Andreas Nieder

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Verified

Andreas verified their affiliation via an institutional email.

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• PhD
• Professor at University of Tübingen

The perception of geometric regularity in shapes, a form of elementary Euclidean geometry, is a fundamental mathematical intuition in humans. We demonstrate this geometric understanding in an animal, the carrion crow. Crows were trained to detect a visually distinct intruder shape among six concurrent arbitrary shapes. The crows were able to immedi...

In their feature article, Lorenzi et al. (2025) compiled extensive biological evidence on the ontogenetic origins of the number sense. Drawing on both behavioral and neurobiological data, they convincingly argue that the “number sense” is fundamentally innate and present from birth in numerically competent animals, including humans. At the same tim...

Crows are corvid songbirds that exhibit remarkable cognitive control, including their ability to vocalize on command. The activity of single neurons from the crow's associative telencephalic structure nidopallium caudolaterale (NCL) is correlated with the execution of this vocal and many non‐vocal behaviors. However, whether anatomical connections...

Like humans and many other animal species, birds exhibit left–right asymmetries in certain behaviours due to differences in hemispheric brain functions. While the lateralization of sensory and motor functions is well established in birds, the potential lateralization of high-level executive control functions, such as volitional attention, remains u...

Crows, known for advanced cognitive abilities and vocal communication, rely on intricate auditory systems. While the neuroanatomy of corvid auditory pathways is partially explored, the underlying neurophysiological mechanisms are largely unknown. This study used functional ultrasound imaging (fUSi) to investigate sound-induced cerebral blood volume...

Modular organization, the division of the cerebral cortex into functionally distinct subregions, is well established in the primate sensorimotor cortex, but debated in the cognitive association cortex, including the lateral prefrontal cortex (PFC). So far, single-unit recordings have not confirmed the prefrontal rostro-caudal gradients observed in...

Crows are corvid songbirds that exhibit remarkable cognitive control over their actions, including their vocalizations. They can learn to vocalize on command and the activity of single neurons from the crow's associative telencephalic structure nidopallium caudolaterale (NCL) is correlated with the execution of this vocal and many non-vocal skilled...

Producing a specific number of vocalizations with purpose requires a sophisticated combination of numerical abilities and vocal control. Whether this capacity exists in animals other than humans is yet unknown. We show that crows can flexibly produce variable numbers of one to four vocalizations in response to arbitrary cues associated with numeric...

The avian telencephalic structure nidopallium caudolaterale (NCL) functions as an analog to the mammalian prefrontal cortex. In crows, corvid songbirds, it plays a crucial role in higher cognitive and executive functions. These functions rely on the NCL's extensive telencephalic connections. However, systematic investigations into the brain-wide co...

The emergence of consciousness from brain activity constitutes one of the great riddles in biology. It is commonly assumed that only the conscious perception of the presence of a stimulus elicits neuronal activation to signify a “neural correlate of consciousness,” whereas the subjective experience of the absence of a stimulus is associated with a...

Working memory processing in primate lateral prefrontal cortex (lPFC) is characterized by complex spatiotemporal activity patterns. These patterns could arise from a modular functional organization, as has been described in sensory and motor cortices. However, most working memory theories do not incorporate this idea and instead assume that the pre...

Decision-making requires processing of sensory information, comparing the gathered evidence to make a judgment, and performing the action to communicate it. How neuronal representations transform during this cascade of representations remains a matter of debate. Here, we studied the succession of neuronal representations in the primate prefrontal c...

Modern neuroscience has seen the rise of a population-doctrine that represents cognitive variables using geometrical structures in activity space. Representational geometry does not, however, account for how individual neurons implement these representations. Leveraging the principle of sparse coding, we present a framework to dissect representatio...

Categorization is crucial for behavioral flexibility because it enables animals to group stimuli into meaningful classes that can easily be generalized to new circumstances. A most abstract quantitative category is set size, the number of elements in a set. This review explores how categorical number representations are realized by the operations o...

Dopamine neurons respond to reward-predicting cues but also modulate information processing in the prefrontal cortex essential for cognitive control. Whether dopamine controls reward expectation signals in prefrontal cortex that motivate cognitive control is unknown. We trained two male macaques on a working memory task while varying the reward siz...

