Math for AI safety: an invitation for mathematicians

2026-09-14

AI Summary

本文呼吁数学家通过逻辑、概率论、代数和分析等数学分支解决AI的可理解性、可控性和合作性问题。

Abstract

Artificial intelligence threatens to outrun human understanding and control. New mathematics is needed to design AI that is legible, steerable, and cooperative with humanity. I organize this invitation by mathematical field, so you can turn straight to your own: logic and game theory for cooperation; probability for agency and world-models; algebra and representation theory for learned features; analysis and geometry for generalization and training dynamics. Each section ends with an open problem that is accessible to a working mathematician with no prior experience in AI safety.

Problem

• Artificial Intelligence
• Human Control
• Mathematics
• AI Safety
• Cooperation

Innovation

• logic and game theory
• probability
• algebra and representation theory
• analysis and geometry