Comparing Parietal Quantity-Processing Mechanisms between Humans and Macaques

Innate numerosity perception and its roots in early vision

In the current issue of Cerebral Cortex, Lorenzi et al. (2025) discuss evidence for an innate sense of object number (numerosity) in the brains of many species, without the need for visual experience. This commentary discusses how numerosity processing can be understood as an innate property of vision, derived from the spatial frequency-based representation of images in the visual systems of many animals.

The calculating brain

The human brain possesses neural networks and mechanisms enabling the representation of numbers, basic arithmetic operations, and mathematical reasoning. Without the ability to represent numerical quantity and perform calculations, our scientifically and technically advanced culture would not exist. However, the origins of numerical abilities are grounded in an intuitive understanding of quantity deeply rooted in biology. Nevertheless, more advanced symbolic arithmetic skills require a cultural background with formal mathematical education. In the past two decades, cognitive neuroscience has seen significant progress in understanding the workings of the calculating brain through various methods and model systems. This review begins by exploring the mental and neuronal representations of nonsymbolic numerical quantity and then progresses to symbolic representations acquired in childhood. During arithmetic operations (addition, subtraction, multiplication, and division), these representations are processed and transformed according to arithmetic rules and principles, leveraging different mental strategies and types of arithmetic knowledge that can be dissociated in the brain. Although it was once believed that number processing and calculation originated from the language faculty, it is now evident that mathematical and linguistic abilities are primarily processed independently in the brain. Understanding how the healthy brain processes numerical information is crucial for gaining insights into debilitating numerical disorders, including acquired conditions like acalculia and learning-related calculation disorders such as developmental dyscalculia.

Spatial attention in mental arithmetic: A literature review and meta-analysis

We review the evidence for the conceptual association between arithmetic and space and quantify the effect size in meta-analyses. We focus on three effects: (a) the operational momentum effect (OME), which has been defined as participants' tendency to overestimate results of addition problems and underestimate results of subtraction problems; (b) the arithmetic cueing effect, in which arithmetic problems serve as spatial cues in target detection or temporal order judgment tasks; and (c) the associations between arithmetic and space observed with eye- and hand-tracking studies. The OME was consistently found in paradigms that provided the participants with numerical response alternatives. The OME shows a large effect size, driven by an underestimation during subtraction while addition was unbiased. In contrast, paradigms in which participants indicated their estimate by transcoding their final estimate to a spatial reference frame revealed no consistent OME. Arithmetic cueing studies show a reliable small to medium effect size, driven by a rightward bias for addition. Finally, eye- and hand-tracking studies point to replicable associations between arithmetic and eye or hand movements. To account for the complexity of the observed pattern, we introduce the Adaptive Pathways in Mental Arithmetic (APiMA) framework. The model accommodates central notions of numerical and arithmetic processing and helps identifying which pathway a given paradigm operates on. It proposes that the divergence between OME and arithmetic cueing studies comes from the predominant use of non-symbolic versus symbolic stimuli, respectively. Overall, our review and findings clearly support an association between arithmetic and spatial processing.

Cortical quantity representations of visual numerosity and timing overlap increasingly into superior cortices but remain distinct

Many sensory brain areas are organized as topographic maps where neural response preferences change gradually across the cortical surface. Within association cortices, 7-Tesla fMRI and neural model-based analyses have also revealed many topographic maps for quantities like numerosity and event timing, often in similar locations. Numerical and temporal quantity estimations also show behavioral similarities and even interactions. For example, the duration of high-numerosity displays is perceived as longer than that of low-numerosity displays. Such interactions are often ascribed to a generalized magnitude system with shared neural responses across quantities. Anterior quantity responses are more closely linked to behavior. Here, we investigate whether common quantity representations hierarchically emerge by asking whether numerosity and timing maps become increasingly closely related in their overlap, response preferences, and topography. While the earliest quantity maps do not overlap, more superior maps overlap increasingly. In these overlapping areas, some intraparietal maps have consistently correlated numerosity and timing preferences, and some maps have consistent angles between the topographic progressions of numerosity and timing preferences. However, neither of these relationships increases hierarchically like the amount of overlap does. Therefore, responses to different quantities are initially derived separately, then progressively brought together, without generally becoming a common representation. Bringing together distinct responses to different quantities may underlie behavioral interactions and allow shared access to comparison and action planning systems.