Many animals can associate signs with numerical values and use these signs in a goal-directed way during task performance. However, the neuronal basis of this semantic association has only rarely been investigated, and so far only in primates. How mechanisms of number associations are implemented in the distinctly evolved brains of other animal tax...

The psychophysical laws governing the judgment of perceived numbers of objects or events, called the number sense, have been studied in detail. However, the behavioral principles of equally important numerical representations for action are largely unexplored in both humans and animals. We trained two male carrion crows ( Corvus corone) to judge nu...

Whether small numerical quantities are represented by a special subitizing system that is distinct from a large-number estimation system has been debated for over a century. Here we show that two separate neural mechanisms underlie the representation of small and large numbers. We performed single neuron recordings in the medial temporal lobe of ne...

Behavioural signatures of voluntary, endogenous selective attention have been found in both mammals and birds, but the relationship between performance benefits at attended and costs at unattended locations remains unclear. We trained two carrion crows (Corvus corone) on a Posner-like spatial cueing task with dissociated cue and target locations, u...

Crows, a group of corvid songbird species, show superb behavioral flexibility largely stemming from their advanced cognitive control functions. These functions mainly originate from the associative avian pallium that evolved independently from the mammalian cerebral cortex. This article presents a brief overview of cognitive control functions and t...

Statistical inference, the ability to use limited information to draw conclusions about the likelihood of an event, is critical for decision-making during uncertainty. The ability to make statistical inferences was thought to be a uniquely human skill requiring verbal instruction and mathematical reasoning.1 However, basic inferences have been demo...

The ability to group abstract continuous magnitudes into meaningful categories is cognitively demanding but key to intelligent behavior. To explore its neuronal mechanisms, we trained carrion crows to categorize lines of variable lengths into arbitrary "short" and "long" categories. Single-neuron activity in the nidopallium caudolaterale (NCL) of b...

The prefrontal cortex (PFC) enables a staggering variety of complex behaviors, such as planning actions, solving problems, and adapting to new situations according to external information and internal states. These higher-order abilities, collectively defined as adaptive cognitive behavior, require cellular ensembles that coordinate the tradeoff be...

Modern neuroscience has seen the rise of a population-doctrine that represents cognitive variables using geometrical structures in activity space. Representational geometry does not, however, account for how individual neurons implement these representations. Here, leveraging the principle of sparse coding, we present a framework to dissect represe...

The neuronal basis of the songbird's song system is well understood. However, little is known about the neuronal correlates of the executive control of songbird vocalizations. Here, we record single-unit activity from the pallial endbrain region "nidopallium caudolaterale" (NCL) of crows that vocalize to the presentation of a visual go-cue but refr...

Working memory, the ability to actively maintain and manipulate information across time, is key to intelligent behavior. Due to the limited capacity of working memory, relevant information needs to be protected against distracting representations. Whether birds can resist distractors and safeguard memorized relevant information is unclear. We train...

Attention describes the ability to selectively process a particular aspect of the environment at the expense of others. Despite the significance of selective processing, the types and scopes of attentional mechanisms in nonprimate species remain underexplored. We trained four carrion crows in Posner spatial cueing tasks using two separate protocols...

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 neu...

Recursion, the process of embedding structures within similar structures, is often considered a foundation of symbolic competence and a uniquely human capability. To understand its evolution, we can study the recursive aptitudes of nonhuman animals. We adopted the behavioral protocol of a recent study demonstrating that humans and nonhuman primates...

Complex cognition requires coordinated neuronal activity at the network level. In mammals, this coordination results in distinct dynamics of local field potentials (LFP) central to many models of higher cognition. These models often implicitly assume a cortical organization. Higher associative regions of the brains of birds do not have cortical lay...

Whether animals have subjective experiences about the content of their sensory input, i.e., whether they are aware of stimuli, is a notoriously difficult question to answer. If consciousness is present in animals, it must share fundamental characteristics with human awareness. Working memory and voluntary/endogenous attention are suggested as diagn...

Corvidae, passerine songbirds such as jays, crows, and ravens known as corvids, have become model systems for the study of avian cognition. The superior cognitive capabilities of corvids mainly emerge from a disproportionally large telencephalon found in these species. However, a systematic mapping of the neuroanatomy of the corvid brain, and the t...

