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)
• Autoconvolution: Strengthened bounds for f*f type operations
• Sidon sets: Asymptotic bounds on g-Sidon set sizes in {1,...,n}
• Szarek-type: Optimal balanced inequalities for norm comparisons

Prompt Templates for LLM Collaboration

Given [mathematical object], find the tightest known/provable bound for [quantity].
Provide: (1) conjectured bound, (2) heuristic justification, (3) known related results.

Improve the following inequality: [current inequality].
Suggest: (1) tighter constant, (2) additional conditions, (3) equality cases.

Verification Checklist

• Conjecture stated precisely with all assumptions
• Numerical evidence for small cases (n=1,2,3,...)
• Asymptotic behavior matches intuition
• Known special cases are recovered
• Proof technique identified and validated
• Equality/ extremal cases characterized
• Comparison with existing literature

Error Modes

AI Hallucination in Math

• LLM may generate plausible-looking but false statements
• Always verify claims independently
• Check references the LLM cites actually exist

Overfitting to Examples

• LLM may generalize from limited numerical examples
• Test conjectures across different parameter regimes
• Look for counterexamples systematically

Suboptimal Bounds

• AI often finds loose bounds first
• Iterate: "Can this bound be improved? What prevents it?"
• Compare with known results in literature

Resources

• Paper: "Grokability in five inequalities" (arXiv:2605.05193)
• Authors: Paata Ivanisvili, Xinyuan Xie
• Categories: math.PR, cs.AI, math.AP, math.CA, math.FA