Human brain representations of internally generated outcomes of approximate calculation revealed by ultra-high-field brain imaging

Much of human culture's advanced technology owes its existence to the ability to mentally manipulate quantities. Neuroscience has described the brain regions overall recruited by numerical tasks and the neuronal codes representing individual quantities during perceptual tasks. Nevertheless, it remains unknown how quantity representations are combined or transformed during mental computations and how specific quantities are coded in the brain when generated as the result of internal computations rather than evoked by a stimulus. Here, we imaged the brains of adult human subjects at 7 Tesla during an approximate calculation task designed to disentangle in- and outputs of the computation from the operation itself. While physically presented sample numerosities were distinguished in activity patterns along the dorsal visual pathway and within frontal and occipito-temporal regions, a representation of the internally generated result was most prominently detected in higher order regions such as angular gyrus and lateral prefrontal cortex. Behavioral precision in the task was related to cross-decoding performance between sample and result representations in medial IPS regions. This suggests the transformation of sample into result may be carried out within dorsal stream sensory-motor integration regions, and resulting outputs maintained for task purposes in higher-level regions in a format possibly detached from sensory-evoked inputs.

Spatiotemporal dynamics of successive activations across the human brain during simple arithmetic processing

Previous neuroimaging studies have offered unique insights about the spatial organization of activations and deactivations across the brain, however these were not powered to explore the exact timing of events at the subsecond scale combined with precise anatomical source information at the level of individual brains. As a result, we know little about the order of engagement across different brain regions during a given cognitive task. Using experimental arithmetic tasks as a prototype for human-unique symbolic processing, we recorded directly across 10,076 brain sites in 85 human subjects (52% female) using intracranial electroencephalography (iEEG). Our data revealed a remarkably distributed change of activity in almost half of the sampled sites. Notably, an orderly successive activation of a set of brain regions - anatomically consistent across subjects-was observed in individual brains. Furthermore, the temporal order of activations across these sites was replicable across subjects and trials. Moreover, the degree of functional connectivity between the sites decreased as a function of temporal distance between regions, suggesting that information is partially leaked or transformed along the processing chain. Furthermore, in each activated region, distinct neuronal populations with opposite activity patterns during target and control conditions were juxtaposed in an anatomically orderly manner. Our study complements the prior imaging studies by providing hitherto unknown information about the timing of events in the brain during arithmetic processing. Such findings can be a basis for developing mechanistic computational models of human-specific cognitive symbolic systems.

Significance statement

Our study elucidates the spatiotemporal dynamics and anatomical specificity of brain activations across >10,000 sites during arithmetic tasks, as captured by intracranial EEG. We discovered an orderly, successive activation of brain regions, consistent across individuals, and a decrease in functional connectivity as a function of temporal distance between regions. Our findings provide unprecedented insights into the sequence of cognitive processing and regional interactions, offering a novel perspective for enhancing computational models of cognitive symbolic systems.

The involvement of the semantic neural network in rule identification of mathematical processing

The role of the visuospatial network in mathematical processing has been established, but the involvement of the semantic network in mathematical processing is still poorly understood. The current study utilized a number series completion paradigm with the event-related potential (ERP) technique to examine whether the semantic network supports mathematical processing and to find the corresponding spatiotemporal neural marker. In total, 32 right-handed undergraduate students were recruited and asked to complete the number series completion as well as the arithmetical computation task in which numbers were presented in sequence. The event-related potential and multi-voxel pattern analysis showed that the rule identification process involves more semantic processing when compared with the arithmetical computation processes, and it elicited higher amplitudes for the late negative component (LNC) in left frontal and temporal lobes. These results demonstrated that the semantic network supports the rule identification in mathematical processing, with the LNC acting as the neural marker.

