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This paper introduces a framework for LLMs to discover and prove interesting mathematical theorems by optimizing for a metric based on proof difficulty, leading to more novel and useful mathematical knowledge with reduced overlap with existing libraries.
This paper defines intrinsic interestingness for mathematical theorems using proof-to-statement length ratio and trains a 27B model to predict proof difficulty, enabling the generation of more interesting theorems and self-expanding mathematical libraries with reduced overlap with existing knowledge like Mathlib.
Mario Carneiro discovered that CIC plus LEM proves the consistency of ZF set theory, enabling a proof in axiom-free Lean with LEM, advancing type theoretic metamathematics.
The article discusses how artificial intelligence is revolutionizing the production of deep theorems in mathematics, challenging traditional measures of success, with a focus on the Nivat conjecture.
OpenAI reportedly spent $10M worth of tokens to solve the Navier-Stokes Millennium Prize Problem, winning a $1M math prize by using an advanced AI model.
StochBench introduces a domain-specific benchmark of 450 graduate stochastic processes problems in Lean 4, evaluated with an AI agent achieving a 34.9% proof rate, to advance formal theorem proving in applied mathematics.
OpenAI claims to have solved one of the Millennium Prize Problems in mathematics, marking a potential major breakthrough in AI and mathematical research.
This paper introduces C*, a proof-integrated language that unifies C programming with formal verification, enabling real-time verification through embedded proof-code blocks.
OpenAI has released new Lean theorem proving repositories on GitHub, ahead of their upcoming Astra release.
ProofEvolve is a neuro-symbolic framework that evolves formally verified proof structures using neural models to enhance automated theorem proving, achieving high solve rates on Lean benchmarks by preserving verified knowledge from incomplete attempts.
FaithSieve is a Lean-assisted framework for fine-grained evaluation of mathematical proofs that uses semantic alignment scoring to ensure faithful formal evidence, achieving higher accuracy than baseline methods on expert-verified datasets.
MathAdv is a diagnostic benchmark for formal theorem proving in mathematics, covering 13 domains with auxiliary tasks to evaluate knowledge, reasoning, and robustness. The study reveals formalization bottlenecks and performance variations across models.
This paper introduces a compiler-guided adaptive proof search framework for context-dependent theorem proving in Lean 4, using cross-model synergy to improve proof success rates while reducing computational cost.
MathCode is an AI-powered coding assistant that converts mathematical problems into Lean 4 theorems and attempts formal proofs, featuring a persistent REPL, theorem libraries, and agent-mode proving.
This paper presents Prove-RT, an LLM-assisted framework for generating Prosa/Rocq mechanized theorem prover scripts for schedulability analysis in real-time systems, achieving a 44.7% success rate on a curated evaluation set.
OpenAI reports that an internal version of its next major model (Astra) solved 10 long-standing open problems in math and theoretical computer science for roughly $2,000 in tokens, with formal Lean certificates.
OpenAI announces ten results on long-standing open problems in mathematics and theoretical computer science, achieved by an internal version of its next model Astra, with proofs formalized in Lean.
A technical blog post argues that Rocq (Coq) is better than Lean for program verification due to Rocq's native support for coinductive types and cofixpoints, contrasting with Lean's less mature, library-based approach.
A research paper introducing a failure-triggered cascade approach to safely integrate machine learning into Lean 4's grind tactic, achieving improved efficiency and solving previously unsolvable proofs without regressions.
LeanFlow is an LLM agent system for translating mathematical papers into formalized Lean projects, evaluated through case studies and benchmarks with Kimi-K2.6 and GPT-5.5, achieving high completion rates within budget constraints.