Origins of the brain networks for advanced mathematics in expert mathematicians

Amalric, Dehaene · Proceedings of the National Academy of Sciences · 2016 · neuroscience · 10.1073/pnas.1603205113 · record Amalric2016-origins-of-the-brain-networks-for-advanced-m
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Where this record's text came from. faceted 2026-08 by reading the locally held text (html); every evidence string verified as an exact substring of that text before merging. Claim type is 'existence' rather than 'mechanism': the paper's headline claim is that a specific non-linguistic network is engaged by, and shared between, advanced maths and number processing, not that maths works because of a stated causal process. The contradicts relation is admissible because the language-origin hypothesis is attributed to a named person (Chomsky) in the article text, unlike almost all other citations, which are numeric. The paper also notes that its one apparent math/language overlap in left BA 44 failed to survive single-subject analysis; that is a result caveat rather than a stated limitation, so it is not listed. 2026-08-13 and 2026-08-15 schema-0.3 passes: every quote verified as an exact substring of the staged text and anchored at merge time; concept terms verified present; every edge endpoint an existing node.
2 quotations on this page contain a reference number where the paper printed a superscript. This journal style prints citations as raised numerals — parameters12,13 — and the extraction flattened them into the line, so the sentence reads parameters 12 , 13 . The digits are citation markers and not part of what the author wrote. The quotes keep them for the same reason they keep every other extraction fault: a quote is reproduced exactly or it proves nothing.
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Other fields define these differently the same word, defined another way in another discipline
immediacy 3 fields · fmri 2 fields · semantic 2 fields · topology 2 fields

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Every tag the record carries, each linking to every other paper in the corpus that carries it. A tag appears here whether or not its words occur in the article — the spans below are only the ones a sentence in this paper licenses. Of the 18 concept tags on this paper, none is grounded in a quoted sentence. All carry the tagger's gloss of what the term means in this paper, which is not something the article can license.
mathematicians controls IPS IT VNFA angular gyrus multiple demand system meaningless semantic calculation localizer representational similarity analysis formulas FFA caudate core knowledge topology imageability Prolonged exposure to mathematical symbols reshapes ventral visual cortex, amplifying symbol responses and displacing face responses, in the same way reading expertise does for letters Because advanced mathematics and basic arithmetic share the same cortical circuit, early number skills and later mathematical achievement are developmentally linked through that shared substrate visual number form area immediacy task difficulty t-test Student t tests ANOVA second-level whole-brain ANOVA with stimulus category as within-subject factor F-test an F-test at the whole-brain level signal-detection sensitivity index Mean d′ values correction for multiple comparisons correlation matrix of correlations between the activations evoked by each of the experimental conditions cluster P < 0.05 corrected fmri

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second readingalternativesan independent re-reading of a facet, recorded whether or not it agrees
relation to other workclaim_relationshow this paper stands to another: agrees, contradicts, extends, qualifies
claim typeclaim_typethe shape of the claim: existence, mechanism, method, critique, prediction, null
content tagcontent_tagsa finding, definition, quantity, statistic or variable named in the paper
contributioncontributionwhat the paper claims to add
controlcontrolsan experiment run to eliminate a rival explanation
limitationlimitationswhat the paper says its evidence cannot support
mechanismmechanismshow the reported effect is said to come about
methodmethodhow the paper produced its evidence
object of studyobject_of_studywhat the paper is about — the thing it investigates
phenomenonphenomenonthe effect or regularity under study
research questionresearch_questionthe question the paper sets itself
sensesensesa distinct use of a term, quoted where the paper fixes it
transfertransfersa method or concept carried in from another field

The paper

The full text is not reproduced here. This article is not cleared for redistribution, so the page carries the tag layer only. Its evidence sentences are withheld; the grounding status remains with each tag, and the article itself is at https://doi.org/10.1073/pnas.1603205113. The reading view exists for the papers whose licence permits it.

