Cerebral underpinning of advanced mathematical activity

Abstract

Abstract The human brain is especially unique within the animal kingdom in its understanding of abstract mathematical concepts. We are able to conceive irrational numbers, idealized geometrical shapes, abstract topological properties, and so on without ever perceiving them. How, then, do such concepts develop in the human mind? And what is the neural basis underlying the manipulation of high-level math concepts? While previous work mainly focused on arithmetic processing, the work reported in the present chapter focuses on more advanced math knowledge. This gives better account for the diversity of math domains such as analysis, algebra, topology, geometry, and so on that could call upon very different skills. One way to assess the brain mechanisms underlying advanced mathematical concepts’ ontogeny is to use functional MRI and study various mathematically skilled populations such as math professors or researchers, math students, or more generally math learners. The present chapter offers an overview of various neuroimaging studies assessing the cerebral underpinnings of advanced mathematical reflection and logical reasoning, as well as the effect of mathematical expertise on the brain. In professional mathematicians, including the exceptional cases of three blind mathematicians, these studies revealed that mathematical concepts are encoded in a very abstract manner. Notably, a set of brain areas including the bilateral intraparietal sulci and bilateral inferior-temporal regions appears to be systematically involved in mathematical activity. I then discuss the relation of this math-related network with language vs numerical-spatial processing in the brain, as well as its potential link to visual processes. I also discuss the potential overlap of the math-related network with the neural correlates of deductive reasoning, a process that is at the heart of the modern mathematical practice of proofs. Finally, this chapter briefly reviews the main brain markers that have been found to accompany mathematical expertise or giftedness.