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Seed-prover: Deep and broad reasoning for automated theorem proving
27 Pith papers cite this work. Polarity classification is still indexing.
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abstract
LLMs have demonstrated strong mathematical reasoning abilities by leveraging reinforcement learning with long chain-of-thought, yet they continue to struggle with theorem proving due to the lack of clear supervision signals when solely using natural language. Dedicated domain-specific languages like Lean provide clear supervision via formal verification of proofs, enabling effective training through reinforcement learning. In this work, we propose \textbf{Seed-Prover}, a lemma-style whole-proof reasoning model. Seed-Prover can iteratively refine its proof based on Lean feedback, proved lemmas, and self-summarization. To solve IMO-level contest problems, we design three test-time inference strategies that enable both deep and broad reasoning. Seed-Prover proves $78.1\%$ of formalized past IMO problems, saturates MiniF2F, and achieves over 50\% on PutnamBench, outperforming the previous state-of-the-art by a large margin. To address the lack of geometry support in Lean, we introduce a geometry reasoning engine \textbf{Seed-Geometry}, which outperforms previous formal geometry engines. We use these two systems to participate in IMO 2025 and fully prove 5 out of 6 problems. This work represents a significant advancement in automated mathematical reasoning, demonstrating the effectiveness of formal verification with long chain-of-thought reasoning.
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representative citing papers
Introduces Relaxed NFL intermediate language for LLM-based auto-formalization, with rule-plus-LLM elaboration to Core NFL and tactic-language discharge of verification conditions.
LeanMarathon uses four contract-scoped agents on an evolving blueprint coordinated by a two-stage orchestrator to formalize seven theorems from Erdős problems in Lean, proving 258 lemmas with no sorry across three runs.
A multi-agent framework called AutoformBot autoformalized 26 textbooks spanning analysis, algebra, topology, combinatorics and probability into a verified Lean 4 library of 45k declarations, demonstrating scalable formalization of graduate math.
CAM-Bench is a new Lean 4 theorem-proving benchmark of 1,000 problems in computational and applied mathematics, built from textbook exercises using a dependency-recovery pipeline to reconstruct local context.
Lean Atlas visualizes Lean 4 dependency graphs and applies Lean Compass to reduce the nodes needing human semantic review by 27-99% across six evaluated projects.
CORE is a concept-oriented RL method that synthesizes quizzes, injects concept snippets into rollouts, and reinforces conceptual trajectories to close the gap between restating definitions and applying them in math problems.
SageMath-augmented ReAct agents raise solve rates by +9.7 pp on average on a curated 133-problem RealMath subset, with GPT-5.5 reaching 75.2%.
LLM formal provers must shift from competition solvers to research agents that handle open-ended, under-specified frontier mathematics under machine-checked rigor.
Visored is a controlled-natural-language prover for LLM math that automates omitted routine steps and emits checked Lean output, with early miniF2F results showing LLMs can use it without prover-specific training.
OProver-32B achieves top Pass@32 scores on MiniF2F, ProverBench, and PutnamBench by combining continued pretraining with iterative agentic proving, retrieval, SFT on repairs, and RL on unresolved cases using a 6.86M-proof dataset.
Segment-level supervision extracts coherent proof segments to train policy models that achieve 61-66% success on miniF2F, outperforming step-level and whole-proof methods while also improving existing provers.
Synthetic data improves models only in information-open generation-training loops with external signals, and coarser signals like binary correctness enable better generalization by converging to the most information-efficient component.
Training Qwen3-8B on symbolic execution traces from Soteria improves violation detection in C programs by over 17 points, transfers across five property types, and shows superadditive gains with chain-of-thought.
Network analysis of Mathlib reveals 50.9% coupling between human taxonomies and logical dependencies, median 1.6% import usage by developers, and centrality driven by infrastructure rather than mathematical content.
A minimal agentic system achieves competitive performance in automated theorem proving with a simpler design and lower cost than state-of-the-art methods.
Ax-Prover is a tool-using multi-agent LLM system that matches state-of-the-art provers on public math benchmarks and outperforms them on new abstract-algebra and quantum-theory benchmarks while also assisting an expert with a cryptography proof.
Aristotle reaches gold-medal-equivalent performance on 2025 IMO problems via integrated Lean proof search, informal lemma formalization, and a dedicated geometry solver.
An agentic theorem prover in Lean uses a control plane to route actions based on cost and success estimates, achieving 28.9% lower average cost than a fixed-step baseline on a PutnamBench subset while preserving performance.
RLVR training raises verified Dafny pass rates from 9.7% to 31.1% on a filtered benchmark while a Lean proof scaffold lifts success from 46.2% to 69.2% on a pilot set and solves 7 of 42 prior unsolved tasks.
IMAX trains soft prefixes with an InfoMax reward to drive diverse exploration in RLVR, yielding up to 11.60% gains in Pass@4 over standard RLVR across model scales.
Agentic Claude reaches 98.8% valid specs, 87.5% implementation certification, and 98.1% end-to-end success on CLEVER, revealing a mismatch between benchmark difficulty and current prover performance.
LLMs can execute specific technical steps in statistical proofs when given precise guidance but become unreliable for open-ended problem formulation or multi-step reasoning, relocating rather than reducing the demand for human expertise.
citing papers explorer
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Statistical Proof as a Window into Human-AI Collaboration: Practical Insights and a Community Agenda
LLMs can execute specific technical steps in statistical proofs when given precise guidance but become unreliable for open-ended problem formulation or multi-step reasoning, relocating rather than reducing the demand for human expertise.