The nidopallium caudolaterale (NCL), an integration centre in the telencephalon of birds, plays a crucial role in representing and maintaining abstract categories and concepts. However, the computational principles allowing pallial microcircuits consisting of excitatory and inhibitory neurons to shape the tuning to abstract categories remain elusiv...

Complex cognition requires coordinated neuronal activity at the network level. In mammals, this coordination results in distinct dynamics of local field potentials (LFP) that have been central in many models of higher cognition. Because these models are based on mammalian data, they often implicitly assume a cortical organization. Higher associativ...

Arithmetic is a cornerstone of scientifically and technologically advanced human culture, but its neuronal mechanisms are poorly understood. Calculating with numbers requires temporary maintenance and manipulation of numerical information according to arithmetic rules. We explored the brain mechanisms involved in simple arithmetic operations by rec...

The ability to represent approximate quantities appears to be phylogenetically widespread, but the selective pressures and proximate mechanisms favouring this ability remain unknown. We analysed quantity discrimination data from 672 subjects across 33 bird and mammal species, using a novel Bayesian model that combined phylogenetic regression with a...

Complex cognition relies on flexible working memory, which is severely limited in its capacity. The neuronal computations underlying these capacity limits have been extensively studied in humans and in monkeys, resulting in competing theoretical models. We probed the working memory capacity of crows ( Corvus corone ) in a change detection task, dev...

Sensory consciousness — the awareness and ability to report subjective experiences — is a property of biological nervous systems that has evolved out of unconscious processing over hundreds of millions of years. From which brain structures and based on which mechanisms can conscious experience emerge? Based on the body of work in human and nonhuman...

Behavioral responses to novelty, including fear and subsequent avoidance of novel stimuli, i.e., neophobia, determine how animals interact with their environment. Neophobia aids in navigating risk and impacts on adaptability and survival. There is variation within and between individuals and species; however, lack of large-scale, comparative studie...

Conceiving “nothing” as a numerical value zero is considered an sophisticated numerical capability that humans share with cognitively-advanced animals. We demonstrate that representation of zero spontaneously emerges in a deep learning neural network without any number training. As a signature of numerical quantity representation, and similar to re...

Complex cognition relies on flexible working memory, which is severely limited in its capacity. The neuronal computations underlying these capacity limits have been extensively studied in humans and in monkeys, resulting in competing theoretical models. We probed the working memory capacity of crows ( Corvus corone ) in a change detection task, dev...

Feature-based attention enables privileged processing of specific visual properties. During feature-based attention, neurons in visual cortices show “gain modulation” by enhancing neuronal responses to the features of attended stimuli due to top-down signals originating from prefrontal cortex (PFC). Attentional modulation in visual cortices require...

Different species of animals can discriminate numerosity, the countable number of objects in a set. The representations of countable numerosities have been deciphered down to the level of single neurons. However, despite its importance for human number theory, a special numerical quantity, the empty set (numerosity zero), has remained largely unexp...

Humans and other animals share a ‘number sense’, an intuitive understanding of countable quantities. Having evolved independent from one another for hundreds of millions of years, the brains of these diverse species, including monkeys, crows, zebrafishes, bees, and squids, differ radically. However, in all vertebrates investigated, the pallium of t...

Many species from diverse and often distantly related animal groups (e.g. monkeys, crows, fish and bees) have a sense of number. This means that they can assess the number of items in a set – its ‘numerosity’. The brains of these phylogenetically distant species are markedly diverse. This Review examines the fundamentally different types of brains...

The planning and execution of head-beak movements are vital components of bird behavior. They require integration of sensory input and internal processes with goal-directed motor output. Despite its relevance, the neurophysiological mechanisms underlying action planning and execution outside of the song system are largely unknown. We recorded singl...

The ventrolateral frontal lobe (Broca's area) of the human brain is crucial in speech production. In macaques, neurons in the ventrolateral prefrontal cortex, the suggested monkey homologue of Broca's area, signal the volitional initiation of vocalizations. We explored whether this brain area became specialized for vocal initiation during primate e...

The song system of songbirds (oscines) is one of the best studied neuroethological model systems. So far, it has been treated as a relatively constrained sensorimotor system. Some songbirds, however, are also known for their capability to cognitively control their audio‐vocal system. Yet, the neuroanatomy of the corvid song system has never been ex...

