Summary:
A neuroimaging study led by cognitive neuroscientists at the INSERM-CEA Cognitive Neuroimaging Unit (Unicog) reveals that the human brain constructs a continuous, highly structured spatial semantic map in the intraparietal sulcus to represent numerical magnitudes. Functional MRI scans of adults comparing fractions and whole numbers demonstrate that while fractions demand greater cognitive effort, both distinct numerical formats are projected onto a shared mental number line to enable mathematical reasoning.
Key Facts:
- Continuous Spatial Map: High-resolution fMRI scans revealed that patterns of neural activation across the intraparietal sulcus shift in an orderly spatial trajectory corresponding to numerical magnitude, providing direct empirical evidence for a neural number line.
- Shared Abstract System: Despite integers and fractions engaging distinct computational processing steps, the brain plots both numerical formats along the same shared representational map when assessing relative quantity.
- Fraction Comparison Cost: Participants demonstrated slower response latencies and higher error rates when comparing fractions of close numerical values, reflecting the elevated cognitive burden of computing ratios versus discrete whole integers.
Source: PLOS / INSERM-CEA Cognitive Neuroimaging Unit (Unicog)
From basic counting in early childhood to navigating algebraic equations and advanced calculus, mathematical cognition requires the brain to categorize and organize abstract values. For decades, cognitive neuroscientists have investigated how the cerebral cortex encodes non-physical, abstract concepts.
A prominent model in cognitive science posits that the brain builds “semantic maps”—topographically organized neural networks where semantically related concepts are represented by adjacent patterns of neural activity. Because numbers follow a rigid, universally defined order of magnitude, they provide an ideal model to test whether the brain organizes abstract knowledge into continuous internal coordinate systems.
Now, an investigation led by Stanislas Dehaene, PhD, and Daniela Valério, PhD, at the INSERM-CEA Cognitive Neuroimaging Unit (Unicog) in France confirms that the brain plots quantities onto a precise, unified spatial architecture.
Publishing October 22 in the open-access journal PLOS Biology, the researchers used dynamic functional magnetic resonance imaging (fMRI) to capture the human brain’s internal number line in action as adults compared integers and fractions.
Mapping Magnitude in the Intraparietal Sulcus
The study recruited 20 native French-speaking adults who were presented with sequences of whole numbers (such as 3, 7, 12) and fractional values (such as 1/4, 2/3, 5/8). While undergoing fMRI scanning, participants were tasked with deciding whether each successive number was larger or smaller than the preceding value.
By analyzing voxel-level activity patterns during these comparisons, the investigators identified a structured, geometric layout of neural activation within the intraparietal sulcus (IPS)—a parietal lobe region historically implicated in spatial attention, magnitude estimation, and mathematical calculation.
As participants evaluated changing numerical values, patterns of cortical activity shifted systematically according to relative size. This continuous topological gradient indicates that the intraparietal sulcus contains a true spatial map of numerical magnitude, smoothly transitioning from small to large values.
Unifying Whole Numbers and Fractions
A central question addressed by the researchers was whether complex, non-integer values rely on their own independent neural circuits or merge into the existing whole-number system.
Individual participant analyses revealed that the brain handles the initial decoding of integers and fractions differently. Whole numbers are processed directly as discrete quantities, whereas fractions require the brain to process the numerical ratio between numerator and denominator.
Consequently, participants were slower to respond and made more sorting errors when evaluating fractions—especially when two fractional quantities were numerically close (e.g., comparing 5/7 to 3/4), reflecting a classic numerical distance effect.
Crucially, however, once the brain extracts the absolute magnitude of a fraction, it projects that value onto the exact same intraparietal coordinate map used for integers.
“Our study shows that when we focus on the magnitude of numbers, the brain organizes quantities into a highly structured internal map,” the authors explained. “This map brings fractions and integers together along a shared mental number line, allowing us to represent and compare different kinds of numbers within the same system. This organization may help us process quantities and make mathematical decisions more efficiently.”
Implications for Mathematical Cognition and Education
The finding that fractions and integers converge onto a shared spatial continuum sheds light on why learning fractions poses such a persistent challenge in primary education. Children must transition from counting discrete, whole entities to understanding continuous ratios, requiring the parietal cortex to integrate two separate digits into a single coordinate point on the mental number line.
By showing how the intraparietal sulcus organizes abstract mathematical magnitudes into a common geometric framework, the research reinforces the geometric foundation of human arithmetic, providing a biological baseline for diagnosing mathematical learning disabilities like developmental dyscalculia and refining pedagogical strategies in mathematics.
Funding: This work was supported by the European Research Council (ERC; https://erc.europa.eu/) under the ERC grant “MathBrain” to SD (grant number ERC-2022-ADG 101095866). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Editorial Notes:
- This article was edited by a Neuroscience News editor.
- Journal paper reviewed in full.
- Additional context added by our staff.
About this neuroscience and math Research:
- Media Contact: Claire Turner
- Source: PLOS
- Image Credit: Image credited to Neuroscience News
- Original Research is Open Access: PLOS Biology (Oct 1, 2026). “A cortical semantic map integrates fractions and integers in the human brain.” Authors: Daniela Valério, Samuel Debray, Alireza Karami, Maxime Cauté, Nicolás Gravel, and Stanislas Dehaene.
- 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? Some theories postulate the existence of semantic spaces where concepts occupy positions that reflect their conceptual relationships. In the number domain, psychological evidence suggests that integers are represented along a mental number line which, with education, integrates higher-level number concepts such as fractions.
To test this hypothesis, we recorded whole-brain 7T fMRI responses to integer and fraction symbols during an active magnitude comparison task designed to engage magnitude processing. Consistent with predictions, we found both behavioral and neural numerical distance effects.
Activation vectors in intraparietal, inferior temporal, prefrontal, hippocampal, and parahippocampal cortices formed a two-dimensional semantic space organized by numerical magnitude and domain (fractions versus integers). Gaussian fits revealed a topographic map of numerical preferences in the anterior inferior parietal cortex, common to both domains.
Our results suggest that, when educated adults engage in an explicit magnitude comparison task, their brain can construct an ordered representation that integrates fractions and integers, with a topographic organization in the anterior IPS/IPL.