Visual adaptation reveals multichannel coding for numerosity

Visual numerosity is represented automatically and rapidly, but much remains unknown about the computations underlying this perceptual experience. For example, it is unclear whether numerosity is represented with an opponent channel or multichannel coding system. Within an opponent channel system, all numerical values are represented via the relative activity of two pools of neurons (i.e., one pool with a preference for small numerical values and one pool with a preference for large numerical values). However, within a multichannel coding system, all numerical values are represented directly, with separate pools of neurons for each (discriminable) numerical value. Using an adaptation paradigm, we assessed whether the visual perception of number is better characterized by an opponent channel or multichannel system. Critically, these systems make distinct predictions regarding the pattern of aftereffects exhibited when an observer is adapted to an intermediate numerical value. Opponent channel coding predicts no aftereffects because both pools of neurons adapt equally. By contrast, multichannel coding predicts repulsive aftereffects, wherein numerical values smaller than the adapter are underestimated and those larger than the adapter are overestimated. Consistent with multichannel coding, visual adaptation to an intermediate value (50 dots) yielded repulsive aftereffects, such that participants underestimated stimuli ranging from 10-50 dots, but overestimated stimuli ranging from 50-250 dots. These findings provide novel evidence that the visual perception of number is supported by a multichannel, not opponent channel, coding system, and raise important questions regarding the contributions of different cortical regions, such as the ventral and lateral intraparietal areas, to the representation of number.

Structural and functional connectivity of the inferior temporal numeral area

A growing body of evidence suggests that in adults, there is a spatially consistent "inferior temporal numeral area" (ITNA) in the occipitotemporal cortex that appears to preferentially process Arabic digits relative to non-numerical symbols and objects. However, very little is known about why the ITNA is spatially segregated from regions that process other orthographic stimuli such as letters, and why it is spatially consistent across individuals. In the present study, we used diffusion-weighted imaging and functional magnetic resonance imaging to contrast structural and functional connectivity between left and right hemisphere ITNAs and a left hemisphere letter-preferring region. We found that the left ITNA had stronger structural and functional connectivity than the letter region to inferior parietal regions involved in numerical magnitude representation and arithmetic. Between hemispheres, the left ITNA showed stronger structural connectivity with the left inferior frontal gyrus (Broca's area), while the right ITNA showed stronger structural connectivity to the ipsilateral inferior parietal cortex and stronger functional coupling with the bilateral IPS. Based on their relative connectivity, our results suggest that the left ITNA may be more readily involved in mapping digits to verbal number representations, while the right ITNA may support the mapping of digits to quantity representations.

Number selective sensorimotor neurons in the crow translate perceived numerosity into number of actions

Translating a perceived number into a matching number of self-generated actions is a hallmark of numerical reasoning in humans and animals alike. To explore this sensorimotor transformation, we trained crows to judge numerical values in displays and to flexibly plan and perform a matching number of pecks. We report number selective sensorimotor neurons in the crow telencephalon that signaled the impending number of self-generated actions. Neuronal population activity during the sensorimotor transformation period predicted whether the crows mistakenly planned fewer or more pecks than instructed. During sensorimotor transformation, both a static neuronal code characterized by persistently number-selective neurons and a dynamic code originating from neurons carrying rapidly changing numerical information emerged. The findings indicate there are distinct functions of abstract neuronal codes supporting the sensorimotor number system.

Numerosity tuning in human association cortices and local image contrast representations in early visual cortex

Human early visual cortex response amplitudes monotonically increase with numerosity (object number), regardless of object size and spacing. However, numerosity is typically considered a high-level visual or cognitive feature, while early visual responses follow image contrast in the spatial frequency domain. We find that, at fixed contrast, aggregate Fourier power (at all orientations and spatial frequencies) follows numerosity closely but nonlinearly with little effect of object size, spacing or shape. This would allow straightforward numerosity estimation from spatial frequency domain image representations. Using 7T fMRI, we show monotonic responses originate in primary visual cortex (V1) at the stimulus's retinotopic location. Responses here and in neural network models follow aggregate Fourier power more closely than numerosity. Truly numerosity tuned responses emerge after lateral occipital cortex and are independent of retinotopic location. We propose numerosity's straightforward perception and neural responses may result from the pervasive spatial frequency analyses of early visual processing.

