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First unified Lean 4 framework for neural-network specification, execution, and verification; tensor shapes are part of the types, models are executable Lean programs, and the same definitions can be used by training code, graph transformations, certificate checkers, and proofs with CPU/CUDA backends (123+ stars, MIT License)

First bioinformatics-native AI agent skill library enabling local-first, reproducible genomic and population-genetics research workflows built on OpenClaw (871+ stars, MIT License, 2026)

Lean 4 formalizations of ten major advances in mathematics and theoretical computer science, including improved sphere-packing bounds, non-sofic groups, a counterexample to Connes's rigidity conjecture, and quantum parallel repetition; released with the OpenAI paper and reasoning walkthroughs (57+ stars, Apache 2.0)

First open-source agentic AI physicist turning research questions into structured workflows with rigorous verification and multi-step analytical work for long-horizon physics projects; integrates with Claude Code, Codex, Gemini CLI, and OpenCode (804+ stars, Apache 2.0, 2026)

LLM-driven formal proof search system that pairs large language models with Lean verification to solve open mathematics problems; autonomously resolved 9 of 353 Erdős problems and 44 of 492 OEIS conjectures, with proofs and natural-language prose released for combinatorics, optimization, graph theory, algebraic geometry, and quantum optics collaborations (282+ stars, Apache 2.0)

Reinforcement-learning-trained AI agent for treatment reasoning over a universe of 212 biomedical tools, performing multi-step evidence gathering and spawning parallel reasoning branches to reach evidence-grounded clinical decisions (55+ stars, MIT License, 2026)

LLMs as copilots for theorem proving in Lean 4, exposing native tactics (`suggest_tactics`, `search_proof`, `select_premises`) that embed language model inference and premise retrieval directly inside the Lean proof environment, supporting local CTranslate2/CUDA inference as well as remote model APIs for interactive and automated proof search (Caltech & NVIDIA, NeurIPS 2024, 1.2K+ stars)

General-purpose biomedical AI agent integrating LLM reasoning with retrieval-augmented planning and code-based execution to autonomously execute diverse biomedical research tasks and generate testable hypotheses (Stanford SNAP, bioRxiv 2025)

Terminal AI coding assistant with a built-in math formalization engine that converts plain-language math problems into Lean 4 theorems and attempts formal proofs; bundles a local Lean toolchain and WebUI for interactive mathematical reasoning (math-ai-org, 582+ stars, 2026)

End-to-end composable multi-agent framework for automating OpenFOAM-based CFD simulations from natural language prompts, managing meshing, case setup, execution, error correction, and post-processing; achieves 100% success rate on 110 FoamBench tasks with Claude Opus 4.6 through Architect-Input Writer-Runner-Reviewer agent collaboration with RAG-enhanced generation and MCP tool integration (RPI CSML, 242+ stars, MIT License)

Multimodal LLM-based AI agent enabling deep research in spatial transcriptomics, automating analysis and interpretation of spatial gene expression data (Harvard LiuLab, bioRxiv 2025)

LLM agents for working with the SRA (Sequence Read Archive) and associated bioinformatics databases, enabling natural language querying of high-throughput sequencing data and metadata across genomic repositories (Arc Institute, 169+ stars, 2024-2026)

Open-ended AI scientist for computational fluid dynamics that spans literature-grounded ideation, OpenFOAM execution via Foam-Agent, vision-language physics verification of rendered flow fields, source-code modification for new physical models, and figure-grounded LaTeX manuscript writing within a single inspectable workflow (43+ stars, Python)

Fully autonomous medical image segmentation research system that generates complete manuscripts end-to-end from datasets with zero human intervention, beating strongest baselines on 24 of 31 datasets and achieving T1-T2 tier manuscript quality in double-blind evaluations (USTC & Shanghai AI Lab, 2026)

First agentic framework for weather science, pairing an LLM with ZephyrusWorld (a code-execution environment exposing WeatherBench 2 data, geolocation, forecasting, simulation, and climatology tools) and ZephyrusBench (2,230 Q&A pairs across 49 weather-science tasks); outperforms text-only baselines by up to 44.2 percentage points (UC San Diego Rose-STL-Lab, 99+ stars, MIT License, 2026)

Open-source toolkit and benchmark for learning-based theorem proving in Lean, providing programmatic Lean interaction, a 98K+ theorem dataset extracted from 217 Lean projects, and ReProver—the first retrieval-augmented LLM-based theorem prover for Lean—with reproducible training pipelines underpinning much subsequent Lean prover research (Caltech & NVIDIA, NeurIPS 2023 Outstanding Paper, Datasets & Benchmarks)

DeepMind's Olympiad-level geometry theorem prover combining neural language model with symbolic deduction engine, AlphaGeometry2 solves 84% of IMO geometry problems (42/50) at gold-medalist level (Nature 2024)

Strongest open-source automated theorem prover in Lean 4, 8B model matches DeepSeek-Prover-V2-671B at 84.6% MiniF2F, 32B model achieves 90.4% with self-correction, using scaffolded data synthesis and verifier-guided proof refinement (Princeton, 2025)

AI agent for therapeutic reasoning across a universe of tools, achieving 92.1% accuracy in drug reasoning and outperforming GPT-4o by 25.8% (Harvard MIMS, 2025)

DeepSeek's open-source large language model for formal theorem proving in Lean 4, integrating informal and formal mathematical reasoning through recursive subgoal decomposition and reinforcement learning powered by DeepSeek-V3, with open weights and ProverBench evaluation (2025)

AI agent for biological discovery and research automation

Bioinspired multi-agent intelligent graph reasoning system that autonomously traverses ontological knowledge graphs to generate, critique, and refine novel research hypotheses, demonstrated on bio-inspired materials discovery with cross-disciplinary connection mining (MIT Lamm Group, 2024)

Large Language Models for automated open-domain scientific hypotheses discovery (ACL 2024, ICML Best Poster)