To date, the literature has emphasized the role of humans’ neocortical regions in arithmetic abilities. However, very little is known about the neuroevolutionary development of numerical abilities. A central question addressed by the present study is whether evolutionarily primitive mechanisms and neural substrates are involved in humans’ arithmetic abilities.

The pattern of results arising from our experiments provides evidence for the notion that primitive subcortical regions have a functional role in the performance of symbolic arithmetic calculations. Humans’ primitive subcortical regions are involved in basic numerical abilities26, and such rudimentary skills are the building blocks of more advanced arithmetic abilities18. In contrast to most of the literature, our findings lend support to the claim that primitive subcortical brain regions that are shared by different species are involved not only in rudimentary numerical skills, but also in arithmetic calculations. The results suggest that neocortical regions are not the only parts of the human brain that are involved in arithmetic, and that a cortico-subcortical loop may supports arithmetic calculations.

Indeed, although most previous literature emphasized the involvement of cortical regions, some studies do support the hypothesis that subcortical regions have a role in general arithmetic processes40–42. These studies have demonstrated the relation between subcortical regions (e.g., basal ganglia, thalamus) and general arithmetic processes. Interestingly, one study has showed that stimulation of the thalamus impaired arithmetic processes, and in particular, calculation involving lower numbers. This previous result is in line with our results of Experiment 4 which suggest that the role of subcortical regions is limited to solving lower numbers equations. However, note that all of the above studies have demonstrated the relation between subcortical regions and general arithmetic processes, but none of them, have demonstrated a direct causal role of subcortical regions specifically in arithmetic calculation. In addition, previous studies did not dissociate between different processes involved in solving arithmetic problems such as perceptual, memory retrieval, and comparison processes. In three different experiments, using sensitive-behavioral manipulation, the current pattern of results demonstrated the role of lower visual channels specifically in calculation, and not in other general arithmetic processes.

The current study findings also converge with others which imply that cultural constructions are grounded upon evolutionarily ancient representations, such as space and number 18,43. In accordance with previous literature 43,44, we suggest that the current fully developed numerical system of humans may have been mediated by the use of more basic nonsymbolic processes (e.g., spatial abilities and conceptual size). Using neurosurgical patients, a recent study has provided evidence of the involvement of non-neocortical regions by demonstrating that single neurons in the human medial temporal lobe encode symbolic and nonsymbolic numerical information45. In particular, the study found that numerosity and abstract numerals are encoded by distinct neuronal populations in the medial temporal lobe and suggested that representation of symbolic numerals may evolve from more basic numerosity representations.

Some theoretical accounts even suggest the compositionality of number concepts (e.g., seven is composed of other, smaller numbers). That is, the representation of numbers is itself an arithmetic (set-based) calculation46. Accordingly, the involvement of non-neocortical regions in the representation of numbers suggests the involvement of those regions in a more fundamental form of arithmetic calculations. In addition, conceptual size representation is necessary for an organism’s survival in an ever-changing environment (e.g., the ability to determine a predator’s approximate size). Conceptual sizes can thus be viewed as evolutionarily early measurement units of continuous numerical values. That is, conceptual sizes carry long-term knowledge of an object’s size, regardless of the object’s actual retinal size. Thus, they might be considered equivalent to numerals, which (symbolically) denote long-term knowledge of specific quantities. In addition, recent data support the idea that the basic approximation number system and higher symbolic numerical abilities are intrinsically linked47. Congenitally blind and blindfolded sighted participants completed an auditory numerical approximation task and a symbolic arithmetic task. It was found that the precision of approximate number representations was identical across congenitally blind and sighted groups. This finding suggests that the development of the approximate number system does not depend on visual experience, and that the basic approximation number system and the higher symbolic numerical abilities are strongly associated47. This proposal is also in line with the recent finding of numerosity representation in human subcortical regions26, which indicates the involvement of evolutionarily primitive brain regions in humans’ basic numerical abilities. It is noteworthy that the cited study did not find evidence for subcortical involvement in an Arabic numeral comparison task. This result is in line with our findings of no subcortical involvement in Arabic numeral comparison processes (as we found null effects for the solution to a different-eye condition vs. all in one-eye condition), yet our results do demonstrate a specific subcortical involvement in computational arithmetic processes. Finally, although the modal view in the literature suggests that consciousness is encoded by neocortical regions and is necessary for arithmetic, findings have demonstrated that humans can solve arithmetic equations nonconsciously48.

