Ramanujan Challenge Results: AI-Assisted Evaluation Pipeline for Multi-Format Proofs

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 The Ramanujan Challenge is a benchmark comprised of research-level problems in number theory, including unpublished results and open conjectures.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.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-29
DOI
https://doi.org/10.48550/arxiv.2610.40551
Primary Topic
Mathematics, Computing, and Information Processing
Type
preprint
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preprint

Ramanujan Challenge Results: AI-Assisted Evaluation Pipeline for Multi-Format Proofs

Elyasheev Leibtag, Ashvni Narayanan, Tali Monderer, Alan Sorani et al.
arXiv (Cornell University)
Mathematics, Computing, and Information Processing
preprint

Ramanujan Challenge Results: AI-Assisted Evaluation Pipeline for Multi-Format Proofs

Elyasheev Leibtag, Ashvni Narayanan, Tali Monderer, Alan Sorani, Rotem Kalisch, Michael Shalyt, John M. Campbell, Shachar Weinbaum, Carsten Schneider, Hila Barkan, Ido Kaminer
preprint en

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.

arXiv (Cornell University)
Mathematics, Computing, and Information Processing
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Ramanujan Challenge Results: AI-Assisted Evaluation Pipeline for Multi-Format Proofs — Elyasheev Leibtag, Ashvni Narayanan, et al. · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS