abstract Marie Amalric

Marie Amalric (Université Pierre-et-Marie-Curie, Université Paris 06, Sorbonne Universités, Paris, France)

Brain representations of complex mathematical concepts and rules: behavioral and fMRI findings

How does the brain learn, represent and manipulate advanced mathematical concepts?

Mathematics can be considered as a cultural construction process whose foundations lie in basic intuitions of space, time and number provided by innate “core knowledge” systems. A first fMRI study of advanced mathematical reflection in expert mathematicians tends to show that mathematical expertise for abstract non-numerical concepts relies on a “neuronal recycling” of regions involved in basic number sense and spatial coding such as the intraparietal sulcus or the recently discovered “visual number form areas”. Moreover, the math-responsive network identified in this experiment was completely dissociated from language regions, activated regardless of math domain or problem difficulty, and developed even in the absence of visual experience.

Even if language is not required to think about advanced mathematical concepts, it could be involved during learning. At least mathematics and language could share some learning mechanisms. In particular, during language processing, humans form complex embedded representations from sequential inputs. In a second experiment, we asked whether a “geometrical language” comprising elementary primitives and recursive rules also underlies the human ability to encode sequences of spatial locations. Adults, preschoolers, and adult members of an indigene group in the Amazon, the Munduruku, who have a restricted numerical and geometrical lexicon and limited access to schooling, were thus exposed to various sequences of spatial locations on an octagon, and were asked to predict future locations. All subjects were able to detect and use primitives of symmetry and rotation and readily combined these geometrical primitives into hierarchically organized expressions. A theoretical model, based on minimum description length, proved to fit well participants’ behavior, suggesting that human subjects “compress” spatial sequences into a minimal internal rule or program.