A connectome-based neuromarker of nonverbal number acuity and arithmetic skills

The approximate number system (ANS) is vital for survival and reproduction in animals and is crucial for constructing abstract mathematical abilities in humans. Most previous neuroimaging studies focused on identifying discrete brain regions responsible for the ANS and characterizing their functions in numerosity perception. However, a neuromarker to characterize an individual's ANS acuity is lacking, especially one based on whole-brain functional connectivity (FC). Here, based on the resting-state functional magnetic resonance imaging (rs-fMRI) data obtained from a large sample, we identified a distributed brain network (i.e. a numerosity network) using a connectome-based predictive modeling (CPM) analysis. The summed FC strength within the numerosity network reliably predicted individual differences in ANS acuity regarding behavior, as measured using a nonsymbolic number-comparison task. Furthermore, in an independent dataset of the Human Connectome Project (HCP), we found that the summed FC strength within the numerosity network also specifically predicted individual differences in arithmetic skills, but not domain-general cognitive abilities. Therefore, our findings revealed that the identified numerosity network could serve as an applicable neuroimaging-based biomarker of nonverbal number acuity and arithmetic skills.

Reduced 2D form coherence and 3D structure from motion sensitivity in developmental dyscalculia

Developmental dyscalculia (DD) is a specific learning disability affecting the development of numerical and arithmetical skills. The origin of DD is typically attributed to the suboptimal functioning of key regions within the dorsal visual stream (parietal cortex) which support numerical cognition. While DD individuals are often impaired in visual numerosity perception, the extent to which they also show a wider range of visual dysfunctions is poorly documented. In the current study we measured sensitivity to global motion (translational and flow), 2D static form (Glass patterns) and 3D structure from motion in adults with DD and control subjects. While sensitivity to global motion was comparable across groups, thresholds for static form and structure from motion were higher in the DD compared to the control group, irrespective of associated reading impairments. Glass pattern sensitivity predicted numerical abilities, and this relation could not be explained by recently reported differences in visual crowding. Since global form sensitivity has often been considered an index of ventral stream function, our findings could indicate a cortical dysfunction extending beyond the dorsal visual stream. Alternatively, they would fit with a role of parietal cortex in form perception under challenging conditions requiring multiple element integration.

When A is greater than B: Interactions between magnitude and serial order

Processing ordinal information is an important aspect of cognitive ability, yet the nature of such ordinal representations remains largely unclear. Previously, it has been suggested that ordinal position is coded as magnitude, but this claim has not yet received direct empirical support. This study examined the nature of ordinal representations using a Stroop-like letter order judgment task. If ordinal position is coded as magnitude, then letter ordering and font size should interact. Experiments 1 and 2 identified a significant interaction between letter size and ordering. Specifically, a facilitation effect was observed for alphabetically ordered sequences with decreasing font size (e.g., B C D). This suggests an overlap in the mechanisms for order and magnitude processing. The finding also suggests that earlier ranks may be represented as "more" in such a magnitude-based code, and vice versa for later ranks.