The ability to group sensory data into behaviorally meaningful classes and to maintain these perceptual categories active in working memory is key to intelligent behavior. Here, we show that carrion crows, highly vocal and cognitively advanced corvid songbirds, possess categorical auditory working memory. The crows were trained in a delayed match-t...

Consciousness shared Humans have tended to believe that we are the only species to possess certain traits, behaviors, or abilities, especially with regard to cognition. Occasionally, we extend such traits to primates or other mammals—species with which we share fundamental brain similarities. Over time, more and more of these supposed pillars of hu...

The question of whether some non-human animal species are more intelligent than others is a reoccurring theme in comparative psychology. To convincingly address this question, exact comparability of behavioral methodology and data across species is required. The current article explores one of the rare cases in which three vertebrate species (human...

Our sense of number rests on the activity of neurons that are tuned to the number of items and show great invariance across display formats and modalities. Whether numerosity coding becomes abstracted from local spatial representations characteristic of visual input is not known. We mapped the visual receptive fields (RFs) of numerosity-selective n...

Individual recognition is the ability to differentiate between conspecifics based on their individual features. It forms the basis of many complex communicative and social behaviours. Here, we review studies investigating individual recognition in the auditory and visual domain in birds. It is well established that auditory signals are used by many...

The mirror mark test is generally considered to be an indicator of an animal's ability to recognize itself in the mirror. For this test, an animal is confronted with a mirror and has a mark placed where it can see the mark only with the help of the mirror. When the animal extensively touches or interacts with the mark, compared with control conditi...

Evolution selects for traits that are of adaptive value and increase the fitness of an individual or population. Numerical competence, the ability to estimate and process the number of objects and events, is a cognitive capacity that also influences an individual’s survival and reproduction success. Numerical assessments are ubiquitous in a broad r...

Humans’ symbolic counting skills are built on a primordial ability to approximately estimate the number of items, or numerosity. To date it is debated whether numerosities presented in categorically different formats, that is as temporal sequences versus spatial arrays, are represented abstractly in the brain. To address this issue, we identified t...

The neurotransmitter dopamine, which acts via the D1-like receptor (D1R) and D2-like receptor (D2R) family, may play an important role in gating sensory information to the prefrontal cortex (PFC). We tested this hypothesis in awake macaques and recorded visual motion-direction tuning functions of single PFC neurons. Using micro-iontophoretic drug a...

The ongoing activity of prefrontal neurons after a stimulus has disappeared is considered a neuronal correlate of working memory. It depends on the delicate but poorly understood interplay between excitatory glutamatergic and inhibitory GABAergic receptor effects. We administered the NMDA receptor antagonist MK-801 and the GABA(A) receptor antagoni...

True counting and arithmetic abilities are unique to humans and are inextricably linked to symbolic competence. However, our unprecedented numerical skills are deeply rooted in our neuronal heritage as primates and vertebrates. In this article, I argue that numerical competence in humans is the result of three neural constraints. First, I propose t...

How our intuitive understanding of numbers is deeply rooted in our biology, traceable through both evolution and development. Humans' understanding of numbers is intuitive. Infants are able to estimate and calculate even before they learn the words for numbers. How have we come to possess this talent for numbers? In A Brain for Numbers, Andreas Nie...

Vocalization is an ancient vertebrate trait essential to many forms of communication, ranging from courtship calls to free verse. Vocalizations may be entirely innate and evoked by sexual cues or emotional state, as with many types of calls made in primates, rodents and birds; volitional, as with innate calls that, following extensive training, can...

Songbirds are renowned for their acoustically elaborate songs. However, it is unclear whether songbirds can cognitively control their vocal output. Here, we show that crows, songbirds of the corvid family, can be trained to exert control over their vocalizations. In a detection task, three male carrion crows rapidly learned to emit vocalizations in...

Birds are renowned for their excellent spatial cognition. Corvid songbirds, in particular, rely on explicit representation of spatial cues in memory when caching food and retrieving caches for later consumption. However, the neuronal correlates of flexible spatial memory abilities are largely unknown in birds. We therefore trained carrion crows (Co...

