmas. The authors formulate a metric for intrinsic mathematical interestingness—defined by the compression ratio between proof length and statement brevity. Powered by a specialized 27B proof-difficulty model, the framework autonomously conjectures, verifies, and curates high-value theorems, enabling self-expanding formal mathematical libraries without human-specified goals.

Key Takeaways

  • ✓Establishes a quantitative mathematical metric for intrinsic theorem interestingness based on proof-to-statement complexity ratios.
  • ✓Demonstrates robust correlation between intrinsic syntactic interestingness and downstream extrinsic utility across mathematical domains.
  • ✓Trains a 27B proof-difficulty predictor that outperforms frontier general-purpose LLMs in evaluating proof feasibility.
  • ✓Reduces Mathlib redundant theorem overlap from 91.9% down to 30.6%, driving 69.4% of exploration into entirely out-of-distribution math.
  • ✓Preprint, Lean verification harnesses, and autonomous conjecture pipelines released openly on arXiv and Hugging Face.
🔗

Project Links & Resources

Direct Access
Direct access to official project resources and documentation
🌐
ArXiv 论文预印本 (2609.28603)
arxiv.org/abs/2609.28603
↗
📝
Hugging Face Daily Papers 讨论主页
huggingface.co/papers/2609.28603
↗
🔬

In-Depth Technical Analysis

Core Background & Industry Pain Points While AI systems demonstrate superhuman proficiency in proving human-authored mathematical conjectures in Lean 4 and Isabelle, they remain passive solvers. When tasked with open-ended mathematical discovery, models generate millions of mathematically correct but trivially useless tautologies (e.g. redundant identity variations). Without human targets, formal math libraries lack an automated compass to distinguish worthwhile mathematical breakthroughs from combinatorial spam. ### Architecture Highlights & Internals NYU and DeepMind establish an automated engine for mathematical intuition: (1) Intrinsic Interestingness is formalized as the compression ratio between an optimal proof's length and its premise statement's brevity, identifying concise statements that necessitate intricate deductive reasoning; (2) A specialized 27B proof-difficulty predictor evaluates prospective conjectures without executing exhaustive search passes; and (3) A self-expanding verification cycle generates candidate hypotheses, ranks them via interestingness priors, and integrates formally checked theorems into expanding Lean libraries. ### Authoritative Benchmarks & Measured Scores Tested across automated Lean theorem expansion suites: the framework triples human-judged mathematical interestingness compared to unguided generation. Critically, substantial overlap with Mathlib plummeted from 91.9% to 30.6%, driving nearly 70% of generation into novel, out-of-distribution mathematical territories. Using the interestingness metric as a search heuristic pruned unpromising proof branches by 54.2%. ### Developer Hands-on Guide AI for Science and automated deduction researchers can review Lean 4 pipeline specifications and prompt strategies on arXiv and Hugging Face Papers.