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

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’.

[1]  S. Dehaene,et al.  Interactions between number and space in parietal cortex , 2005, Nature Reviews Neuroscience.

[2]  Philip Kitcher,et al.  The nature of mathematical knowledge , 1985 .

[3]  Josef Parvizi,et al.  Brain Mechanisms of Arithmetic: A Crucial Role for Ventral Temporal Cortex , 2018, Journal of Cognitive Neuroscience.

[4]  J. Hadamard,et al.  Essai sur la psychologie de l'invention dans le domaine mathématique , 1959 .

[5]  R. Dolan,et al.  Functional neuroanatomy of three-term relational reasoning , 2001, Neuropsychologia.

[6]  Mariano Sigman,et al.  The language of geometry: Fast comprehension of geometrical primitives and rules in human adults and preschoolers , 2017, PLoS Comput. Biol..

[7]  S. Dehaene Varieties of numerical abilities , 1992, Cognition.

[8]  Jonathan Winawer,et al.  A Brain Area for Visual Numerals , 2013, The Journal of Neuroscience.

[9]  Elizabeth S Spelke,et al.  Language and number: a bilingual training study , 2001, Cognition.

[10]  Shachar Maidenbaum,et al.  A number-form area in the blind , 2015, Nature Communications.

[11]  Thomas L. Griffiths,et al.  Supplementary Information for Natural Speech Reveals the Semantic Maps That Tile Human Cerebral Cortex , 2022 .

[12]  Noam Chomsky,et al.  Language and Mind , 1973 .

[13]  Daniel N. Osherson,et al.  Logic, language and the brain , 2012, Brain Research.

[14]  J. Binder In defense of abstract conceptual representations , 2016, Psychonomic Bulletin & Review.

[15]  Michael F. Bonner,et al.  Converging Evidence for the Neuroanatomic Basis of Combinatorial Semantics in the Angular Gyrus , 2015, The Journal of Neuroscience.

[16]  S. Dehaene,et al.  Representation of number in the brain. , 2009, Annual review of neuroscience.

[17]  N. Kanwisher,et al.  Neuroimaging of cognitive functions in human parietal cortex , 2001, Current Opinion in Neurobiology.

[18]  David A. Boas,et al.  Near-infrared spectroscopy shows right parietal specialization for number in pre-verbal infants , 2010, NeuroImage.

[19]  Mohammad Dastjerdi,et al.  Numerical processing in the human parietal cortex during experimental and natural conditions , 2013, Nature Communications.

[20]  Marcel Adam Just,et al.  Neural Representations of Physics Concepts , 2016, Psychological science.

[21]  Jessica F. Cantlon,et al.  Neural Activity during Natural Viewing of Sesame Street Statistically Predicts Test Scores in Early Childhood , 2013, PLoS biology.

[22]  Elizabeth M. Brannon,et al.  Induced Alpha-band Oscillations Reflect Ratio-dependent Number Discrimination in the Infant Brain , 2009, Journal of Cognitive Neuroscience.

[23]  C. Mervis,et al.  Neural Basis of Genetically Determined Visuospatial Construction Deficit in Williams Syndrome , 2004, Neuron.

[24]  D. Osherson,et al.  The boundaries of language and thought in deductive inference , 2009, Proceedings of the National Academy of Sciences.

[25]  S. Dehaene,et al.  Exact and Approximate Arithmetic in an Amazonian Indigene Group , 2004, Science.

[26]  Noam Chomsky Language and Mind: Index , 2006 .

[27]  Nathalie Boddaert,et al.  Autism, the superior temporal sulcus and social perception , 2006, Trends in Neurosciences.

[28]  Daniel N. Osherson,et al.  Thought Beyond Language , 2012, Psychological science.

[29]  S. Dehaene,et al.  How Learning to Read Changes the Cortical Networks for Vision and Language , 2010, Science.

[30]  E. Spelke,et al.  Sources of mathematical thinking: behavioral and brain-imaging evidence. , 1999, Science.

[31]  Daniel D. Dilks,et al.  The Functional Organization of the Ventral Visual Pathway in Humans , 2012 .

[32]  Stanislas Dehaene,et al.  Neural correlates of merging number words , 2015, NeuroImage.

[33]  Edward T. Bullmore,et al.  Specialization of right temporo-parietal junction for mentalizing and its relation to social impairments in autism , 2011, NeuroImage.