Humans and animals have a “number sense,” an innate capability to intuitively assess the number of visual items in a set, its numerosity. This capability implies that mechanisms to extract numerosity indwell the brain’s visual system, which is primarily concerned with visual object recognition. Here, we show that network units tuned to abstract num...

Cognitive control, the ability to orchestrate behavior in accord with our goals, depends on the prefrontal cortex. These cognitive functions are heavily influenced by the neuromodulator dopamine. We review here recent insights exploring the influence of dopamine on neuronal response properties in prefrontal cortex (PFC) during ongoing behaviors in...

Our human-specific symbolic number skills that underpin science and technology spring from nonsymbolic set size representations. Despite the significance of numerical competence, its single-neuron mechanisms in the human brain are unknown. We therefore recorded from single neurons in the medial temporal lobe of neurosurgical patients that performed...

How is neuronal activity across distant brain regions orchestrated to allow multiple stimuli to be stored together in working memory, yet maintained separate for individual readout and protection from distractors? Using paired recordings in the prefrontal and parietal cortex of monkeys discriminating numbers of items (numerosities), we found that w...

Social communication has traditionally been studied from the point of view of an isolated spectator not participating in social interaction. In this issue of Neuron, using advanced functional imaging, Shepherd and Freiwald (2018) explore the functional neuroanatomy of social communication in the brain of socially interacting nonhuman primates and d...

Lesion studies suggest a role of the avian hippocampus in spatial and episodic memory. However, whether the avian hippocampus is also involved in processing categorical information and non-spatial working memory contents remains unknown. To address this question, we trained two crows in a delayed-match-to-sample test to assess and briefly memorize...

Honey bees join a select number of animals shown to understand the concept of nothing

Neural oscillations in distinct frequency bands in the prefrontal cortex (pFC) are associated with specialized roles during cognitive control. How dopamine modulates oscillations to structure pFC functions remains unknown. We trained macaques to switch between two numerical rules and recorded local field potentials from pFC while applying dopamine...

Endowed with an elaborate cerebral cortex, humans and other primates can assess the number of items in a set, or numerosity, from birth on [1] and without being trained [2]. Whether spontaneous numerosity extraction is a unique feat of the mammalian cerebral cortex [3-7] or rather an adaptive property that can be found in differently designed and i...

Adaptive sequential behaviors rely on the bridging and integration of temporally separate information for the realization of prospective goals. Corvids’ remarkable behavioral flexibility is thought to depend on the workings of the nidopallium caudolaterale (NCL), a high-level avian associative forebrain area. We trained carrion crows to remember vi...

Number sense, a spontaneous ability to process approximate numbers, has been documented in human adults, infants and newborns, and many other animals. Species as distant as monkeys and crows exhibit very similar neurons tuned to specific numerosities. How number sense can emerge in the absence of learning or fine tuning is currently unknown. We int...

Brains that are capable of representing numerosity, the number of items in a set, have arisen repeatedly and independently in different animal taxa. This review compares the cognitive and physiological mechanisms found in a nonhuman primate, the rhesus macaque, and a corvid songbird, the carrion crow, in order to elucidate the evolutionary adaptati...

Humans show impaired recognition of faces that are presented upside down, a phenomenon termed face inversion effect, which is thought to reflect the special relevance of faces for humans. Here, we investigated whether a phylogenetically distantly related avian species, the carrion crow, with similar socio-cognitive abilities to human and non-human...

Humans show impaired recognition of faces that are presented upside down, a phenomenon termed face inversion effect, which is thought to reflect the special relevance of faces for humans. Here, we investigated whether a phylogenetically distantly related avian species, the carrion crow, with similar socio-cognitive abilities to human and non-human...

Cognitive vocal control is indispensable for human language. Frontal lobe areas are involved in initiating purposeful vocalizations, but their functions remain elusive. We explored the respective roles of frontal lobe areas in initiating volitional vocalizations. Macaques were trained to vocalize in response to visual cues. Recordings from the vent...

The concept of receptive field (RF) describes the responsiveness of neurons to sensory space. Neurons in the primate association cortices have long been known to be spatially selective but a detailed characterization and direct comparison of RFs between frontal and parietal association cortices is missing. We sampled the RFs of a large number of ne...

