The neural roots of mathematical expertise

The neural roots of mathematical expertise Ansari

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The neural roots of mathematical expertise 2016 Proceedings of the National Academy of Sciences 10.1073/pnas.1604758113 Ansari2016-the-neural-roots-of-mathematical-expertise Ansari2016-the-neural-roots-of-mathematical-expertise.txt, the project's staged copy f2da0d117b6c5eb5816b30e8e16221fd5daa8ab5 not-redistributable neuroscience

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them Amalric and Dehaene's fMRI comparison of expert mathematicians with non-mathematicians, read for what it settles about the relation between mathematics and language in the brain. Quotation withheld because this record is not cleared for redistribution. critique Quotation withheld because this record is not cleared for redistribution. mathematical expertise Quotation withheld because this record is not cleared for redistribution. review review Quotation withheld because this record is not cleared for redistribution. mechanisms Acquiring mathematical expertise drives plastic change in ventral visual cortex for formulas and digits, which in turn reorganises responses to other visual categories such as faces Quotation withheld because this record is not cleared for redistribution. mechanisms Expertise redirects attention toward domain-relevant information, which could by itself produce the frontoparietal activation differences Quotation withheld because this record is not cleared for redistribution. The commentary's own Neurosynth analysis supports the dissociation independently: regions reported alongside the term numerical are largely separate from those reported alongside language Quotation withheld because this record is not cleared for redistribution. The overlap between advanced mathematical reflection and simple calculation is read as evidence that expertise is built on elementary symbolic number circuits rather than separate from them Quotation withheld because this record is not cleared for redistribution. Expertise may reorganise the ventral visual stream, with gains for formulas and digits accompanied by reduced response to faces Quotation withheld because this record is not cleared for redistribution. The commentary's own alternative account: expertise may change where attention goes rather than which systems are recruited, and the design cannot separate the two Quotation withheld because this record is not cleared for redistribution. A test is proposed that would separate them - compare mathematicians on mathematics with experts in another field on their own domain Quotation withheld because this record is not cleared for redistribution. The commentary bounds its own conclusion: language may still matter for the acquisition of expertise, or via connectivity rather than direct recruitment. what this limits: the commentary's own reading of the language result: LANGUAGE MAY HAVE PLAYED A ROLE IN THE INITIAL ACQUISITION OF MATHEMATICAL EXPERTISE OR ... AT THE LEVEL OF FUNCTIONAL CONNECTIVITY WITH LANGUAGE AREAS ... RATHER THAN THROUGH THEIR DIRECT RECRUITMENT Quotation withheld because this record is not cleared for redistribution. The evidence discussed is correlational and cannot establish that expertise causes the reported plastic changes. what this limits: any causal reading of the expertise-related differences: SUCH CORRELATIONAL DATA CANNOT BE USED TO INFER CAUSALITY Quotation withheld because this record is not cleared for redistribution. The commentary's own caution, echoing the original authors: the expertise-related brain differences are correlational and cannot establish causality duplicate of: limitations[1] · what this limits: the same scope as limitations[1], and it is an amplification rather than a new objection: AS AMALRIC AND DEHAENE ACKNOWLEDGE Quotation withheld because this record is not cleared for redistribution. Genetic differences between the groups are as compatible with the data as expertise-driven plasticity what this limits: the plasticity interpretation specifically: IT IS EQUALLY PLAUSIBLE THAT GENETIC DIFFERENCES BETWEEN EXPERT MATHEMATICIANS AND NONMATHEMATICIANS AFFECT THE ORGANIZATION OF THE VENTRAL VISUAL STREAM Quotation withheld because this record is not cleared for redistribution. The refutation of the language hypothesis is qualified in two ways the data cannot reach what this limits: the same scope as limitations[0] - the refutation of the language hypothesis is qualified in two ways these data cannot reach Quotation withheld because this record is not cleared for redistribution. Whether the link to elementary number extends to nonsymbolic representations is untested and not implied what this limits: the extension to nonsymbolic number: A CONNECTION BETWEEN SYMBOLIC NUMBERS AND MATHEMATICAL EXPERTISE IN THE