A critical question for the study of numerical cognition is whether the complex, symbolic mathematical abilities of adult humans share a neurobiological and developmental origin with non-symbolic numerical abilities. A growing body of evidence suggests that the ability to judge numerical values nonverbally was an important evolutionary precursor to adult human symbolic numerical abilities [

15,

60,

61], and that it is a language-independent cognitive capacity [

7,

9]. Our study provides additional evidence that there is an important neurobiological link between symbolic and non-symbolic numerical cognition in adults and thus helps to resolve current controversies in the adult literature [

28,

29]. Most importantly, our study further demonstrates that the IPS is recruited for non-symbolic numerical processing early in development, before formal schooling has begun.

A great many studies have investigated how children acquire the verbal counting system [

2,

36,

44]. Furthermore, there are disparate hypotheses about how children begin to map the meaning of number words onto nonverbal representations of number [

4,

35,

36,

44,

62]. Our study provides new evidence of a neurobiological link between the early approximate numerical abilities of children, and the more sophisticated non-symbolic and approximate symbolic numerical abilities of adults. We therefore suggest that non-symbolic numerical activity in the IPS may be a developmental origin of adult mathematical knowledge [

15,

17]. Ultimately, a full description of how children learn the meaning of number words must incorporate these new findings.

As mentioned, previous work with adult participants has implicated the IPS in processing Arabic numerals and number words but has remained inconclusive on the role of the IPS in processing non-symbolic number [

28,

29,

30]. One study [

28] used an event-related adaptation design and found that activity in the IPS correlated with the numerical distance between standard numerical stimuli and numerical deviants. However, unlike the present study, in the study by Piazza and colleagues [

28], number-related activity in the IPS was not directly contrasted with activity related to a class of non-numerical stimuli in a random-effects analysis and compared against baseline activity. Thus, the authors could not definitively demonstrate number-specific brain activity for visual arrays. Similarly, number specificity in the IPS was not definitively demonstrated in a study by Ansari et al. [

30], which nicely demonstrated parametric modulation of IPS activity by numerical distance but did not test whether the IPS responds significantly above baseline to non-numerical stimuli. The current study directly contrasted number-related activity in the IPS with activity related to shape changes in a random-effects analysis and compared this against baseline activity, providing strong evidence in favor of the argument that the IPS is sensitive to numerical changes for sets of visual objects and that this region does not respond equally to all stimulus changes (i.e., shape changes; [

28]).

In contrast to our result, Shuman and Kanwisher [

29] found no difference in IPS activity between blocks in which number varied and those in which number was held constant. One possible explanation of the conflicting results between these two studies is that in the study by Shuman and Kanwisher [

29], surface area varied in the “number constant” blocks, which could have elicited IPS activity because the IPS has been shown to respond to changes in surface area [

63]. Consequently, the IPS may have responded to number changes in the “number varied” condition, but responded to surface area changes in the “number constant” condition. These two responses in the IPS could have canceled each other out in a statistical contrast [

30]. This explanation of the Shuman and Kanwisher [

29] result assumes that the IPS plays a more general role in magnitude judgments and is not selective for number per se. Yet it leaves open the possibility that the IPS responds to changes in magnitude as suggested by Pinel and colleagues [

63] but not to changes along other dimensions (e.g., shape).

Alternative explanations of the IPS response to numerical deviants such as a non-numerical recovery response, a non-numerical novelty response, a general novelty response, or a response reflecting changes in visual attention cannot account for our result. First, the recovery response exhibited by the IPS to numerical deviants cannot be attributed to non-numerical dimensions such as cumulative surface area, density, or element size because these non-numerical dimensions were constantly varied in the standard stimuli while number and shape were held constant. Thus, given the known characteristics of an fMRI-adaptation design [

48], the IPS could not adapt to these dimensions. Second, the IPS response to numerical deviants cannot be explained as a novelty effect evoked by the non-numerical dimensions of cumulative surface area or density because shape and number deviants were equated on these dimensions and their effect, if any, would cancel out in the number > shape contrast. The element size of the deviant stimuli would also fail to evoke a novelty response because element sizes for deviant stimuli were taken from the distribution of values from the standard stimuli and were thus never novel compared to the range of standard stimuli to which the IPS adapted. Third, because we directly contrasted the brain response to two categories of deviant stimuli, alternate explanations of IPS activity, such as a general novelty effect, cannot easily account for our result. Additionally, the IPS responded to numerical deviants regardless of whether deviants increased or decreased in their number of elements from the standard stimuli. This result indicates that a greater IPS response to numerical deviants does not simply reflect increased attention with the number of visual objects presented. Lastly, our study did not require participants to perform an explicit number-related task, indicating that task difficulty is not necessarily a correlate of IPS activity. An implication of this finding is that the IPS responds automatically to numerical information when participants passively view numerically relevant stimuli. Taken together with previous studies, our results suggest that the IPS plays a role in both symbolic and non-symbolic numerical processing and is thus important for processing number independent of notation. Further, our comparable results from both children and adults make a case for an early-developing neural substrate for notation-independent numerical processing.

Behavioral studies of children's developing numerical abilities have highlighted important similarities and differences in numerical competence over development [

4,

17,

35,

59]. Studies of numerical processing in adults have revealed number-selective brain regions in and around the IPS [

28,

21,

30]. Our study provides evidence that numerical processing invokes a common neural substrate in adults and children during the presentation of non-symbolic numerical stimuli; by 4 y, the IPS responds more strongly to numerical changes than to shape changes. Therefore, the similarities in numerical performance across ontogeny may reflect reliance on a single substrate for numerical processing from childhood to adulthood. However, symbolic numerical abilities are reported to recruit a broader network of number-specific brain regions than the IPS alone [

21]. For example, the ability to solve multiplication tables and other math facts appears to recruit regions in and around the left angular gyrus [

20,

21,

64–

66]. Some researchers have suggested that this brain region is important for the explicit manipulation of numerical values that is characteristic of adult human mathematics [

35,

66]. Thus, conceptual development related to cultural, linguistic, and symbolic numerical practices might cause changes in the network of brain regions involved in precise, sophisticated adult mathematics [

2,

20]. However, the neural basis of notation-independent numerical processes in the IPS may be the nucleus of this sophisticated mathematical network over development.

It is possible that the IPS also supports non-symbolic numerical discrimination in infancy. As mentioned, the behavioral signatures of non-symbolic numerical processing in infants, children, and adults indicate that numerical discrimination employs similar psychological mechanisms over development. Studies with human infants in the 6th mo of life have demonstrated that, like adults and children, infants also show ratio-dependent numerical discrimination [

37–

39]. Similarly, studies of non-human animals also show striking parallels in the behavioral and neural signatures of number processing [

1–

8,

15,

16,

67–

69]. The neural bases of numerical cognition may be, therefore, both ontogenetically and phylogenetically primitive.

In conclusion, our data provide strong evidence in favor of the view that the IPS, known to be part of a cerebral network important for symbolic number processing, is also recruited in non-symbolic numerical processing. Further, by testing one of the youngest samples of healthy children in a cognitive fMRI study, we have shown that by 4 y, the IPS is already recruited when children represent number non-symbolically. Our results are therefore consistent with the view that the IPS is the ontogenetic and phylogenetic origin of non-symbolic number processing and serves as a foundation upon which symbolic number processing is built. Although our data further demonstrate the ubiquitous role of the IPS in numerical processing, additional work is necessary to determine whether any region of the IPS is truly number-specific or instead plays a more general role in magnitude processing.