[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85130-en":3,"doc-seo-85130-105":28,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":13,"seo_description":14,"update_tm":26,"read_time":27},85130,2336464648746,"Skyler","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","The Ramanujan Challenge for AI","The Ramanujan Machine Group proposes a benchmark for evaluating current AI mathematical abilities using explicit formulas for fundamental constants. Each problem is concrete enough for numerical checking to arbitrary precision, while corresponding proofs may demand non-obvious techniques. The set includes two categories: formulas with proofs known to the authors (initially encrypted) and formulas not yet proven. The introduction motivates the benchmark through the need for contamination-resistant, authentic, research-level questions.","arXiv :2607 .09721v1 [math .HO] 27 Jun 2026  \nTHE RAMANUJAN CHALLENGE FOR AI  \nRamanujan Machine Group*  \nABSTRACT  \nTo help evaluate the mathematical skills of current AI systems, we present a set of formulas for fundamental mathematical constants. These problems are attractive for AI evaluation because they are concrete and can be checked numerically to arbitrary precision, yet proving them may require non-obvious mathematics. Mathematical constants such as π , e, Catalan’s constant, and special values of the Riemann zeta function have fascinated mathematicians for centuries. The search for formulas evaluating mathematical constants has produced some of the most beautiful mathematics in the field, especially in cases that yield irrationality proofs or fast convergence rates. Ramanujan’s legacy is emblematic of this tradition. The list we provide contains two types of problems: formulas whose proofs are known to the authors but will remain encrypted for a short initial period; and formulas that are not yet proven. We are curious to see the achievements of AI in both cases.  \n\n| Problem | Name | Contributor |\n| --- | --- | --- |\n| 2.1 | Polynomial continued fraction for π | Michael Shalyt 1 |\n| 2.2\u003Cbr>2.3 | Euler’s constant γ as an Apéry limit\u003Cbr>The sum π + e as an Apéry limit | Rotem Kalisch 1 |\n| 2.4 | A series of harmonic numbers converging to a polylogarithm combined with zeta values | Carsten Schneider2 |\n| 2.5\u003Cbr>2.6 | Efficient rational approximation of Catalan’s constant GA series for ζ(2) + ζ(3) | Hila Barkan 1 |\n| 2.7\u003Cbr>2.8 | Efficient four-term recurrence for ζ(2) + ζ(3) Very fast rational approximation of √10005/π | Elyasheev Leibtag3 |\n| 3.1 | An integral over knot polynomial roots expressing π 2 | John Campbell4 |\n| 3.2 | Optimality of Apéry’s irrationality-measure bound for ζ(3) | Shachar Weinbaum 1 |\n\n\n| Role | Name | Email |\n| --- | --- | --- |\n| Proof Collection | Tali Monderer 1 | [talimon@campus.technion.ac.il](talimon@campus.technion.ac.il) |\n| Validation | Ashvni Narayanan 1 | [ashvni.n@campus.technion.ac.il](ashvni.n@campus.technion.ac.il) |\n| Principal Investigator | Ido Kaminer 1 | [kaminer@technion.ac.il](kaminer@technion.ac.il) |\n\n1Ramanujan Machine Group, Technion, Haifa, Israel.  \n2Research Institute for Symbolic Computation, Johannes Kepler Universität Linz, Linz, Austria.  \n3Department of Mathematics, Computer Science and Statistics, Ghent University, Ghent, Belgium.  \n4Department of Mathematics and Statistics, Toronto Metropolitan University, Toronto, Canada.  \n*[ramanujan.machine@gmail.com](ramanujan.machine@gmail.com)  \n1 INTRODUCTION  \nRecent progress in AI for mathematics has made quantitative evaluation increasingly urgent. We increasingly need university-level and research-level questions that test whether AI systems can contribute to genuine mathematical work. Several recent benchmarks address this need from different directions. RealMath and LemmaBench study mathematical questions drawn from research papers and mathematical forums [Zhang et al. 2025; Peyronnet et al. 2026] . A central difficulty  \nis contamination: if a problem or its solution appears in the AI training data, success may reflect retrieval rather than reasoning. One response is to perturb existing problems, as in GSM-Symbolic [Mirzadeh et al. 2025] and ASyMOB [Shalyt et al. 2025], reducing dependence on uncontaminated original questions. A stronger response is to use authentic research problems that have not yet appeared publicly. FrontierMath [Glazer et al. 2024], Riemann-Bench [Garre et al. 2026], and part of Humanity’s Last Exam [Phan et al. 2025] emphasize original difficult questions with structured verification, while First Proof [Abouzaid et al. 2026] focuses on unpublished research problems whose answers were known to experts.  \nThe present manuscript follows the spirit of First Proof, but concentrates on a more focused domain with a long mathematical tradition: explicit formulas involving fundamental mathematic","cbCaitevIROzWCgo","https://ap.wps.com/l/cbCaitevIROzWCgo","pdf",252952,1,"English","en",105,"# Introduction\n# Collected Problems\n## Formulas for Special Constants\n## Integral and Irrationality Results","[{\"question\":\"What is the goal of the Ramanujan Challenge for AI?\",\"answer\":\"To evaluate the mathematical skills of current AI systems using formulas for fundamental mathematical constants, with tasks that can be numerically verified yet may require difficult proofs.\"},{\"question\":\"How are the problems in this challenge classified?\",\"answer\":\"The collection includes two types: formulas whose proofs are known to the authors but remain encrypted for an initial period, and formulas that are not yet proven.\"},{\"question\":\"Why are numerical checks central to these AI evaluation problems?\",\"answer\":\"Candidate formulas for constants can often be tested to thousands of digits, enabling immediate and objective validation, while proofs may still require specialized mathematical 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is the goal of the Ramanujan Challenge for AI?","Question",{"text":74,"@type":75},"To evaluate the mathematical skills of current AI systems using formulas for fundamental mathematical constants, with tasks that can be numerically verified yet may require difficult proofs.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How are the problems in this challenge classified?",{"text":79,"@type":75},"The collection includes two types: formulas whose proofs are known to the authors but remain encrypted for an initial period, and formulas that are not yet proven.",{"name":81,"@type":72,"acceptedAnswer":82},"Why are numerical checks central to these AI evaluation problems?",{"text":83,"@type":75},"Candidate formulas for constants can often be tested to thousands of digits, enabling immediate and objective validation, while proofs may still require specialized mathematical 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