Mathematics for and by human cognition: A resource-rational search for bottlenecks in problem-solving

Human cognitive constraints are generally viewed as limiting factors in problem-solving. We argue that these constraints can instead play a critical role in driving advances in mathematics and beyond. We propose a theory of mathematical abstraction as a resource-rational search for bottlenecks in problem-solving. Bottlenecks arising from cognitive constraints create pressure to restructure existing knowledge, potentially giving rise to novel formalisms with applications beyond the problems that originally motivated them. Drawing on episodes from the history of mathematics, we illustrate how such bottlenecks can drive the development of novel abstractions and examine how cognitive constraints and affective responses shape this process. Finally, we discuss the implications of this account for machine mathematical discovery and argue that incorporating human-like constraints may facilitate the discovery of useful mathematical abstractions.