Adaptation to visual numerosity changes neural numerosity selectivity

Perceiving numerosity, i.e. the set size of a group of items, is an evolutionarily preserved ability found in humans and animals. A useful method to infer the neural underpinnings of a given perceptual property is sensory adaptation. Like other primary perceptual attributes, numerosity is susceptible to adaptation. Recently, we have shown numerosity-selective neural populations with a topographic organization in the human brain. Here, we investigated whether numerosity adaptation can affect the numerosity selectivity of these populations using ultra-high field (7 Tesla) functional magnetic resonance imaging (fMRI). Participants viewed stimuli of changing numerosity (1 to 7 dots), which allowed the mapping of numerosity selectivity. We interleaved a low or high numerosity adapter stimulus with these mapping stimuli, repeatedly presenting 1 or 20 dots respectively to adapt the numerosity-selective neural populations. We analyzed the responses using custom-build population receptive field neural models of numerosity encoding and compared estimated numerosity preferences between adaptation conditions. We replicated our previous studies where we found several topographic maps of numerosity-selective responses. We found that overall, numerosity adaptation altered the preferred numerosities within the numerosity maps, resulting in predominantly attractive biases towards the numerosity of the adapter. The differential biases could be explained by the difference between the unadapted preferred numerosity and the numerosity of the adapter, with attractive biases being observed with higher difference. The results could link perceptual numerosity adaptation effects to changes in neural numerosity selectivity.

A Sensorimotor Numerosity System

Incoming sensory input provides information for the planning and execution of actions, which yield motor outcomes that are themselves sensory inputs. One dimension where action and perception strongly interact is numerosity perception. Many non-human animals can estimate approximately the number of external elements as well as their own actions, and neurons have been identified that respond to both. Recent psychophysical adaptation studies on humans also provide evidence for neural mechanisms responding to both the number of externally generated events and self-produced actions. Here we advance the idea that these strong connections may arise from dedicated sensorimotor mechanisms in the brain, part of a more generalized system interfacing action with the processing of other quantitative magnitudes such as space and time.

How visual is the « number sense »? Insights from the blind

Is vision a necessary building block for the foundations of mathematical cognition? A straightforward model to test the causal role visual experience plays in the development of numerical abilities is to study people born without sight. In this review we will demonstrate that congenitally blind people can develop numerical abilities that equal or even surpass those of sighted individuals, despite representing numbers using a qualitatively different representational format. We will also show that numerical thinking in blind people maps onto regions typically involved in visuo-spatial processing in the sighted, highlighting how intrinsic computational biases may constrain the reorganization of numerical networks in case of early visual deprivation. More generally, we will illustrate how the study of arithmetic abilities in congenitally blind people represents a compelling model to understand how sensory experience scaffolds the development of higher-level cognitive representations.

A parietal region processing numerosity of observed actions: An FMRI study

When observing others' behavior, it is important to perceive not only the identity of the observed actions (OAs), but also the number of times they were performed. Given the mounting evidence implicating posterior parietal cortex in action observation, and in particular that of manipulative actions, the aim of this study was to identify the parietal region, if any, that contributes to the processing of observed manipulative action (OMA) numerosity, using the functional magnetic resonance imaging technique. Twenty‐one right‐handed healthy volunteers performed two discrimination tasks while in the scanner, responding to video stimuli in which an actor performed manipulative actions on colored target balls that appeared four times consecutively. The subjects discriminated between two small numerosities of either OMAs (“Action” condition) or colors of balls (“Ball” condition). A significant difference between the “Action” and “Ball” conditions was observed in occipito‐temporal cortex and the putative human anterior intraparietal sulcus (phAIP) area as well as the third topographic map of numerosity‐selective neurons at the post‐central sulcus (NPC3) of the left parietal cortex. A further region of interest analysis of the group‐average data showed that at the single voxel level the latter area, more than any other parietal or occipito‐temporal numerosity map, favored numerosity of OAs. These results suggest that phAIP processes the identity of OMAs, while neighboring NPC3 likely processes the numerosity of the identified OAs.