To conclude, the present study pattern of results is in line with very recent studies that, in contrast to most of the previous literature, have demonstrated the involvement of noncortical regions in symbolic spatial abilities in humans and fish (Saban et al., 2017; Saban et al., 2018), nonsymbolic and symbolic numerical abilities in humans26,45, and even symbolic numerical abilities in very simple organisms such as bees25. Recently, using the stereoscopic manipulation, it was demonstrated that the subcortex has a causal role in cognitive transfer of complex cognitive skills in humans13. Such cognitive transfer was found for both novel figural-spatial problems (near transfer) and novel subtraction problems (far transfer). These results challenge the exclusive role of the cortex in cognitive transfer as was previously assumed. Most pertinent for the current work, this recent finding demonstrates the direct relations between spatial and arithmetic abilities, but also converge with the notion that the subcortex functionally supports arithmetic13.

The present study extends previous literature by demonstrating that subcortical mechanisms support the ability of humans to solve symbolic arithmetic equations. Although nonsymbolic numerical abilities (such as approximation and conceptual size representation) and symbolic numerical abilities might be phylogenetically and ontogenetically distinct, they might have been linked throughout human development. From an evolutionary perspective, one possibility is that basic nonsymbolic numerical abilities may have served as basic units of present-day more formal and complex arithmetic abilities. It is possible that subcortical regions might contribute to numerical representations (such as space and conceptual size) and are used as evolutionary scaffolding for higher arithmetic abilities. We suggest that in a larger conceptual framework, all these novel findings call for a significant update of the modal view of the exclusive role of neocortical mechanisms in higher cognitive functions.

The results have major implications for our understanding of the neuroevolutionary development of numerical abilities. The current findings suggest a parsimonious explanation for higher numerical abilities of different animals, despite their lack of neocortical structures similar to those that have been suggested to support higher cognition in humans. Based on these and other results9,14,26,50–53 and on evolutionary and developmental theories of the human brain54, we propose a general conceptual framework, according to which Ubiquitous Neural Systems (UNS; e.g., subcortical regions) may have a functional role in the development and evolution of cognition. According to this framework, since UNS developed early in evolution, and have survived and remained functional up to the present, these systems are essential for cognitive operations that enable organisms to adapt to an ever-changing environment. UNS perform fundamental computations, with the neocortex using these computations to allow the emergence of more complex cognitive abilities. Neocortical regions have access to UNS computations, resulting in a dynamic network that allows more complex cognitive representations such as arithmetic. This conceptual notion predicts that: 1) UNS are involved in the evolution and development of cognition, and 2) UNS are involved in cognition in species that do not have fully developed cortex (e.g., fish), and 3) UNS are involved in cognitive abilities in the mature human brain even in what is considered “higher-order” cognition, such as arithmetic. We term this conceptual framework the “*UNS hypothesis*.” We propose that UNS, which are ubiquitous across the animal kingdom, enable cognitive operations essential for the emergence of complex cognition (see also13). UNS can be reused and manipulated by neocortical mechanisms, and jointly, novel skills can be developed during evolution.

It should be noted that perceptual differences, integration cost, binocular rivalry, and intraocular suppression cannot fully explain the differences in performance observed between the eye-of-origin conditions in the current experiments. First, to preclude any confounding effect of perceptual differences between the eye-of-origin conditions and to determine whether participants experienced a well-fused percept in all the conditions, the stereoscope apparatus was calibrated for each participant individually to ensure perceptual fusion of the images presented in all the conditions (see Methods section for more details). Second, both in the solution to a different-eye condition and in the computational term split condition, one of the numbers in the equation was presented to a different eye. If presenting one number to a different eye hampers performance, regardless of the involvement of a symbolic computational process, performance should be impaired in the solution to a different-eye condition compared with the all in one-eye condition. This was not case in all four experiments. Third, when looking at the computational term split condition, there was no significant difference between equations in which the number presented to the different eye was from the first or third location. This indicates that the spatial location of the number that was presented to the other eye cannot fully explain the findings. Lastly, the same perceptual factors are involved both in equations containing single-digit numbers and in equations containing double-digit numbers. In Experiment 4, which included double-digit numbers, there was no difference in performance between the eye-of-origin conditions (in contrast to Experiments 1–3), indicating that the stereoscope manipulation by itself cannot account for the findings in the first three experiments. Singly and collectively, the above-mentioned considerations render alternative, nonnumerical explanations for the observed differences unlikely.