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alternatives 2 · claim_relations 7 · claim_type 1 · content_tags 55 · contribution 1 · controls 1 · limitations 7 · mechanisms 7 · method 1 · object_of_study 1 · phenomenon 1 · research_question 1 · senses 5 · transfers 2

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facettagfieldconf.whose words
object_of_studywhether advanced mathematical thought rests on the language faculty or on evolutionarily older circuits for number and space
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object_of_studythe paper's words
research_questionwhich brain areas professional mathematicians engage when judging advanced mathematical statements, and whether they are language areas or number areas
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research_questionthe paper's words
contributionshows a bilateral parietal, inferior temporal and prefrontal network active for all four branches of mathematics in experts only, sparing language areas and overlapping the circuits for numerals and arithmetic
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contributionthe paper's words
claim_typeexistence
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claim_typethe paper's words
phenomenonhigh-level mathematical reasoning in expert mathematicians
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phenomenonthe paper's words
methodfmri
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also in: fmri
methodthe paper's words
mechanismsmechanisms
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mechanisms[0]the tagger's words
mechanismsmechanisms
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mechanisms[1]the tagger's words
mechanismsexpertise amplifies responses at sites that already respond to numerals and formulas in non-experts, rather than recruiting new territory
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mechanisms[2]1.0the tagger's words
mechanismsthe ventral visual change mirrors literacy, where learning to read shifts responses toward letters and away from faces
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mechanisms[3]1.0the tagger's words
mechanismsthe enhanced formula response reflects a genuine increase in activated cortical volume, not just tighter anatomical alignment in the expert group
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mechanisms[4]1.0the tagger's words
mechanismsthe caudate shifts its engagement to whichever domain the subject is expert in, consistent with a role in motivation and attention
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mechanisms[5]0.8the tagger's words
mechanismslanguage contributes transiently at the angular gyrus during sentence comprehension, and that area is deactivated during the reflection itself
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mechanisms[6]1.0the tagger's words
limitationsThe group differences in ventral visual responses (formulas, tools, faces) cannot yet be tied to behaviour or shown to be caused by mathematical training.
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what this limits: the ventral visual group differences: THESE INTRIGUING DIFFERENCES MUST BE CONSIDERED WITH CAUTION BECAUSE THEIR BEHAVIORAL IMPACT AND CAUSAL LINK TO MATHEMATICAL TRAINING REMAINS PRESENTLY UNKNOWN
limitations[0]the tagger's words
limitationsThe design cannot rule out a transient role of language areas during the acquisition of mathematical concepts; only learning studies could settle it.
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what this limits: the claim that language areas are not involved: a transient role during acquisition is not excluded, and IMAGING STUDIES OF THE LEARNING PROCESS WOULD BE NEEDED TO RESOLVE THIS POINT
limitations[1]the tagger's words
limitationsMathematicians and controls may differ on uncontrolled dimensions such as IQ or musical talent, which the authors argue is irrelevant to the within-group dissociation but is not measured.
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what this limits: the between-group comparison but not the within-mathematician one: MATHEMATICIANS AND CONTROLS MAY STILL DIFFER ON DIMENSIONS SUCH AS IQ, MUSICAL TALENT, HOBBIES ... SUCH PUTATIVE DIFFERENCES ARE IRRELEVANT TO OUR MAIN CONCLUSION OF A DISSOCIATION ... WITHIN THE MATHEMATICIANS
limitations[2]the tagger's words
limitationsthe authors flag the ventral visual group differences as needing caution, since their behavioural impact and causal link to mathematical training are unknown
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what this limits: the same scope as limitations[0] - the ventral visual differences are flagged by the authors as needing caution
limitations[3]1.0the tagger's words
limitationsa small language-area overlap in left BA44 appeared only in smoothed group images and failed to reach significance in single subjects
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what this limits: the language-overlap result: THIS SMALL OVERLAP WAS PRESENT ONLY IN SMOOTHED GROUP IMAGES AND FAILED TO REACH SIGNIFICANCE IN HIGHER RESOLUTION analyses
limitations[4]1.0the tagger's words
limitationscontrols were near chance on the mathematical statements, so the expertise interaction rests on a group that could not do the task
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what this limits: any expertise contrast that uses the control group's maths performance: THEY FELL CLOSE TO CHANCE LEVEL WITH MATH (37% CORRECT, CHANCE LEVEL = 33%) ... COULD NOT IDENTIFY THEIR TRUTH VALUE (d' = 0.38, n.s.)
