Why Machines Cannot Learn Mathematics, Yet

TL;DR

This paper investigates the limitations of current machine learning techniques in understanding mathematical language within scientific documents and discusses what is needed for machines to learn mathematics effectively.

Contribution

It demonstrates the inadequacy of existing text embedding methods for mathematical content and explores the missing components necessary for machines to learn mathematics.

Findings

Current ML embeddings fail to capture mathematical semantics

Mathematical language's ambiguity hinders machine understanding

Identifies key aspects needed for machines to learn mathematics

Abstract

Nowadays, Machine Learning (ML) is seen as the universal solution to improve the effectiveness of information retrieval (IR) methods. However, while mathematics is a precise and accurate science, it is usually expressed by less accurate and imprecise descriptions, contributing to the relative dearth of machine learning applications for IR in this domain. Generally, mathematical documents communicate their knowledge with an ambiguous, context-dependent, and non-formal language. Given recent advances in ML, it seems canonical to apply ML techniques to represent and retrieve mathematics semantically. In this work, we apply popular text embedding techniques to the arXiv collection of STEM documents and explore how these are unable to properly understand mathematics from that corpus. In addition, we also investigate the missing aspects that would allow mathematics to be learned by computers.