BRAIN DOES NOT NECESSARILY IMPLY THAT THE SAME IS TRUE FOR NONSYMBOLIC NUMBER PROCESSING Quotation withheld because this record is not cleared for redistribution. Whether the reorganisation has behavioural consequences is left as an open question what this limits: the functional significance of the reorganisation: DOES A REDUCED RESPONSE TO FACES TRANSLATE INTO POORER FACE-PROCESSING SKILLS AMONG EXPERT MATHEMATICIANS? Quotation withheld because this record is not cleared for redistribution. number processing - symbolic: numerals and written formulas, which the commented study ties to advanced mathematics Quotation withheld because this record is not cleared for redistribution. number processing - nonsymbolic: quantity as in dot arrays, shared with other species, and explicitly NOT covered by the result Quotation withheld because this record is not cleared for redistribution. expertise effect - domain-general: attention, working memory and difficulty, which the frontoparietal network also serves Quotation withheld because this record is not cleared for redistribution. expertise effect - domain-specific: information processing particular to the domain, which is the reading the commented paper needs and the design cannot yet secure Quotation withheld because this record is not cleared for redistribution. the language claim - Hurford's strong form: numeracy is impossible without language Quotation withheld because this record is not cleared for redistribution. the language claim - the surviving weak forms: language may matter for ACQUIRING expertise, or through connectivity rather than recruitment Quotation withheld because this record is not cleared for redistribution. phenomenon: mathematical expertise a second reading reaching the same value. Recorded: mathematical expertise — note: a second reading reaching the same value from a different sentence. Not applied - a person decides. Quotation withheld because this record is not cleared for redistribution. builds-on → Amalric & Dehaene, "Origins of the brain networks for advanced mathematics in expert mathematicians" (PNAS 2016) - the companion article this piece comments on Quotation withheld because this record is not cleared for redistribution. contradicts → Hurford (ref. 7, p. 305), "without language, no numeracy" Quotation withheld because this record is not cleared for redistribution. critiques → Hurford's claim that there is no numeracy without language Quotation withheld because this record is not cleared for redistribution. supports → Amalric and Dehaene (2016), the commented paper Quotation withheld because this record is not cleared for redistribution. supports → Dehaene and Cohen's prediction of a visual number form area Quotation withheld because this record is not cleared for redistribution. critiques → the early structural studies of Einstein's brain Quotation withheld because this record is not cleared for redistribution. EVIDENCE CORRECTED (RE-GROUNDED) · mathematical expertise —distinct-from→ language mathematical expertise language EVIDENCE CORRECTED: RE-GROUNDED. The old span named only the brain regions. This sentence names both and states the distinction AS THE FIELD'S OPEN DISAGREEMENT - some argue language is the basis, others that the abilities are nonverbal - which is a more honest ground for 'distinct-from' than an assertion. — strength of the relation: 0.9 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span writes 'expert mathematicians', not 'mathematical expertise'. Quotation withheld because this record is not cleared for redistribution. symbolic number processing —part-of→ mathematical expertise symbolic number processing mathematical expertise strength of the relation: 0.9 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span reports a CONNECTION between the circuits for elementary number processing and higher mathematics; part-of is loose. Quotation withheld because this record is not cleared for redistribution. nonsymbolic —distinct-from→ symbolic number processing nonsymbolic symbolic number processing strength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but endpoint by anaphora: 'symbolic numbers' = symbolic number processing (previous sentence); the span says a connection 'does not necessarily imply' the same for nonsymbolic processing; distinct-from is loose. Quotation withheld because this record is not cleared for redistribution. visual number form area —part-of→ ventral visual cortex visual number form area ventral visual cortex strength of the relation: 1 Quotation withheld because this record is not cleared for redistribution. visual number form area —operationalised-as→ inferior temporal gyri visual number form area inferior temporal gyri strength of the relation: 0.9 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span says regions in the bilateral inferior temporal gyri