It should also be noted that solving arithmetic equations might involve memory-based retrieval processes and not only arithmetic calculations. However, the current pattern of results cannot be fully explained only by memory processes. It is widely accepted that young children's performance on arithmetic tasks is often based on counting or other procedural strategies, although some memory-retrieval processes can be found for small problems such as 2 + 255. However, how we mentally represent and process basic arithmetic such as 5 + 7 has been debated for over three decades56,57. While multiplication rely on memory processes, subtraction and addition, as used in our experiments, are considered to rely more on computational processes/arithmetic reasoning36,38,58. Several studies demonstrated that simple addition of two-digits equations is not exclusively based on memory-retrieval and does require computational processes38,59. This is also true for subtraction60. In addition, Sklar et al (2012) report that 3 term addition and subtraction take roughly a 1000ms more than two-term addition/subtraction. This is highly indicative of a computation. Accordingly, the arithmetic equations employed in Experiment 1 and Experiment 2 were three-digit equations (e.g., 4+3+8=15).

Indeed, we are unaware of any indications in the literature that such equations can be solved using arithmetical fact retrieval alone. Hence, the possibility that memory retrieval processes could account for the results of Experiment 1 and Experiment 2 is unlikely. Moreover, most of the equations used in Experiment 1, Experiment 2, and Experiments 3 required double-digit complex arithmetic calculations (e.g., sum of 18) which involves computational/arithmetic reasoning. Since solving three-digit equations requires using computational processes, we believe that our findings reflect the involvement of subcortical regions in computationally demanding arithmetic reasoning processes. In addition, in Experiment 1 and Experiment 2, both in the solution to a different-eye condition and in the computational term split condition, one of the numbers in the equation was presented to a different eye. In both conditions, presenting one number to a different eye should hamper memory processes to the same extent. This was not evident in Experiment 1 and Experiment 2, in which performance was hampered only in the computational term split condition. Hence, the current pattern of results cannot be fully explained only by memory-retrieval processes, and some computational processes should be involved. This convergent evidence makes the memory explanation less plausible.

One remaining question is which specific lower visual region is involved in arithmetic abilities. The three main candidates of the visual system are V1, thalamus, and the superior colliculus (SC), but the proposed method and logic do not allow to localize the specific subcortical region involved in those abilities. However, recent studies have suggested the involvement of the SC in symbolic spatial abilities in humans10 and fish51, and even in numerical processes26. It is possible that the SC is also involved in more complex symbolic arithmetic processes. Even when V1 is not activated, visual input from the SC can activate the dorsal visual stream61,62. The direct connection of the SC to parietal regions supports a functional relationship between these regions and may suggest the SC as a favorite candidate through which subcortical regions are involved in arithmetic calculations.

To conclude, in contrast to most literature, research conducted in recent years has taught us that many of the high-level functions, which were traditionally associated with neocortical regions, can functionally involve lower subcortical regions10,13,14,26,30. The current findings demonstrate that a uniquely human cultural product, such as solving arithmetic equations, does not solely involve neocortical regions, and they suggest a primitive mechanism for arithmetic abilities that might be shared by different species. As we have discussed, the results may have major implications for our understanding of the neuroevolutionary development of numerical abilities in general. Finally, these results suggest that the modal view of higher cognition and lower cognition, a view that ties together humans’ unique neocortical regions with humans’ unique (at least as assumed in the literature) arithmetic capacities, should be significantly updated. In a larger conceptual framework, these findings, and others, call for a significant shift from the modal view of the exclusive role of the neocortex in high-level cognition and arithmetic processes to a view that emphasizes the interplay between subcortical and cortical brain mechanisms.