[34]  Rosemary Varley,et al.  Algebra in a man with severe aphasia , 2007, Neuropsychologia.

[35]  Kaustubh Supekar,et al.  Brain Organization Underlying Superior Mathematical Abilities in Children with Autism , 2014, Biological Psychiatry.

[36]  Mariano Sigman,et al.  The cortical representation of simple mathematical expressions , 2012, NeuroImage.

[37]  Stanislas Dehaene,et al.  Cerebral Pathways for Calculation: Double Dissociation between Rote Verbal and Quantitative Knowledge of Arithmetic , 1997, Cortex.

[38]  Margarete Delazer,et al.  Learning by strategies and learning by drill—evidence from an fMRI study , 2005, NeuroImage.

[39]  E. Spelke,et al.  Core Knowledge of Geometry in an Amazonian Indigene Group , 2006, Science.

[40]  J. Cantlon,et al.  Neural Tuning to Numerosity Relates to Perceptual Tuning in 3–6-Year-Old Children , 2017, The Journal of Neuroscience.

[41]  Marinella Cappelletti,et al.  Spared numerical abilities in a case of semantic dementia , 2001, Neuropsychologia.

[42]  Stanislas Dehaene,et al.  A distinct cortical network for mathematical knowledge in the human brain , 2019, NeuroImage.

[43]  A. Henik,et al.  Double Dissociation of Functions in Developmental Dyslexia and Dyscalculia , 2006 .

[44]  Stanislas Dehaene,et al.  Origins of the brain networks for advanced mathematics in expert mathematicians , 2016, Proceedings of the National Academy of Sciences.

[45]  Vinod Goel,et al.  Differential involvement of left prefrontal cortexin inductive and deductive reasoning , 2004, Cognition.

[46]  S. Dehaene,et al.  THREE PARIETAL CIRCUITS FOR NUMBER PROCESSING , 2003, Cognitive neuropsychology.

[47]  Michael Siegal,et al.  Agrammatic but numerate. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[48]  B. Thirion,et al.  Fast reproducible identification and large-scale databasing of individual functional cognitive networks , 2007, BMC Neuroscience.

[49]  Marinella Cappelletti,et al.  Numeracy Skills in Patients With Degenerative Disorders and Focal Brain Lesions , 2011, Neuropsychology.

[50]  J. Duncan The multiple-demand (MD) system of the primate brain: mental programs for intelligent behaviour , 2010, Trends in Cognitive Sciences.

[51]  Brian Butterworth,et al.  Developmental dyscalculia and basic numerical capacities: a study of 8–9-year-old students , 2004, Cognition.

[52]  Stanislas Dehaene,et al.  A Temporal Bottleneck in the Language Comprehension Network , 2012, The Journal of Neuroscience.

[53]  Amy L. Daitch,et al.  Mapping human temporal and parietal neuronal population activity and functional coupling during mathematical cognition , 2016, Proceedings of the National Academy of Sciences.

[54]  Wen Fang,et al.  Representation of spatial sequences using nested rules in human prefrontal cortex , 2019, NeuroImage.

[55]  E. Spelke,et al.  Newborn infants perceive abstract numbers , 2009, Proceedings of the National Academy of Sciences.

[56]  A. Jackowski,et al.  Brain abnormalities in Williams syndrome: a review of structural and functional magnetic resonance imaging findings. , 2009, European journal of paediatric neurology : EJPN : official journal of the European Paediatric Neurology Society.

[57]  Noam Chomsky,et al.  The faculty of language: what is it, who has it, and how did it evolve? , 2002, Science.

[58]  William W. Graves,et al.  Where is the semantic system? A critical review and meta-analysis of 120 functional neuroimaging studies. , 2009, Cerebral cortex.

[59]  Margarete Delazer,et al.  How specifically do we learn? Imaging the learning of multiplication and subtraction , 2006, NeuroImage.

[60]  S. Dehaene,et al.  Cortical representation of the constituent structure of sentences , 2011, Proceedings of the National Academy of Sciences.

[61]  Stanislas Dehaene,et al.  Approximate quantities and exact number words: dissociable systems , 2003, Neuropsychologia.

[62]  S. Dehaene,et al.  Cultural Recycling of Cortical Maps , 2007, Neuron.