First Proof — First Batch

A set of ten research-level math questions to evaluate the capabilities of AI systems to autonomously solve problems that arise naturally in the research process.

Questions are drawn from algebraic combinatorics, spectral graph theory, algebraic topology, stochastic analysis, symplectic geometry, representation theory, lattices in Lie groups, tensor analysis, and numerical linear algebra.

• First_Proof.tex — LaTeX source of the paper, including problem statements
• FirstProofSolutionsComments.pdf — Solutions and commentary (released February 13, 2026)
• Supplementary Files/ — Encrypted archive of original solutions and AI logs
• author-solutions/ — Author solutions to the problems as individual LaTeX and PDF files. (There were all included in the original FirstProofSolutionsComments.pdf but are now separated out for ease of access and readability.)
• FirstProof-Gemini3Pro-answers/ — AI-generated answers from the Gemini 3 Pro model. LaTeX source files were originally provided in Supplementary Files\FirstProof_AI_logs.zip, but we include them here for easier access.
• batch-1\FirstProof-GPT5.2Pro-answers\ — AI-generated answers from the GPT-5.2 Pro model. PDF files were originally provided in Supplementary Files\FirstProof_AI_logs.zip, but we include them here for easier access.

• Paper: https://arxiv.org/abs/2602.05192
• Website: https://1stproof.org
• Community discussion: ICARM Zulip channel
• Contact: contact@1stproof.org

© 2026 First Proof Project