The perception of number: towards a topological approach Marco Bacchin Abstract: It has been suggested that our understanding of numbers is rooted in the perception of numerosities. A capacity, that of assessing the approximate number of objects in a scene, which is believed to be available also to other species. The present work fits within the current debate on whether a ‘true sense of number’ is perceptually available. We will provide a comprehensive review of the behavioral, neurophysiological, and computational findings that seems to support the claim, and the limitations of the approaches taken. Importantly, we will argue that without a clear stated definition of numerosity, it’s impossible to answer the question. We will therefore provide a formal definition of numerosity, and show how the framework of tolerance homology might be used to cast light on the debate.