Origins of the brain networks for advanced mathematics in expert mathematicians

Abstract

The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit.

When three is greater than five: EEG and fMRI signatures of errors in numerical and physical comparisons

“…More evident is a link to the recently established 'number network' (Amalric and Dehaene 2016;Nieder 2016), which comprises bilateral intraparietal, inferior temporal, and dorsal prefrontal sites. The network is activated by all domains of mathematics such as analysis, algebra, topology, and geometry (Amalric and Dehaene 2016).…”

“…The network is activated by all domains of mathematics such as analysis, algebra, topology, and geometry (Amalric and Dehaene 2016). As indicated by studies using intracranial electrophysiological recordings in humans, the inferior temporal gyrus selectively responds to written Arabic numerals, but not to morphologically, semantically, or phonologically similar stimuli (Shum et al 2013).…”

“…In general, number processing consists of two steps: the transformation of an external sensory number input to an internal number representation, and the transformation of a numerical representation to a task-relevant decision before the execution of a motor response (Verguts and Fias 2008). According to functional magnetic resonance imaging (fMRI) studies, perceptual encoding into a numerical representation occurs in the inferior temporal gyrus, which selectively responds to written Arabic numerals (Shum et al 2013;Amalric and Dehaene 2016). The intraparietal sulcus (IPS) acts as a cortical hub to extract quantitative information to estimate magnitude, space, or time (Hubbard et al 2005;Nieder and Dehaene 2009), all of which are necessary when making decisions.…”

Invited Lectures from the 13th International Congress on Mathematical Education

“…The findings contradicted previous findings of studies on numerical cognition, which had demonstrated connections between activation evoked by numerical processing and by language. The research by Amalric and Dehaene (2016) shows that language may play a role in the initial acquisition of mathematical competencies and that brain activation during elementary numerical processing and higher level mathematics are connected; they thus demonstrated that advanced mathematical processing is connected to symbolic number processing.…”

“…To the best of my knowledge, the connections between expertise at earlier ages and expertise in research mathematicians remain unexplored. Neurocognitive research by Amalric and Dehaene (2016) demonstrated connections between numerical processing and relatively advanced mathematical thinking. The researchers performed an investigation into the neuronal origins and consequences of mathematical expertise.…”