AI for Mathematics: A Cognitive Science Perspective

TL;DR

This position paper argues that to achieve human- or superhuman-level mathematical AI, researchers should incorporate cognitive-science insights into sample-efficient learning, representation and world-models, goal-directed planning, resource-aware design, and communication. It outlines how core knowledge, conceptual representations, and world models support mathematical reasoning, and why planning, explanations, and multi-agent collaboration are essential. The authors call for cross-disciplinary collaboration, accessible forums, and novel platforms (e.g., a 'Mechanical Turk for mathematics') to accelerate progress and refine our understanding of mathematical cognition. The work highlights the potential of cognitive-science-guided AI to not only advance mathematics but also illuminate the nature of human cognitive feats in mathematics.

Abstract

Mathematics is one of the most powerful conceptual systems developed and used by the human species. Dreams of automated mathematicians have a storied history in artificial intelligence (AI). Rapid progress in AI, particularly propelled by advances in large language models (LLMs), has sparked renewed, widespread interest in building such systems. In this work, we reflect on these goals from a \textit{cognitive science} perspective. We call attention to several classical and ongoing research directions from cognitive science, which we believe are valuable for AI practitioners to consider when seeking to build truly human (or superhuman)-level mathematical systems. We close with open discussions and questions that we believe necessitate a multi-disciplinary perspective -- cognitive scientists working in tandem with AI researchers and mathematicians -- as we move toward better mathematical AI systems which not only help us push the frontier of the mathematics, but also offer glimpses into how we as humans are even capable of such great cognitive feats.