mathlib

Visualizing the network of math theories.

A formal verification of Linear PCP SNARKs.

The Math Algorithm

Riemann Hypothesis in Lean

Tensor-network theory, formalized in Lean 4: the fundamental theorem of matrix product states, canonical forms, parent Hamiltonians, matrix-product density operators, and projected entangled pair states, building on the QICLean quantum-information library

Formally verified mathematical finance in Lean 4. Black–Scholes/Greeks/PDE, Itô calculus, FTAP/Girsanov, CRR→BS convergence, Merton jump-diffusion.

OpenATP is an open-source Python package providing a common interface for Automated Theorem Proving (ATP)

Workspace-first orchestration for long-horizon Lean 4 formalization agents.

A Lean 4 + Mathlib proof service for the agent working on your code

The intent of this repository is to build a database of control theoretic proofs in lean.

A Lean 4 library for formal linguistics.

C library to work with complex numbers.

The open workbench for AI safety, made formal. Turn safety questions into machine-checked Lean proofs — a shared launchpad where researchers and AI agents build provable safety together.

Lean4 kernel for synthetic formalization and discovery of statistical learning theory. First and complete formalization of the 5 way fundamental theorem. Typed premise + human-guided, AI-driven proof search across PAC, online, and Gold paradigms. The infrastructure forced by the types produced original mathematics.

Lean 4 formalization of Leray–Hopf weak solution existence for the three-dimensional incompressible Navier–Stokes equations.

Trusted AI mathematics workbench: ProblemContract to Attempt to verified proof/counterexample bundles with SymPy and Lean evidence gates.

Interactive Lean 4 + Mathlib formalization from a Claude Code conversation

Connected bipartite graphs of degeneracy exactly r with ex(n,H) ≥ c·n^(2−1/r+1/(28r²)), refuting the Erdős–Simonovits degeneracy conjecture (Erdős problem #146) for every r ≥ 2, with the exact limits of the method. Machine-checked in Lean 4.

From Chirality to the Standard Model. Paper, LaTeX source, and an executable notebook with exact verification and Lean proofs.

Semantic search for PhysLib — the formal Lean 4 physics library. Find theorems and definitions using plain English.