Mental Shopping Calculations: A Transcranial Magnetic Stimulation Study

One of the most critical skills behind consumer's behavior is the ability to assess whether a price after a discount is a real bargain. Yet, the neural underpinnings and cognitive mechanisms associated with such a skill are largely unknown. While there is general agreement that the posterior parietal cortex (PPC) on the left is critical for mental calculations, and there is also recent repetitive transcranial magnetic stimulation (rTMS) evidence pointing to the supramarginal gyrus (SMG) of the right PPC as crucial for consumer-like arithmetic (e.g., multi-digit mental addition or subtraction), it is still unknown whether SMG is involved in calculations of sale prices. Here, we show that the neural mechanisms underlying discount arithmetic characteristic for shopping are different from complex addition or subtraction, with discount calculations engaging left SMG more. We obtained these outcomes by remodeling our laboratory to resemble a shop and asking participants to calculate prices after discounts (e.g., $8.80-25 or $4.80-75%), while stimulating left and right SMG with neuronavigated rTMS. Our results indicate that such complex shopping calculations as establishing the price after a discount involve SMG asymmetrically, whereas simpler calculations such as price addition do not. These findings have some consequences for neural models of mathematical cognition and shed some preliminary light on potential consumer's behavior in natural settings.

Receptor-driven, multimodal mapping of cortical areas in the macaque monkey intraparietal sulcus

The intraparietal sulcus (IPS) is structurally and functionally heterogeneous. We performed a quantitative cyto-/myelo- and receptor architectonical analysis to provide a multimodal map of the macaque IPS. We identified 17 cortical areas, including novel areas PEipe, PEipi (external and internal subdivisions of PEip), and MIPd. Multivariate analyses of receptor densities resulted in a grouping of areas based on the degree of (dis)similarity of their receptor architecture: a cluster encompassing areas located in the posterior portion of the IPS and associated mainly with the processing of visual information, a cluster including areas found in the anterior portion of the IPS and involved in sensorimotor processing, and an ‘intermediate’ cluster of multimodal association areas. Thus, differences in cyto-/myelo- and receptor architecture segregate the cortical ribbon within the IPS, and receptor fingerprints provide novel insights into the relationship between the structural and functional segregation of this brain region in the macaque monkey.

A Network of Topographic Maps in Human Association Cortex Hierarchically Transforms Visual Timing-Selective Responses

Accurately timing sub-second sensory events is crucial when perceiving our dynamic world. This ability allows complex human behaviors that require timing-dependent multisensory integration and action planning. Such behaviors include perception and performance of speech, music, driving, and many sports. How are responses to sensory event timing processed for multisensory integration and action planning? We measured responses to viewing systematically changing visual event timing using ultra-high-field fMRI. We analyzed these responses with neural population response models selective for event duration and frequency, following behavioral, computational, and macaque action planning results and comparisons to alternative models. We found systematic local changes in timing preferences (recently described in supplementary motor area) in an extensive network of topographic timing maps, mirroring sensory cortices and other quantity processing networks. These timing maps were partially left lateralized and widely spread, from occipital visual areas through parietal multisensory areas to frontal action planning areas. Responses to event duration and frequency were closely linked. As in sensory cortical maps, response precision varied systematically with timing preferences, and timing selectivity systematically varied between maps. Progressing from posterior to anterior maps, responses to multiple events were increasingly integrated, response selectivity narrowed, and responses focused increasingly on the middle of the presented timing range. These timing maps largely overlap with numerosity and visual field map networks. In both visual timing map and visual field map networks, selective responses and topographic map organization may facilitate hierarchical transformations by allowing neural populations to interact over minimal distances.

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Many brain areas show neural responses to specific ranges of visual event timing

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Timing preferences change gradually in these areas, forming topographic timing maps

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Neural response properties hierarchically transform from visual to premotor areas

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Timing, numerosity, and visual field map networks are distinct but largely overlap

Challenging the neurobiological link between number sense and symbolic numerical abilities

A significant body of research links individual differences in symbolic numerical abilities, such as arithmetic, to number sense, the neurobiological system used to approximate and manipulate quantities without language or symbols. However, recent findings from cognitive neuroscience challenge this influential theory. Our current review presents an overview of evidence for the number sense account of symbolic numerical abilities and then reviews recent studies that challenge this account, organized around the following four assertions. (1) There is no number sense as traditionally conceived. (2) Neural substrates of number sense are more widely distributed than common consensus asserts, complicating the neurobiological evidence linking number sense to numerical abilities. (3) The most common measures of number sense are confounded by other cognitive demands, which drive key correlations. (4) Number sense and symbolic number systems (Arabic digits, number words, and so on) rely on distinct neural mechanisms and follow independent developmental trajectories. The review follows each assertion with comments on future directions that may bring resolution to these issues.

