Scanning 20 adults as they compared quantities, a Paris team found an orderly map of magnitude in the parietal cortex that accommodated one-third alongside three.

People talk about numbers spatially without noticing it. Quantities are high or low, they go up and down, one number is close to another. Whether that is a feature of language or of the brain has been argued over for decades.

A study in PLOS Biology from the INSERM-CEA Cognitive Neuroimaging Unit in France finds the spatial organisation in the tissue. Scanning adults while they judged numerical magnitude, the team found a structured activity map in which quantities are arranged in order — and found that fractions sit on the same map as 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 write. “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.”

Why fractions are the interesting case

Integers having a neural representation is not news. The approximate number system — a capacity to judge quantity without counting — is present in infants and in other animals, and its home in the intraparietal sulcus has been mapped for twenty years.

Fractions are a different proposition. They are a cultural invention rather than a perceptual primitive, acquired late, taught with difficulty, and famously hard: a substantial fraction of adults cannot reliably say whether one-third is larger than one-quarter. There has been a reasonable argument that fractions are handled by symbolic manipulation of their components rather than by any magnitude sense at all — that the brain reads 3/4 as a pair of whole numbers and applies a rule.

The finding that fractions occupy positions on the same magnitude map as integers says otherwise. Whatever the difficulty of learning them, the brain appears to end up representing their value rather than only their notation.

What the scans showed

Twenty native French speakers judged whether each number presented was bigger or smaller than the previous one, while brain activity was recorded with functional MRI.

The resulting activity pattern in the intraparietal sulcus was organised: the authors describe evidence of individual voxels tuned to specific numbers, and of an overall numerotopic map — meaning that adjacent patches of cortex respond to adjacent quantities, in the way that adjacent patches of visual cortex respond to adjacent locations in the visual field.

That kind of orderly spatial layout is a recurring motif in the brain. Vision is retinotopic, hearing tonotopic, touch somatotopic — each mapping a continuous dimension onto the cortical sheet. A numerotopic map puts abstract magnitude in the same category, which is a stronger claim than merely saying a region is active during arithmetic.

Integers and fractions were processed differently within individual participants while still fitting inside the shared system — the distinction preserved, the common scale maintained.

The behaviour matched

Two behavioural results support the neural picture, and both are the kind of effect that would be predicted if numbers really are laid out on a line.

Participants made more ordering errors when fractions were involved, which is the expected penalty for a less practised and less precisely represented class of number.

More tellingly, participants were slower when two fractions were close in value. That is the signature of magnitude comparison: deciding between quantities takes longer the nearer they are, because the representations overlap. A system that computed fractions by applying rules to their numerators and denominators would not necessarily show that pattern — a rule is a rule regardless of how close the values are.

Twenty people

The sample is small, and that deserves stating. Twenty participants is normal for this kind of high-resolution fMRI work, where the analysis depends on fine-grained patterns within each individual brain rather than on averaging across many, but it limits how much can be said about variation between people — including the variation that matters most practically, between those who find fractions manageable and those who do not.

The participants were also all native French speakers, and number words differ across languages in ways known to affect numerical cognition. Whether the map looks the same in speakers of languages with more transparent number systems is not addressed.

And the task was magnitude comparison specifically. The authors are careful on this point, framing the finding as what happens “when we focus on the magnitude of numbers” — which leaves open how numbers are handled in tasks that do not call for comparing quantities, such as exact calculation.

What it might be for

The authors suggest the organisation may help us process quantities and make mathematical decisions more efficiently, which is a reasonable inference from the architecture: a map in which nearby values sit in nearby tissue makes comparison a local operation rather than a search.

The educational implication is more speculative and more interesting. If fractions are ultimately represented as magnitudes on a shared line, then teaching that builds that representation — number lines, estimation, comparing sizes — would be working with the underlying system rather than against it, and teaching that treats fractions purely as a pair of integers under a bar would not. The study does not test any of that.

The work was led by Dr Daniela Valério and Dr Stanislas Dehaene at the INSERM-CEA Cognitive Neuroimaging Unit, with co-authors S. Debray, A. Karami, M. Cauté and N. Gravel. It was funded by the European Research Council under the MathBrain grant to Dehaene (ERC-2022-ADG 101095866); the funder had no role in the study’s design, data collection and analysis, publication decision or manuscript preparation.

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Notes

1. Valério, D., et al. PLOS Biology, 2026, 24(10): e3003820. DOI: 10.1371/journal.pbio.3003820.
2. PLOS. “Your brain maps out numbers, including integers and fractions.” EurekAlert!, 22 October 2026. https://www.eurekalert.org/news-releases/1147756.