Summary:
A neuroimaging investigation led by cognitive neuroscientists at the INSERM-CEA Cognitive Neuroimaging Unit (Unicog) shows that the human brain constructs a continuous, highly organized spatial semantic map in the intraparietal sulcus to represent numerical magnitudes. High-resolution functional MRI (fMRI) scans comparing whole numbers and fractions in adults reveal that, although fractions require additional computation and slow responses, both formats are represented along a single shared mental number line that supports numerical reasoning.
Key Facts:
- Continuous Spatial Map: High-resolution fMRI patterns across the intraparietal sulcus show orderly shifts in neural activation that correspond to numerical magnitude, providing direct neural evidence for a spatial number line.
- Shared Abstract System: Despite different computational demands for integers and fractions, both kinds of numbers are projected onto the same representational map when the brain evaluates relative magnitude.
- Fraction Comparison Cost: Participants responded more slowly and made more errors when comparing fractional values that were close in magnitude, reflecting the increased cognitive cost of computing ratios versus discrete integers.
Source: PLOS / INSERM-CEA Cognitive Neuroimaging Unit (Unicog)
From counting in early childhood to solving algebra and calculus, mathematical thought depends on the brain’s ability to represent, compare, and manipulate abstract quantities. Cognitive neuroscience has long sought to understand how the cerebral cortex encodes these non-physical concepts.
One influential idea is that the brain builds semantic maps—topographic neural organizations where semantically related entries occupy neighboring positions of neural activity. Numbers, which form a strict and universal order of magnitude, are an ideal test case for whether abstract knowledge is arranged in continuous internal coordinate spaces.
Researchers at Unicog, led by Stanislas Dehaene, PhD, and Daniela Valério, PhD, used dynamic fMRI to observe the brain’s internal number line in action while adults compared integers and fractions. The work identifies a precise spatial architecture that the brain uses to represent numerical magnitude.
Mapping Magnitude in the Intraparietal Sulcus
Twenty native French-speaking adults were scanned while viewing sequences of whole numbers (for example, 3, 7, 12) and fractional values (for example, 1/4, 2/3, 5/8). During fMRI acquisition, participants judged whether each number was larger or smaller than the previous one.
Voxel-level analyses of brain activity during these comparisons revealed a structured, geometric pattern of activation within the intraparietal sulcus (IPS), a parietal region long associated with spatial attention, magnitude estimation, and arithmetic. As values changed, cortical activity patterns followed a continuous topological gradient aligned with numerical size, indicating a smooth transition from representations of small to large magnitudes.
Unifying Whole Numbers and Fractions
A key question was whether non-integer values rely on specialized neural circuitry or whether they are integrated into the same magnitude representation as integers.
Analyses at the individual level showed distinct initial processing paths: whole numbers are processed as discrete quantities, while fractions require computation of the ratio between numerator and denominator. This additional processing explains longer response times and more errors when participants compared fractions, particularly when two fractions were numerically close—an instance of the numerical distance effect.
Importantly, after the brain extracts a fraction’s absolute magnitude, it maps that magnitude onto the same intraparietal coordinate system used for integers. In other words, once converted into a scalar value, fractions and whole numbers occupy positions along a common internal number line.
“When we focus on magnitude, the brain arranges quantities into a highly structured internal map,” the researchers note. “This organization unites fractions and integers on a shared mental number line, enabling us to represent and compare different numerical formats within a single system and supporting efficient mathematical decision-making.”
Implications for Mathematical Cognition and Education
The convergence of fractions and integers onto a unified spatial continuum helps explain why learning fractions is often difficult in early education. Children must shift from counting discrete whole items to understanding continuous ratios, requiring the parietal cortex to convert two-digit fraction representations into a single coordinate on the mental number line.
By demonstrating a geometric framework in the intraparietal sulcus for abstract mathematical magnitudes, the study provides a neurobiological foundation for arithmetic and offers practical insight for diagnosing and addressing mathematical learning difficulties, including developmental dyscalculia. These findings can inform pedagogical approaches by highlighting the cognitive steps required to integrate fractions into an existing numerical representation.
Funding: This research was funded by the European Research Council (ERC) under the ERC grant “MathBrain” to SD (grant number ERC-2022-ADG 101095866). The funders did not influence study design, data collection and analysis, the decision to publish, or manuscript preparation.
Editorial Notes:
- This article was edited by a Neuroscience News editor.
- The journal paper was reviewed in full.
- Additional context was added by editorial staff.
About this neuroscience and math Research:
- Media Contact: Claire Turner
- Source: PLOS
- Image Credit: Image credited to Neuroscience News
- Original Research (Open Access): PLOS Biology. Title: “A cortical semantic map integrates fractions and integers in the human brain.” Authors include Daniela Valério and Stanislas Dehaene et al.
- DOI: 10.1371/journal.pbio.3003820
Abstract
A cortical semantic map integrates fractions and integers in the human brain
How does the human brain represent the meaning of abstract symbols such as numbers? One proposal is that concepts are embedded in semantic spaces where positions reflect conceptual relationships. In the number domain, behavioral evidence indicates that integers are organized along a mental number line and that, with education, higher-level constructs like fractions become integrated into this dimension.
To evaluate this hypothesis, the researchers recorded high-field whole-brain fMRI responses to integer and fraction symbols during an active magnitude-comparison task designed to engage magnitude processing. Behavioral and neural numerical distance effects were observed, consistent with theoretical predictions.
Activation patterns in intraparietal, inferior temporal, prefrontal, hippocampal, and parahippocampal cortices formed a two-dimensional semantic space organized by numerical magnitude and numerical domain (fractions versus integers). Modeling revealed a topographic map of numerical preferences in anterior inferior parietal cortex that was common across domains.
These results suggest that, when educated adults perform explicit magnitude comparisons, the brain constructs an ordered representation that integrates fractions and integers, with a topographic organization centered in the anterior intraparietal region.