Humanity is able to count numbers and perform complex calculations because the brain organizes numerical information in an orderly way.

The brain does not place integers and fractions in separate spaces, but instead compares and gauges their magnitudes by placing them together on a single vertical number-line map.

The research team led by researcher Daniela Valerio of the Cognitive Neuroimaging Unit under the French National Institute of Health and Medical Research (INSERM) and the French Alternative Energies and Atomic Energy Commission (CEA) identified the existence of a map in the brain that arranges numerical information in the form of a vertical number line, and published the findings in the international journal “PLOS Biology” on the 22nd (local time).

How the brain processes concepts as complex and abstract as fractions has long been a major question in neuroscience. Based on the hypothesis that the brain groups similar concepts through adjacent neural network activity, the team set out to verify whether numbers of similar magnitude are arranged adjacently regardless of whether they are integers or fractions.

To examine how the human brain systematizes numerical information, the brains of 20 adults were scanned using functional magnetic resonance imaging (fMRI). Participants took part in an experiment in which they were presented with sequences of integers and fractions and asked to judge whether each number was larger or smaller than the preceding one.

The researchers measured the participants’ blood-oxygen-level dependent (BOLD) signals during the experiment. BOLD tracks changes in blood flow and oxygen supply to identify which brain regions are activated during specific tasks. The measurements revealed systematic activation patterns in brain areas responsible for mathematical information processing, including the intraparietal sulcus.

The greater the difference between the two consecutively presented numbers, the more pronounced the difference in neural responses. This suggests the existence of an “internal number map” that arranges numbers in order from smaller to larger.

For example, when a participant saw the number “6,” the brain area immediately adjacent to the region responsible for “5” was activated, whereas when a number with a much larger difference, such as “60,” was shown, the activated neural region and signal intensity changed. Compared with the presentation of integers alone, errors in judgment became more frequent when fractions were included, and reaction times slowed as the magnitude difference between two fractions decreased.

It was also confirmed that the brain clearly distinguishes and processes the notational forms of integers and fractions. Because fractions consist of two integers, a numerator and a denominator, they impose a greater computational load on neural networks. When estimating the quantitative magnitudes of integers and fractions, the brain arranged the numbers within a single shared neural network system.

The research team explained, “The internal number map in the brain arranges integers and fractions along a mental vertical number-line map,” adding, “It enables different forms of numbers to be represented and compared within the same framework, helping to make mathematical decisions more efficiently.”

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