The Role of General Intelligence in Mathematical Reasoning

TL;DR

This paper explores how general intelligence underpins mathematical reasoning, proposing a theoretical framework for learning object representations that include mathematical objects, and demonstrates its impact on understanding natural numbers.

Contribution

It introduces an abstract theoretical framework for learning object representations that treats mathematical objects equally with non-mathematical ones.

Findings

A new philosophical and cognitive context for mathematical reasoning.

A case study linking object integration to natural number conception.

Insights into the role of general intelligence in mathematical understanding.

Abstract

Objects are a centerpiece of the mathematical realm and our interaction with and reasoning about it, just as they are of the physical one (if not more). And humans' mathematical reasoning must ultimately be grounded in our general intelligence. Yet in contemporary cognitive science and A.I., the physical and mathematical domains are customarily explored separately, which allows for baking in assumptions for what objects are for the system - and missing potential connections. In this paper, I put the issue into its philosophical and cognitive context. I then describe an abstract theoretical framework for learning object representations, that makes room for mathematical objects on par with non-mathematical ones. Finally, I describe a case study that builds on that view to show how our general ability for integrating different aspects of objects effects our conception of the natural numbers.