Cortical circuits for mathematical knowledge: evidence for a major subdivision within the brain's semantic networks

Abstract

Is mathematical language similar to natural language? Are language areas used by mathematicians when they do mathematics? And does the brain comprise a generic semantic system that stores mathematical knowledge alongside knowledge of history, geography or famous people? Here, we refute those views by reviewing three functional MRI studies of the representation and manipulation of high-level mathematical knowledge in professional mathematicians. The results reveal that brain activity during professional mathematical reflection spares perisylvian language-related brain regions as well as temporal lobe areas classically involved in general semantic knowledge. Instead, mathematical reflection recycles bilateral intraparietal and ventral temporal regions involved in elementary number sense. Even simple fact retrieval, such as remembering that 'the sine function is periodical' or that 'London buses are red', activates dissociated areas for math versus non-math knowledge. Together with other fMRI and recent intracranial studies, our results indicated a major separation between two brain networks for mathematical and non-mathematical semantics, which goes a long way to explain a variety of facts in neuroimaging, neuropsychology and developmental disorders.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

Keywords: advanced mathematical cognition; brain's semantic dissociation; functional MRI.

Figure 1.

A reproducible dissociation between mathematical and general semantic knowledge. The figure shows brain activity in professional mathematicians evoked by (a) complex mathematical and general semantic statements [8], (b) simpler facts asking for an immediate response and (c) elementary declarative, negative and quantified statements. (Left) Brain maps showing areas of greater activation during reflection on mathematical statements versus non-mathematical statements (blue) or vice versa (green). (Right) Average fMRI signal in representative math-related areas. Top panel, Copyright © 2016 National Academy of Sciences.

Figure 2.

Brain activation elicited by word categories contained in naturalistic narrative stories [25]. (a) Snapshot from the explorer proposed by the Gallant lab (http://gallantlab.org/huth2016/), showing a parietal site sensitive to various quantity- and math-related concepts. (b) Brain maps of the first and second principal components of cerebral activation to narrative stories (image courtesy of Alexander Huth and Jack Gallant).

Figure 3.

Intracranial evidence for a cortical network involved in mental arithmetic. (a,b) Parietal and ventrolateral temporal electrodes responding to math (purple) versus verbal memory (green) tasks. (c,d) High-frequency broadband time course in math-active sites within four anatomical regions in an exemplar subject ([30]; Copyright © 2016 National Academy of Sciences).

Figure 4.

Dissociation between mathematical and verbal knowledge in 4- to 10-year-old children. Brain regions showing a significant correlation between children's neural maturity index (derived from fMRI signals) and their performance on mathematical test (a), and verbal test (b) ([51], reproduced with permission).