How working memory and cognitive modeling functions of the cerebellum contribute to discoveries in mathematics

A theory of how connections between working memory (Science 255 (1992) 556; in: G. Bower (Ed.), The Psychology of Learning and Motivation, Vol. 8, Academic Press, New York, p. 47) and cognitive functions of the cerebellum (Trends Neurosci 16(11) (1993) 448; Curr. Opinion Neurobiol. 9 (1999) 718; Behav. Neurosci. 100 (1986) 443, Behav. Neurosci. 103 (1989) 998) lead to mathematical discovery is presented. It is proposed that (a) patterns of repetitious working memory processing are formed in the cerebellum, and (b) when these cerebellar patterns are subsequently fed back to control processing in working memory, they may become cognized in visuospatial imagery and language as the concepts and axioms that underlie mathematical discovery. It is concluded that a neurophysiological explanation of the cognitive origins of mathematics (L. English (Ed.), Mathematical Reasoning: Analogies, Metaphors, and images, Lawrence Erlbaum, Mahwah, NJ, p. 21, where Mathematics comes from: How the embodied mind brings mathematics into being, Basic Books, New York) can be based upon how conceptual constructions arise from the collaborative interactions of working memory and the cognitive functions of the cerebellum.