Nature of Mathematics through the Lens of Cognitive Research

Abstract

The article has the goal to shed light on the sources of mathematics as a science, its conceptual foundation and “scaffolding” constructions. We claim that the starting point of the development of mathematics refers to the phenomenon of “numeros­ity”, which enables living beings instantly perceive and distinguish small quanti­ties of objects. A person has two cognitive systems associated with mathematical abilities, one of which involves an approximate and non-symbolical evaluation of quantities, and another symbolic and linguistic format for presenting digital information. Complex mathematical structures formed as the result of the sim­plest operations that provided by these systems. Quite a number of empirical facts revealed in modern neuroscience relate to a durable discussion between Re­alism (Platonism) and Anti-Realism (Nominalism) in the philosophy of mathe­matics. This discussion has a direct impact on the comprehension of nature and foundations of mathematical knowledge. The results of empirical studies in the neuroscience of the traits of mathematical cognition speak in favor of un­derstanding the nature of mathematics in the line of Anti-Realism, which insists on the emergence and making of basic mathematical concepts within the context of human activity. The author stress the key role of culture in the emergence and development of mathematical thinking, which has the opposite significant effect on the progress of culture. The importance of comprehension of the “sense of number” phenomenon a foundation of mathematical knowledge in terms of the Kantian research program in modern neuroscience and ideas close to intu­itionism of L.E.J. Brouwer stressed.