Attentional amplification of neural codes for number independent of other quantities along the dorsal visual stream

Humans and other animals base important decisions on estimates of number, and intraparietal cortex is thought to provide a crucial substrate of this ability. However, it remains debated whether an independent neuronal processing mechanism underlies this ‘number sense’, or whether number is instead judged indirectly on the basis of other quantitative features. We performed high-resolution 7 Tesla fMRI while adult human volunteers attended either to the numerosity or an orthogonal dimension (average item size) of visual dot arrays. Along the dorsal visual stream, numerosity explained a significant amount of variance in activation patterns, above and beyond non-numerical dimensions. Its representation was selectively amplified and progressively enhanced across the hierarchy when task relevant. Our results reveal a sensory extraction mechanism yielding information on numerosity separable from other dimensions already at early visual stages and suggest that later regions along the dorsal stream are most important for explicit manipulation of numerical quantity.

Numbers and the ability to count and calculate are an essential part of human culture. They are part of everyday life, featuring in calendars, computers or the weekly shop, but also in some of humanity’s biggest achievements: without them the pyramids or space travel would not exist. A precursor of sophisticated mathematical skill could reside in a simpler mental ability: the capacity to assess numerical quantities at a glance. This ‘number sense’ appears in humans in early childhood and it is also present in other animals, but it is still poorly understood.

Brain imaging techniques have identified the parts of the brain that are active when perceiving numbers or making calculations. As techniques have advanced, it has become possible to resolve fine differences in brain activity that occur when people switch their attention between different visual tasks. But how exactly does the human brain process visual information to make sense of numbers? One theory suggests that humans use visual cues, such as the size of a group of objects or how densely packed objects are, to estimate numbers. On the other hand, it is also possible that humans can sense number directly, without reference to other properties of the group being observed.

Castaldi et al. presented twenty adult volunteers with groups of dots and asked them to focus either on the number of dots or on the size of the dots during a brain scan. This approach allowed the separation of brain signals specific to number from signals corresponding to other visual cues, such as size or density of the group. The experiment revealed that brain activity changed depending on the number of dots displayed. The signal related to number became stronger when people focused on the number of dots, while signals related to other properties of the group remained unchanged. Moreover, brain signals for number were observed at the very early stages of visual processing, in the parts of the brain that receive input from the eyes first.

These results suggest that the human visual system perceives number directly, and not by processing information about the size or density of a group of objects. This finding provides insights into how human brains encode numbers, which could be important to understand disorders where number sense can be impaired leading to difficulties learning math and operating with numbers.

A MEG Study on the Processing of Time and Quantity: Parietal Overlap but Functional Divergence

A common magnitude system for the processing of time and numerosity, supported by areas in the posterior parietal cortex, has been proposed by some authors. The present study aims to investigate possible intersections between the neural processing of non-numerical (time) and numerical magnitudes in the posterior parietal lobe. Using Magnetoencephalography for the comparison of brain source activations during the processing of duration and numerosity contrasts, we demonstrate parietal overlap as well as dissociations between these two dimensions. Within the parietal cortex, the main areas of overlap were bilateral precuneus, bilateral intraparietal sulci, and right supramarginal gyrus. Interestingly, however, these regions did not equivalently correlated with the behavior for the two dimensions: left and right precuneus together with the right supramarginal gyrus accounted functionally for durational judgments, whereas numerosity judgments were accounted by the activation pattern in the right intraparietal sulcus. Present results, indeed, demonstrate an overlap between the neural substrates for processing duration and quantity. However, the functional relevance of parietal overlapping areas for each dimension is not the same. In fact, our data indicates that the same parietal sites rule differently non-numerical and numerical dimensions, as parts of broader networks.