limitations[5]0.9the tagger's words
limitationsobjective performance was matched but each group rated its own domain as more comfortable
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what this limits: the matched-performance argument: OBJECTIVE PERFORMANCE ON NONMATH PROBLEMS DID NOT DIFFER ... their SUBJECTIVE RATINGS ... REVEALED THAT EACH GROUP FELT MORE COMFORTABLE WITH ITS RESPECTIVE EXPERTISE DOMAIN
limitations[6]1.0the tagger's words
transfersthe expertise-driven ventral visual shift toward symbols and away from faces, transposed from literacy to mathematics
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transfers[0]1.0the tagger's words
transfersrepresentational similarity, used to test whether math, arithmetic and numeral viewing share an activation topography within each subject
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transfers[1]1.0the tagger's words
controlsan eighth stimulus category of circular checkerboards, built so that its retinotopic extent EXCEEDED that of every other category
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eliminates: a difference in retinotopic extent between conditions - the checkerboard is built to exceed every other category, so any area responding to sheer visual extent is exposed rather than counted as mathematical · outcome (stated by the tagger, no quotation): absent-not-in-staged-text · would have ruled out, had it been run: low-level visual drive as the explanation of category-selective responses - a region that answers to mathematical formulas more than to a checkerboard covering MORE of the visual field is not responding to retinotopic extent
controls[0]0.95the tagger's words
sensesmeaningful versus meaningless is the paper's second, ORTHOGONAL criterion - it holds lexical content constant and so tests the same claim without the math-versus-nonmath comparison
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senses[0]1.0the tagger's words
sensesdifficulty here has an objective form (percent correct, matched) and a subjective form (rated, slightly higher for math), and the paper's controls address the second
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senses[1]1.0the tagger's words
sensesthe visual number form area is defined by responding to Arabic numerals more than letters or pictures, and was previously hard to detect because it sits near a zone of fMRI signal loss
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senses[2]1.0the tagger's words
sensesthe multiple demand system is the rival account: a set of areas active in any hard task, which overlaps the math network and is why difficulty had to be excluded
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senses[3]1.0the tagger's words
senseslanguage areas here are defined by an independent localiser in the same subjects, not by anatomy, so the sparing claim is about functionally identified voxels
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senses[4]1.0the tagger's words
alternativesmethod: auditory statement judgement in the scanner with matched non-mathematical statements, plus independent localisers for sentences, calculation and visual categories
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a second reading DIFFERING from the recorded value. Recorded: fmri — note: a second reading, verbatim-verified, disagreeing with the value on the record. Not applied - a person decides.
alternatives.methodthe tagger's words
alternativesphenomenon: the cortical network engaged during reflection on advanced mathematical statements
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a second reading DIFFERING from the recorded value. Recorded: high-level mathematical reasoning in expert mathematicians — note: a second reading, verbatim-verified, disagreeing with the value on the record. Not applied - a person decides.
