Ramanujan Challenge Results: AI-Assisted Evaluation Pipeline for Multi-Format Proofs
Organizations: Ramanujan Machine Group, Technion, Haifa, Israel. · Department of Mathematics, Computer Science and Statistics, Ghent University, Ghent, Belgium. · Research Institute for Symbolic Computation, Johannes Kepler Universität Linz, Linz, Austria. · Department of Mathematics and Statistics, Toronto Metropolitan University, Toronto, Canada.
Abstract
As AI's mathematical capabilities rapidly improve, meaningful benchmarks are shifting from university-level problems and math olympiads to research-level mathematics. The Ramanujan Challenge is a benchmark comprised of research-level problems in number theory, including unpublished results and open conjectures. It presented concrete formulas for mathematical constants whose correctness can be checked numerically, while their proofs may require non-obvious mathematics. Here, we analyze the Challenge submissions, measuring the relative success of different AI models, Computer Algebra Systems (CAS), and formal tools. We find correct submissions that are conceptually distinct from the official solutions, and a proof of one of the published open conjectures. Evaluating the submissions exposed a second challenge: judging complex proofs reliably at scale. We introduce an AI-assisted evaluation pipeline for natural language proofs, CAS code, and Lean formalizations that assesses semantic and logical correctness. Compared with the conventional one-shot LLM judgment, our pipeline reduces false-positive verdicts on natural language proofs from 23% to 6% and improves judgment accuracy on supporting code from 46% to 58%. This approach provides a methodology for evaluating research-level mathematics at scale, with potential applications across mathematics and AI for science.
Figures & tables
| Natural language proof | Computer Algebra System/Lean | |||||||
| Question | Number of submissions | Correct | Partial | Major issues | Correct | Partial | Major issues | No code |
| 1 | 23 | 11 | 6 | 6 | 7 | 11 | 3 | 2 |
| 2 | 16 | 7 | 3 | 6 | 2 | 8 | 4 | 2 |
| 3 | 19 | 10 | 3 | 6 | 5 | 7 | 5 | 2 |
| 4 | 19 | 4 | 7 | 8 | 1 | 13 | 3 | 2 |
| 5 | 11 | 2 | 2 | 7 | 0 | 5 | 4 | 2 |
Mathematical Reasoning Benchmarks
Mathematical reasoning benchmarks test whether AI systems can solve, explain, and verify problems across mathematical levels, formats, and languages.
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