Did evolution endow the human brain with a predisposition to represent and acquire knowledge about numbers? Although the parietal lobe has been suggested as a potential substrate for a domain-specific representation of quantities, it is also engaged in verbal, spatial, and attentional functions that may contribute to calculation. To clarify the organisation of number-related processes in the parietal lobe, we examine the three-dimensional intersection of fMRI activations during various numerical tasks, and also review the corresponding neuropsychological evidence. On this basis, we propose a tentative tripartite organisation. The horizontal segment of the intraparietal sulcus (HIPS) appears as a plausible candidate for domain specificity: It is systematically activated whenever numbers are manipulated, independently of number notation, and with increasing activation as the task puts greater emphasis on quantity processing. Depending on task demands, we speculate that this core quantity system, analogous to an internal "number line," can be supplemented by two other circuits. A left angular gyrus area, in connection with other left-hemispheric perisylvian areas, supports the manipulation of numbers in verbal form. Finally, a bilateral posterior superior parietal system supports attentional orientation on the mental number line, just like on any other spatial dimension.

Number, like color or movement, is a basic property of the environment. Recently, single neurons tuned to number have been observed in animals. We used both psychophysics and neuroimaging to examine whether a similar neural coding scheme is present in humans. When participants viewed sets of items with a variable number, the bilateral intraparietal sulci responded selectively to number change. Functionally, the shape of this response indicates that humans, like other animal species, encode approximate number on a compressed internal scale. Anatomically, the intraparietal site coding for number in humans is compatible with that observed in macaque monkeys. Our results therefore suggest an evolutionary basis for human elementary arithmetic.

Since the time of Pythagoras, numerical and spatial representations have been inextricably linked. We suggest that the relationship between the two is deeply rooted in the brain's organization for these capacities. Many behavioural and patient studies have shown that numerical-spatial interactions run far deeper than simply cultural constructions, and, instead, influence behaviour at several levels. By combining two previously independent lines of research, neuroimaging studies of numerical cognition in humans, and physiological studies of spatial cognition in monkeys, we propose that these numerical-spatial interactions arise from common parietal circuits for attention to external space and internal representations of numbers.

Activation of the horizontal segment of the intraparietal sulcus (hIPS) has been observed in various number-processing tasks, whether numbers were conveyed by symbolic numerals (digits, number words) or by nonsymbolic displays (dot patterns). This suggests an abstract coding of numerical magnitude. Here, we critically tested this hypothesis using fMRI adaptation to demonstrate notation-independent coding of numerical quantity in the hIPS. Once subjects were adapted either to dot patterns or to Arabic digits, activation in the hIPS and in frontal regions recovered in a distance-dependent fashion whenever a new number was presented, irrespective of notation changes. This remained unchanged when analyzing the hIPS peaks from an independent localizer scan of mental calculation. These results suggest an abstract coding of approximate number common to dots, digits, and number words. They support the idea that symbols acquire meaning by linking neural populations coding symbol shapes to those holding nonsymbolic representations of quantities.

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How are comparative judgments performed in the human brain? We scanned subjects with fMRI while they compared stimuli for size, luminance, or number. Regions involved in comparative judgments were identified using three criteria: task-related activation, presence of a distance effect, and interference of one dimension onto the other. We observed considerable overlap in the neural substrates of the three comparison tasks. Interestingly, the amount of overlap predicted the amount of cross-dimensional interference: in both behavior and fMRI, number interfered with size, and size with luminance, but number did not interfere with luminance. The results suggest that during comparative judgments, the relevant continuous quantities are represented in distributed and overlapping neural populations, with number and size engaging a common parietal spatial code, while size and luminance engage shared occipito-temporal perceptual representations.

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Subitizing is the rapid and accurate enumeration of small sets (up to 3-4 items). Although subitizing has been studied extensively since its first description about 100 years ago, its underlying mechanisms remain debated. One hypothesis proposes that subitizing results from numerical estimation mechanisms that, according to Weber's law, operate with high precision for small numbers. Alternatively, subitizing might rely on a distinct process dedicated to small numerosities. In this study, we tested the hypothesis that there is a shared estimation system for small and large quantities in human adults, using a masked forced-choice paradigm in which participants named the numerosity of displays taken from sets matched for discrimination difficulty; one set ranged from 1 through 8 items, and the other ranged from 10 through 80 items. Results showed a clear violation of Weber's law (much higher precision over numerosities 1-4 than over numerosities 10-40), thus refuting the single-estimation-system hypothesis and supporting the notion of a dedicated mechanism for apprehending small numerosities.