The Role of General Intelligence in Mathematical Reasoning
This work addresses the problem of integrating mathematical and physical reasoning in AI systems, which is incremental as it builds on existing cognitive science concepts.
The paper tackles the separation between physical and mathematical reasoning in AI by proposing a theoretical framework for learning object representations that treats mathematical objects equally with non-mathematical ones, and demonstrates through a case study how general intelligence influences the conception of natural numbers.
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.