Evolutionary Foundations of Mathematics

Abstract: We propose a simple cognitive model where qualitative and quantitative com- parisons enable animals to identify objects, associate them with their properties held in memory and make naive inference. Simple notions like equivalence re- lations, order relations are used. We then show that such processes are at the root of human mathematical reasoning by showing that the elements of totally ordered sets satisfy the Peano axioms. The process through which children learn counting is then formalized. Finally association is modeled as a Markov process leading to a stationary distribution.