[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81673-en":3,"doc-seo-81673-105":30,"detail-sidebar-cat-0-en-105":91},{"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},81673,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","First Proof Second Batch June 10, 2026 Research Mathematics AI Benchmark","First Proof Second Batch evaluates how effectively current AI systems solve research-level mathematics problems. Ten problems spanning computability theory, discrete geometry, discrete probability, metric geometry, stochastic PDE, lattice theory, combinatorial topology, matroids and tropical geometry, algebraic combinatorics, and von Neumann algebras were collected from ongoing contributor research. The document presents problem selection, testing schedule, grading process, and results, and links supplementary materials including human solutions, AI-generated solutions, and referee reports and logs.","arXiv :2606 . 18 1 19v 1 [ cs .AI] 16 Jun 2026  \nFirst Proof Second Batch  \nJune 10, 2026  \nMohammed Abouzaid 1 Nikhil Srivastava2  \nStanford University University of California, Berkeley  \nRachel Ward3 Lauren Williams4  \nUniversity of Texas at Austin Harvard University  \nProblem Contributors:  \n1. Dariusz Kalociński, Polish Academy of Sciences5 ; Theodore A. Slaman, UC Berkeley6  \n2. Richard Schwartz, Brown University7  \n3. Aleksa Milojević, ETHZürich8 ; Benny Sudakov, ETHZürich9  \n4. Larry Guth, MIT 10  \n5. Oleg Butkovsky, Weierstrass Institute 11 ; Jonathan Mattingly, Duke University12 ; Lorenzo Zambotti, Sorbonne Université13  \n6. Joshua Evan Greene, Boston College 14 ; Duncan McCoy, Université du Québec à Montréal 15  \n7. Sucharit Sarkar, UCLA 16  \n8. Sam Payne, University of Michigan 17 ; Jidong (Jayden) Wang, University of Michigan 18  \n9. Sylvie Corteel, UC Berkeley 19 ; John Lentfer, UC Berkeley20  \n10. Srivatsav Kunnawalkam Elayavalli, University of Maryland21  \nAbstract  \nTo assess the ability of current AI systems to correctly solve research-level mathematics problems, we tested several AI systems on a set often problems in a broad range of mathematical fields; these problems arose naturally in the research process of the contributors. This document includes the problems, our methodology, and the results of our testing. We provide links to supplementary documents including the human solutions, the AI-generated solutions, and the referee reports and logs for the AI-generated solutions.  \nContents  \n1 Introduction 3  \n1.1 What is mathematics? ................................. 3  \n1.2 Summary of Methodology .............................. 4  \n1.3 Summary and Discussion of Results ......................... 4  \n1.4 What comes next . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6  \n2 Methodology 7  \n2.1 Problem Selection (March to May, 2026) ....................... 7  \n2.2 Testing (May 28-June 1, 2026) ........................... 8  \n2.3 Grading (June 4-8, 2026) ............................... 10  \n2.4 Funding ........................................ 11  \n3 Problems 12  \n3.1 Problem 1: Ted Slaman and Dariusz Kalociński (computability theory) ...... 12  \n3.2 Problem 2: Richard Schwartz (discrete geometry) .................. 13  \n3.3 Problem 3: Aleksa Milojević and Benny Sudakov (discrete probability) ...... 14  \n3.4 Problem 4: Larry Guth (metric geometry) ...................... 15  \n3.5 Problem 5: Oleg Butkovsky, Jonathan C. Mattingly, and Lorenzo Zambotti (stochastic PDE) ........................................ 15  \n3.6 Problem 6: Joshua Greene and Duncan McCoy (lattice theory) ........... 17  \n3.7 Problem 7: Sucharit Sarkar (combinatorial topology) ................ 18  \n3.8 Problem 8: Sam Payne and Jidong (Jayden) Wang (matroids and tropical geometry) 19  \n3.9 Problem 9: Sylvie Corteel and John Lentfer (algebraic combinatorics) ....... 19  \n3.10 Problem 10: Srivatsav Kunnawalkam Elayavalli (von Neumann algebras) ..... 20  \n4 AI Systems Tested 21  \n4.1 System A: IMProofBench ProofCouncil ....................... 21  \n4.2 System B: UCLA Moonshot Harness ......................... 21  \n4.3 System C: OpenAI ChatGPT 5.5 Pro ......................... 22  \n4.4 System D: Princeton Momus ............................. 22  \n5 Results and Costs 22  \n5.1 Problem 1 ....................................... 22  \n5.2 Problem 2 ....................................... 26  \n5.3 Problem 3 ....................................... 27  \n5.4 Problem 4 ....................................... 28  \n5.5 Problem 5 ....................................... 28  \n5.6 Problem 6 ....................................... 29  \n5.7 Problem 7 ....................................... 30  \n5.8 Problem 8 ....................................... 31  \n5.9 Problem 9 ....................................... 32  \n5.10 Problem 10 ...................................... 33  \n6 Supplementary documents 34  \n1 Introduction  \nThe goal of our ongoing First Proof","cbCaid1vCOruDUY8","https://ap.wps.com/l/cbCaid1vCOruDUY8","pdf",561949,3,1,36,"English","en",105,"# Introduction\n## Summary of Methodology\n## Summary and Discussion of Results\n## What comes next\n# Methodology\n## Problem Selection (March to May, 2026)\n## Testing (May 28–June 1, 2026)\n## Grading (June 4–8, 2026)\n## Funding\n# Problems\n## Problem 1–Problem 10\n# AI Systems Tested\n## System A–System D\n# Results and Costs\n## Problem-wise results\n# Supplementary documents","[{\"question\":\"What is the purpose of the First Proof Second Batch?\",\"answer\":\"To measure the ability of current AI systems to correctly solve research-level mathematics problems drawn from active research by the project’s contributors.\"},{\"question\":\"How were the AI systems tested and graded?\",\"answer\":\"The document outlines a timeline covering problem selection, an AI testing window, and a grading period, with results compiled problem by problem.\"},{\"question\":\"What additional materials are provided alongside the problems and results?\",\"answer\":\"Supplementary documents include human solutions, AI-generated solutions, and referee reports and logs for the AI-generated 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