respond to numerals - a LOCATION for the VNFA; operationalised-as is loose. Quotation withheld because this record is not cleared for redistribution. frontoparietal —part-of→ domain-general frontoparietal domain-general strength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the frontoparietal regions are ASSOCIATED WITH processes not specific to mathematics; part-of 'domain-general' is loose. Quotation withheld because this record is not cleared for redistribution. Neurosynth —operationalised-as→ reverse-inference Neurosynth reverse-inference strength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the reverse-inference meta-analysis was CONDUCTED USING Neurosynth; operationalised-as is loose. Quotation withheld because this record is not cleared for redistribution. mathematical expertise —distinct-from→ language mathematical expertise language strength of the relation: 0.9 · note: RE-GROUNDS another row of this record: the old span named ONE endpoint. Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span reports a DEBATE - some argue language is the basis, others that nonverbal processes are; distinct-from is not the paper's own claim. Quotation withheld because this record is not cleared for redistribution. meta-analysis meta-analysis Quotation withheld because this record is not cleared for redistribution. The analysis supports the finding that numerical processing is largely anatomically separate from the circuitry thought to support language. Quotation withheld because this record is not cleared for redistribution. The commentary concludes that the absence of language-area recruitment in expert mathematicians refutes the claim that high-level mathematical ability is grounded in language systems. Quotation withheld because this record is not cleared for redistribution. The commentary argues the overlap between advanced mathematical reflection and elementary number processing implies a deep continuity between rudimentary symbolic number skills and advanced mathematics. Quotation withheld because this record is not cleared for redistribution. The author qualifies the refutation: language may still matter for the initial acquisition of expertise or through functional connectivity rather than direct recruitment. Quotation withheld because this record is not cleared for redistribution. The author raises an alternative: the experts may have attended differently to mathematical statements because these are especially salient to them. Quotation withheld because this record is not cleared for redistribution. As the original authors acknowledge, correlational data like these cannot be used to infer causality. Quotation withheld because this record is not cleared for redistribution. the author's meta-analysis maps regions reported more often in articles whose abstracts mention 'numerical' (89 studies) than in those that do not Quotation withheld because this record is not cleared for redistribution. the commentary reads the result as refuting the hypothesis that higher-level mathematical abilities are grounded in the brain's language systems Quotation withheld because this record is not cleared for redistribution. the commentary's open question: how elementary number circuits are recruited into expertise is not addressed by the data Quotation withheld because this record is not cleared for redistribution. visual number form area (VNFA) visual number form area (VNFA) Quotation withheld because this record is not cleared for redistribution. visual number form area visual number form area Quotation withheld because this record is not cleared for redistribution. reverse-inference meta-analysis reverse-inference meta-analysis Quotation withheld because this record is not cleared for redistribution. 89 studies — Number of studies whose abstracts mention "numerical", pooled in the author's Neurosynth map Quotation withheld because this record is not cleared for redistribution. 885 studies — Number of studies contributing to the "language" term map in the same meta-analysis Quotation withheld because this record is not cleared for redistribution. 15 expert mathematicians and 15 nonmathematicians — Sample of the fMRI study the commentary evaluates Quotation withheld because this record is not cleared for redistribution. 89 studies — abstracts mentioning 'numerical' behind the commentary's own meta-analytic map Quotation withheld because this record is not cleared for redistribution. 885 studies — abstracts mentioning 'language' in the same analysis - ten times the numerical set Quotation withheld because this record is not cleared for redistribution.

The full text of this article is not redistributable, so it is not included here. The evidence sentences are withheld with it; the tag layer and its grounding status remain. The article itself is at https://doi.org/10.1073/pnas.1604758113.