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mathtensor/ai4math-putnam2025

★ 15LeanAudience · researcherComplexity · 4/5ActiveLicenseSetup · moderate

TLDR

Lean 4 formal proofs for all twelve 2025 Putnam Competition problems, machine-verified against Mathlib and pinned to Lean 4.27.0.

Mindmap

mindmap
  root((AI4Math Putnam2025))
    Inputs
      Putnam 2025 problems
      Mathlib library
      Lean 4.27
    Outputs
      problem.lean per task
      solution.lean per task
      Verified proofs
    Use Cases
      Study formal math proofs
      Benchmark AI provers
      Reuse lemmas in Lean projects
    Tech Stack
      Lean 4
      Mathlib

Things people build with this

USE CASE 1

Study AI-generated formal proofs for each of the twelve 2025 Putnam problems

USE CASE 2

Benchmark a new theorem prover against MathTensor's solution lengths and runtimes

USE CASE 3

Reuse formal statements and lemmas in other Lean 4 projects via Mathlib

Tech stack

LeanMathlib

Getting it running

Difficulty · moderate Time to first run · 1h+

Requires Lean 4.27.0 and Mathlib via elan or lake, and replaying the harder proofs can take a long time to compile.

MIT license: anyone can use, modify, and redistribute the code as long as the copyright notice is kept.

In plain English

This repository, from a team called MathTensor, contains formal mathematical proofs for all twelve problems from the 2025 William Lowell Putnam Mathematical Competition. The Putnam is an annual undergraduate math contest known for being very difficult, and the team claims their AI system produced complete, machine-verified solutions to every problem on the exam. The proofs are written in Lean 4, which is a programming language designed for stating mathematics in a precise, computer-checkable way. Each solution uses Mathlib, a large community library of formalized math that Lean programs can build on. Because the proofs are checked by software rather than only by humans, the claim that each problem is solved can be verified by anyone who downloads the repo and runs Lean on it. The environment is pinned to Lean version 4.27.0. The folder layout is simple. There is one directory per problem, named A1 through A6 and B1 through B6, and each directory holds two files: problem.lean with the formal statement of the problem, and solution.lean with the full proof. A summary table in the README lists how long each proof took to produce, how many lines it has, and how many supporting lemmas or theorems it uses. The hardest problem, A5, runs to 857 lines and took over 1300 minutes. The README also notes that some problem statements were adapted from other Lean formalizations released under the MIT license, with attribution kept in file headers. The repo itself is released under the MIT license, and the authors state they have no affiliation with the Mathematical Association of America.

Copy-paste prompts

Prompt 1
Build a Lean 4 4.27 project that imports this repo and re-checks every proof in CI
Prompt 2
Summarize the proof strategy in A5 solution.lean and explain why it runs to 857 lines
Prompt 3
Compare the lemma counts in this repo's README table against a baseline Mathlib tactic search
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Generated 2026-05-22 · Model: sonnet-4-6 · Verify against the repo before relying on details.