Fronto-parietal numerical networks in relation with early numeracy in young children

Early numeracy provides the foundation of acquiring mathematical skills that is essential for future academic success. This study examined numerical functional networks in relation to counting and number relational skills in preschoolers at 4 and 6 years of age. The counting and number relational skills were assessed using school readiness test (SRT). Resting-state fMRI (rs-fMRI) was acquired in 123 4-year-olds and 146 6-year-olds. Among them, 61 were scanned twice over the course of 2 years. Meta-analysis on existing task-based numeracy fMRI studies identified the left parietal-dominant network for both counting and number relational skills and the right parietal-dominant network only for number relational skills in adults. We showed that the fronto-parietal numerical networks, observed in adults, already exist in 4-year and 6-year-olds. The counting skills were associated with the bilateral fronto-parietal network in 4-year-olds and with the right parietal-dominant network in 6-year-olds. Moreover, the number relational skills were related to the bilateral fronto-parietal and right parietal-dominant networks in 4-year-olds and had a trend of the significant relationship with the right parietal-dominant network in 6-year-olds. Our findings suggested that neural fine-tuning of the fronto-parietal numerical networks may subserve the maturation of numeracy in early childhood.

Brain Mechanisms of Arithmetic: A Crucial Role for Ventral Temporal Cortex

Elementary arithmetic requires a complex interplay between several brain regions. The classical view, arising from fMRI, is that the intraparietal sulcus (IPS) and the superior parietal lobe (SPL) are the main hubs for arithmetic calculations. However, recent studies using intracranial electroencephalography have discovered a specific site, within the posterior inferior temporal cortex (pITG), that activates during visual perception of numerals, with widespread adjacent responses when numerals are used in calculation. Here, we reexamined the contribution of the IPS, SPL, and pITG to arithmetic by recording intracranial electroencephalography signals while participants solved addition problems. Behavioral results showed a classical problem size effect: RTs increased with the size of the operands. We then examined how high-frequency broadband (HFB) activity is modulated by problem size. As expected from previous fMRI findings, we showed that the total HFB activity in IPS and SPL sites increased with problem size. More surprisingly, pITG sites showed an initial burst of HFB activity that decreased as the operands got larger, yet with a constant integral over the whole trial, thus making these signals invisible to slow fMRI. Although parietal sites appear to have a more sustained function in arithmetic computations, the pITG may have a role of early identification of the problem difficulty, beyond merely digit recognition. Our results ask for a reevaluation of the current models of numerical cognition and reveal that the ventral temporal cortex contains regions specifically engaged in mathematical processing.

Discriminability of numerosity-evoked fMRI activity patterns in human intra-parietal cortex reflects behavioral numerical acuity

Areas of the primate intraparietal cortex have been identified as an important substrate of numerical cognition. In human fMRI studies, activity patterns in these and other areas have allowed researchers to read out the numerosity a subject is viewing, but the relation of such decodable information with behavioral numerical proficiency remains unknown. Here, we estimated the precision of behavioral numerosity discrimination (internal Weber fraction) in twelve adult subjects based on psychophysical testing in a delayed numerosity comparison task outside the scanner. FMRI data were then recorded during a similar task, to obtain the accuracy with which the same sample numerosities could be read out from evoked brain activity patterns, as a measure of the precision of the neuronal representation. Sample numerosities were decodable in both early visual and intra-parietal cortex with approximately equal accuracy on average. In parietal cortex, smaller numerosities were better discriminated than larger numerosities of the same ratio, paralleling smaller behavioral Weber fractions for smaller numerosities. Furthermore, in parietal but not early visual cortex, fMRI decoding performance was correlated with behavioral number discrimination acuity across subjects (subjects with a more precise behavioral Weber fraction measured prior to scanning showed greater discriminability of fMRI activity patterns in intraparietal cortex, and more specifically, the right LIP region). These results suggest a crucial role for intra-parietal cortex in supporting a numerical representation which is explicitly read out for numerical decisions and behavior.