Auto-formalization, proof synthesis, and mathematical assistance

AIProver is a unified neuro-symbolic framework for translating informal mathematics into Lean 4, supporting working mathematicians, and enabling novel discovery.

The challenge

Research-level mathematics demands both creative leaps and unforgiving rigor. Bridging informal arguments and machine-checkable proof, at scale, is an open problem.

Our approach

An auto-formalizing LLM, with Semantically-Aligned Models (SAMs) to enrich the context window with definitions, produces candidate Lean proofs; SAT/SMT solvers, computer algebra systems, and tactic-level metaprogramming verify and repair them in a tight feedback loop.

The payoff

An ever-expanding, self-improving knowledge base of verified mathematics, and a credible path to attacking long-standing open problems in group theory, analysis, and beyond.

Research Pillars

Five directions, one framework

Core research thrusts driving AIProver toward scalable, verified mathematical reasoning.

01

Auto-formalization & proof synthesis

Translating informal mathematics into Lean 4, then synthesizing and repairing proofs through tight loops between LLMs, SAT/SMT solvers, computer algebra systems, and tactic-level metaprogramming.

02

Mathematical assistant

An interactive, conversational aide for working mathematicians, capable of answering technical questions, suggesting relevant lemmas, sketching proof strategies, and grounding every suggestion in formally verified knowledge.

03

Semantic Contrastive Learning & SAMs

Training Semantic Alignment Models (SAMs) that align informal and formal proofs in a shared embedding space, enabling RAG retrieval, concept search across fields, and hierarchical proof refinement, foundational to ProofBridge.

04

Group theory & abstract algebra

Attacking open problems on simplicity and structure of infinite groups, including those tied to infinite-dimensional Lie algebras and P. M. Neumann's open problem (F21), via G-Simple and GAP integration.

05

Asymptotic analysis & integer sequences

Verifying inequalities and asymptotic estimates with O-Forge, and formalizing the OEIS at scale through Sequencelib.