Hexagon

cs.AI — Artificial Intelligence

First Proof Third Batch

Contributed by Mohammed Abouzaid, Nikhil Srivastava, Rachel Ward, Lauren Williams

To assess the ability of current AI systems to correctly solve research-level mathematics problems, we tested several AI systems on our ``third batch'' of ten 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 assessed the AI-generated solutions based on mathematical correctness, quality of exposition, and quality of attribution and citations. 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.

Primarily human-written textHuman understanding: all partsAI systemsbenchmarklarge language models

Oct 14, 2026PDF ↗View work →

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First Proof Third Batch

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math.AC — Commutative Algebra
math.AG — Algebraic Geometry
math.AP — Analysis of PDEs
math.AT — Algebraic Topology
math.CA — Classical Analysis and ODEs
math.CO — Combinatorics
math.CT — Category Theory
math.CV — Complex Variables
math.DG — Differential Geometry
math.DS — Dynamical Systems
math.FA — Functional Analysis
math.GM — General Mathematics
math.GN — General Topology
math.GR — Group Theory
math.GT — Geometric Topology
math.HO — History and Overview
math.IT — Information Theory
math.KT — K-Theory and Homology
math.LO — Logic
math.MG — Metric Geometry
math.NA — Numerical Analysis
math.NT — Number Theory
math.OA — Operator Algebras
math.OC — Optimization and Control
math.PR — Probability
math.QA — Quantum Algebra
math.RA — Rings and Algebras
math.RT — Representation Theory
math.SG — Symplectic Geometry
math.SP — Spectral Theory
math.ST — Statistics Theory
cs.AI — Artificial Intelligence
cs.CC — Computational Complexity
cs.CG — Computational Geometry
cs.DM — Discrete Mathematics
cs.DS — Data Structures and Algorithms
cs.FL — Formal Languages and Automata Theory
cs.IT — Information Theory
cs.LO — Logic in Computer Science
cs.MS — Mathematical Software
cs.NA — Numerical Analysis
cs.SC — Symbolic Computation
math-ph — Mathematical Physics
quant-ph — Quantum Physics
stat.TH — Statistics Theory