[{"data":1,"prerenderedAt":4},["ShallowReactive",2],{"X1yJbuPeZW":3},"[![](logo.svg)](https://axiommath.ai/)\n\n# AxiomProver at Putnam 2025\n\nPutnam 2025, the world's hardest college-level math test, ended December 6th. By\nthe end of the competition, AxiomProver had solved 8 out of 12 problems. In the\nfollowing days, it solved the remaining 4. AxiomProver is an autonomous\nmulti-agent ensemble theorem prover for Lean 4.21.0, developed by [Axiom\nMath](https://axiommath.ai/).\n\nThis repository contains the solutions generated by AxiomProver. Asterisk\ndenotes solutions found after the competition.\n\n1. **2025 A1**: [[source]](Putnam2025/A1/solution.lean), [[graph]](https://axiommath.github.io/Putnam2025/A1/). Prover: 110 minutes, 7M tokens. Proof: 652 lines, 23 theorems, 561 tactics.\n2. **2025 A2**: [[source]](Putnam2025/A2/solution.lean), [[graph]](https://axiommath.github.io/Putnam2025/A2/). Prover: 185 minutes, 6M tokens. Proof: 556 lines, 26 theorems, 581 tactics.\n3. **2025 A3**: [[source]](Putnam2025/A3/solution.lean), [[graph]](https://axiommath.github.io/Putnam2025/A3/). Prover: 165 minutes, 8M tokens. Proof: 1,333 lines, 78 theorems, 1,701 tactics.\n4. **2025 A4**: [[source]](Putnam2025/A4/solution.lean), [[graph]](https://axiommath.github.io/Putnam2025/A4/). Prover: 107 minutes, 8M tokens. Proof: 960 lines, 32 theorems, 1,107 tactics.\n5. **2025 A5***: [[source]](Putnam2025/A5/solution.lean), [[graph]](https://axiommath.github.io/Putnam2025/A5/). Prover: 518 minutes, 9.1M tokens. Proof: 2,054 lines, 52 theorems, 3,074 tactics.\n6. **2025 A6***: [[source]](Putnam2025/A6/solution.lean), [[graph]](https://axiommath.github.io/Putnam2025/A6/). Prover: 259 minutes, 16M tokens. Proof: 588 lines, 28 theorems, 670 tactics.\n7. **2025 B1**: [[source]](Putnam2025/B1/solution.lean), [[graph]](https://axiommath.github.io/Putnam2025/B1/). Prover: 270 minutes, 7M tokens. Proof: 1,386 lines, 49 theorems, 1,841 tactics.\n8. **2025 B2**: [[source]](Putnam2025/B2/solution.lean), [[graph]](https://axiommath.github.io/Putnam2025/B2/). Prover: 65 minutes, 2M tokens. Proof: 417 lines, 28 theorems, 325 tactics.\n9. **2025 B3**: [[source]](Putnam2025/B3/solution.lean), [[graph]](https://axiommath.github.io/Putnam2025/B3/). Prover: 43 minutes, 2.9M tokens. Proof: 340 lines, 11 theorems, 422 tactics.\n10. **2025 B4***: [[source]](Putnam2025/B4/solution.lean), [[graph]](https://axiommath.github.io/Putnam2025/B4/). Prover: 112 minutes, 249K tokens. Proof: 1,061 lines, 23 theorems, 1,433 tactics.\n11. **2025 B5**: [[source]](Putnam2025/B5/solution.lean), [[graph]](https://axiommath.github.io/Putnam2025/B5/). Prover: 354 minutes, 18M tokens. Proof: 1,495 lines, 66 theorems, 1,967 tactics.\n12. **2025 B6***: [[source]](Putnam2025/B6/solution.lean), [[graph]](https://axiommath.github.io/Putnam2025/B6/). Prover: 494 minutes, 21M tokens. Proof: 1,019 lines, 30 theorems, 1,052 tactics.\n\nTo compile and verify these solutions using\n[SafeVerify](https://github.com/GasStationManager/SafeVerify/tree/e3c776dc864aeac04f6c1a7af925205f43d96a92?tab=readme-ov-file#safeverify),\nrun:\n\n```bash\n$ lake run verify\nVerifying A1 solution ... ✅\nVerifying A2 solution ... ✅\nVerifying A3 solution ... ✅\nVerifying A4 solution ... ✅\nVerifying A5 solution ... ✅\nVerifying A6 solution ... ✅\nVerifying B1 solution ... ✅\nVerifying B2 solution ... ✅\nVerifying B3 solution ... ✅\nVerifying B4 solution ... ✅\nVerifying B5 solution ... ✅\nVerifying B6 solution ... ✅\n```\n\n\n## License\n\nThis repository is licensed under the MIT License. See [LICENSE](LICENSE) for\ndetails.\n\n\n## The Team\n\n*Prover leads:* Chris Cummins, GasStationManager.\n\n*Engineering:* Dejan Grubisic, Leopold Haller, Andranik Kurghinyan, Aram Markosyan, Manooshree Patel, Gaurang Pendharkar, Vedant Rathi, Alex Schneidman, Volker Seeker, Ishan Sinha, Jimmy Xin.\n\n*Mathematics:* Evan Chen, Ben Eltschig, Kenny Lau, Ken Ono, Jujian Zhang.\n\n*Leadership:* Carina Hong, Hugh Leather, Shubho Sengupta.\n",1780846756546]