alternatives.phenomenonthe tagger's words
claim_relationsreplicates → earlier observations of number-sense and number-form areas (cited as references 16, 18, 37)
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claim_relations[0]the tagger's words
claim_relationscontradicts → the hypothesis that mathematics is an offshoot of language syntax, attributed in the article to Noam Chomsky (reference 1)
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claim_relations[1]the tagger's words
claim_relationscontradicts → the hypothesis that mathematical capacity is an abstraction from linguistic operations
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claim_relations[2]1.0the tagger's words
claim_relationssupports → the account grounding mathematics in ancient nonlinguistic intuitions of number and space
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claim_relations[3]1.0the tagger's words
claim_relationsextends → arithmetic imaging work, by answering the objection that number concepts are too simple to represent advanced mathematics
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claim_relations[4]1.0the tagger's words
claim_relationsconfirms → prior reports of visual number form areas, using a sequence that overcomes the signal loss which made them hard to detect
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claim_relations[5]1.0the tagger's words
claim_relationsqualifies → its own language-independence claim, by noting a transient angular gyrus contribution during comprehension
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claim_relations[6]1.0the tagger's words
content_tagst-test
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also in: t-test
content_tags.statistics[0]the tagger's words
content_tagsANOVA
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also in: ANOVA
content_tags.statistics[1]the tagger's words
content_tagsF-test
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also in: F-test
content_tags.statistics[2]the tagger's words
content_tagssignal-detection sensitivity index
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content_tags.statistics[3]the tagger's words
content_tagscorrection for multiple comparisons
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content_tags.statistics[4]the tagger's words
content_tagscorrelation
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also in: correlation
content_tags.statistics[5]the tagger's words
content_tagsStudent t tests
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content_tags.statistics[6]0.9the tagger's words
content_tagsF-test
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also in: F-test
content_tags.statistics[7]0.7the tagger's words
content_tagscluster P < 0.05 corrected
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content_tags.statistics[8]0.8the tagger's words
content_tagsThe activations evoked by mathematical reflection spared areas related to language and to general-knowledge semantics.
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content_tags.findings[0]the tagger's words
content_tagsThe same math network was engaged by all four tested branches of mathematics and even transiently by meaningless mathematical statements.
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content_tags.findings[1]the tagger's words
content_tagsNon-mathematical general-knowledge reflection recruited a separate anterior temporal and angular gyrus semantic network.
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content_tags.findings[2]the tagger's words
content_tagsA region-of-interest analysis of language areas showed mathematics engaged them no more, and often less, than general semantic reasoning did.
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content_tags.findings[3]the tagger's words
content_tagsThe high-level mathematics network overlapped the parietal and inferior temporal sites activated by simple calculation and by the mere sight of numerals, and this overlap survived removal of statements containing any numerical reference.
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content_tags.findings[4]the tagger's words
content_tagsThe math network was active even during simple mathematical reflection, and its greater activation for math than nonmath held irrespective of task difficulty.
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content_tags.findings[5]the tagger's words
content_tagsMathematical expertise was accompanied by expanded number and formula responses in the left visual number form area.
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content_tags.findings[6]the tagger's words
content_tagsmathematicians performed equally on math and non-math statements, 63% against 65% correct
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content_tags.findings[7]1.0the tagger's words
content_tagscontrols matched mathematicians on non-math but were near chance on math
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content_tags.findings[8]1.0the tagger's words
content_tagsall four domains of mathematics activated the math-responsive regions, in a significant intersection
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content_tags.findings[9]1.0the tagger's words
content_tagsthe network stayed active for about fifteen seconds after a math statement and deactivated for non-math
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content_tags.findings[10]1.0the tagger's words
content_tagsin controls the math contrast landed on the sites for meaningless statements
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content_tags.findings[11]1.0the tagger's words
content_tagsessentially no intersection between the math and general-knowledge semantic networks, and none in perisylvian language cortex even at a lenient threshold
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content_tags.findings[12]1.0the tagger's words
content_tagslanguage regions defined by an independent localiser were engaged no more by math than by general reasoning, and often less
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content_tags.findings[13]1.0the tagger's words
content_tagsthe math network overlapped the areas for arithmetic and for merely viewing numerals
