ai-math-discovery

name

ai-math-discovery

description

AI-assisted mathematical discovery methodology. Use when: (1) collaborating with LLMs to generate mathematical conjectures, inequalities, bounds, or proofs; (2) verifying AI-generated mathematical results; (3) structuring human-AI mathematical research workflows; (4) exploring AI's role in mathematical research; (5) analyzing mathematical inequality patterns (Gaussian perimeter, moment comparison, autoconvolution, Sidon sets, Szarek's inequality). Trigger words: AI math discovery, Grokability, mathematical conjecture, inequality bound, AI-assisted proof, 数学发现, AI数学, 不等式.

AI-Assisted Mathematical Discovery

Overview

Methodology for collaborative mathematical discovery between humans and LLMs, based on the "Grokability in five inequalities" framework (arXiv:2605.05193). AI generates mathematical conjectures and bounds; humans verify and formalize proofs.

Core Workflow

Phase 1: Conjecture Generation

• Frame the mathematical problem with precise definitions
• Ask LLM to propose conjectures with supporting intuition
• Request numerical/experimental evidence for conjectures
• Iterate: refine conjecture based on LLM reasoning

Phase 2: Verification

• Independently verify all AI-generated claims
• Check edge cases and boundary conditions
• Formalize proofs using standard mathematical rigor
• Identify gaps where AI reasoning was incomplete

Phase 3: Publication

• Structure results in standard mathematical paper format
• Credit AI collaboration transparently
• Include both conjecture and proof

Key Mathematical Patterns

Inequality Discovery Patterns

• Gaussian perimeter bounds: Maximize perimeter of convex sets in R^n
• Moment comparison: L2-L1 inequalities on discrete domains (Hamming cube)
• : Strengthened bounds for f*f type operations