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content_tags.findings[14]1.0the tagger's words
content_tagsresponses to written formulas were larger in mathematicians, as extra activated volume rather than tighter alignment
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content_tags.findings[15]1.0the tagger's words
content_tagsface responses were reduced in right inferior temporal cortex in mathematicians
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content_tags.findings[16]1.0the tagger's words
content_tagsthe caudate responded to whichever domain each group was expert in
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content_tags.findings[17]1.0the tagger's words
content_tagsCONFOUND REVERSED: easy math contrasted against difficult non-math still produced the same sites
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content_tags.findings[18]1.0the tagger's words
content_tagsCONTROL NULL: contrasting difficult against easy statements within each domain revealed no significant sites at all
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content_tags.findings[19]1.0the tagger's words
content_tagsORTHOGONAL REPLICATION: the meaningful-versus-meaningless math contrast, which holds words constant, reproduced the whole result
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content_tags.findings[20]1.0the tagger's words
content_tagsCONTENT REANALYSIS: excluding statements with any indirect numerical reference left the activation virtually unchanged
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content_tags.findings[21]1.0the tagger's words
content_tagsHAZARD NAMED ABOUT THEIR OWN RESULT: group-level overlap can arise from intersubject averaging, so the overlap was retested within subjects
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content_tags.findings[22]1.0the tagger's words
content_tagsthe within-subject pattern analyses confirmed that advanced math, arithmetic and numeral viewing share cortical sites in trained individuals
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content_tags.findings[23]1.0the tagger's words
content_tagsvisual number form area
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content_tags.definitions[0]the tagger's words
content_tagsmultiple demand system
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content_tags.definitions[1]the tagger's words
content_tagsimmediacy
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also in: immediacy
content_tags.definitions[2]the tagger's words
content_tagsmultiple demand system
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content_tags.definitions[3]1.0the tagger's words
content_tagsVNFA
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also in: VNFA
content_tags.definitions[4]1.0the tagger's words
content_tagscore knowledge
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content_tags.definitions[5]0.7the tagger's words
content_tagstask difficulty
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content_tags.variables[6]the tagger's words
content_tagsmeaningless
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also in: meaningless
content_tags.variables[8]1.0the tagger's words
content_tagsimageability
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also in: imageability
content_tags.variables[9]0.7the tagger's words
content_tagstopology
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also in: topology
content_tags.variables[10]1.0the tagger's words
content_tags15 and 15 — sample size: professional mathematicians and academically matched humanities controls scanned with fMRI
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content_tags.quantities[0]the tagger's words
content_tags63% and 65% correct — mathematicians' accuracy on math and on nonmath statements, showing the two problem types were matched in objective difficulty
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content_tags.quantities[1]the tagger's words
content_tags37% correct, chance level = 33%; P = 0.014 — control subjects' accuracy on mathematical statements, barely above chance
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content_tags.quantities[2]the tagger's words
content_tags∼15 s — duration for which the fMRI signal stayed elevated in the math network after a mathematical statement
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content_tags.quantities[3]the tagger's words
content_tags52.4 ± 3.4 versus 40.0 ± 4.5; t = 2.4, P = 0.03 — mathematicians' subjective difficulty ratings (0–100 scale) for math versus nonmath statements
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content_tags.quantities[4]the tagger's words
content_tagst = 4.72 — whole-brain effect size for reduced face responses in right inferior temporal cortex in mathematicians relative to controls
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content_tags.quantities[5]the tagger's words
content_tags72 and 18 — number of mathematical statements (18 per domain) and of nonmathematical statements presented in the auditory runs
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content_tags.quantities[6]the tagger's words
content_tags15 and 15 — professional mathematicians and non-mathematician controls of equal academic standing
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content_tags.quantities[7]1.0the tagger's words
content_tags63% and 65% — mathematicians' accuracy on math and non-math, the basis for calling the two matched in difficulty
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content_tags.quantities[8]1.0the tagger's words
content_tags37% against 33% chance — controls' accuracy on mathematical statements
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.quantities[9]1.0the tagger's words
content_tags52.4 against 40.0 — subjective difficulty for math and non-math on a 0-100 scale, the only difficulty difference found
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.quantities[10]1.0the tagger's words
content_tagsabout 15 s — how long the math network stayed active after a statement
Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.
content_tags.quantities[11]0.9the tagger's words

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