Serotonin, an important neuromodulator in the brain, is implicated in affective and cognitive functions. However, its role even for basic cortical processes is controversial. For example, in the mammalian primary visual cortex (V1), heterogenous serotonergic modulation has been observed in anesthetized animals. Here, we combined extracellular singl...

Crows quickly learn arbitrary associations. As a neuronal correlate of this behavior, single neurons in the corvid endbrain area nidopallium caudolaterale (NCL) change their response properties during association learning. In crows performing a delayed association task that required them to map both familiar and novel sample pictures to the same tw...

The basic organization principles of the primary visual cortex (V1) are commonly assumed to also hold in the association cortex such that neurons within a cortical column share functional connectivity patterns and represent the same region of the visual field. We mapped the visual receptive fields (RFs) of neurons recorded at the same electrode in...

Leibovich et al. advocate for a single “sense of magnitude” to which a dedicated faculty for number could allegedly be reduced. This conclusion is unjustified as the authors adopt an unnecessarily narrow definition of “number sense,” neglect studies that demonstrate non-symbolic numerosity representation, and furthermore ignore abstract number repr...

Number sense, a spontaneous ability to process approximate numbers, has been documented in human adults, infants and newborns, and many other animals. Species as distant as monkeys and crows exhibit number-selective neuronal activity. How number sense can emerge in the absence of learning or fine tuning is currently unknown. We introduce a random m...

Quantitative features of stimuli may be ordered along a magnitude continuum, or line. Magnitude refers to parameters of different types of stimulus properties. For instance, the frequency of a sound relates to sensory and continuous stimulus properties, whereas the number of items in a set is an abstract and discrete property. In addition, within a...

Significance statement: Birds are known for their capabilities to process numerical quantity. However, birds lack a six-layered neocortex that enables primates with numerical competence. We aimed to decipher the neuronal code for numerical quantity in the independently and distinctly evolved endbrain of birds. We recorded the activity of neurons i...

Single neuron activity in the corvid nidopallium caudolaterale (NCL), the supposed avian functional analog of the prefrontal cortex, represents associations of auditory with visual stimuli. This is of high adaptive value for songbirds that need to rely on audio-visual associations to communicate, find a mate or escape predators. However, it remains...

Explaining the evolution of speech and language poses one of the biggest challenges in biology. We propose a dual network model that posits a volitional articulatory motor network (VAMN) originating in the prefrontal cortex (PFC; including Broca's area) that cognitively controls vocal output of a phylogenetically conserved primary vocal motor netwo...

The prefrontal cortex (PFC) is crucial for maintaining relevant information in working memory and resisting interference. PFC neurons are strongly regulated by dopamine, but it is unknown whether dopamine receptors are involved in protecting target memories from distracting stimuli. We investigated the prefrontal circuit dynamics and dopaminergic m...

Songbirds possess acute vision. How higher brain centers represent basic and parameterized visual stimuli to process sensory signals according to their behavioral importance has not been studied in a systematic way. We therefore examined how carrion crows (Corvus corone) and their nidopallial visual neurons process global visual motion information...

Working memory is associated with persistent activity in the prefrontal cortex (PFC). The neuromodulator dopamine, which is released by midbrain neurons projecting into the frontal lobe, influences PFC neurons and networks via the dopamine D1 (D1R) and the D2 receptor (D2R) families. Although behavioral, clinical and computational evidence suggest...

Zero stands for emptiness, for nothing, and yet it is considered to be one of the greatest achievements of humankind. This review first recapitulates the discovery of the number zero in human history, then follows its progression in human development, traces its evolution in the animal kingdom, and finally elucidates how the brain transforms 'nothi...

The evolutionary origins of human language are obscured by the scarcity of essential linguistic characteristics in non-human primate communication systems. Volitional control of vocal utterances is one such indispensable feature of language.We investigated the ability of two monkeys to volitionally utter species-specific calls over many years. Both...

Humans and non-human primates share an elemental quantification system that resides in a dedicated neural network in the parietal and frontal lobes. In this cortical network, 'number neurons' encode the number of elements in a set, its cardinality or numerosity, irrespective of stimulus appearance across sensory motor systems, and from both spatial...

Neurons in the primate parieto-frontal network represent the number of visual items in a collection, but it is unknown whether this system encodes empty sets as conveying null quantity. We recorded from the ventral intraparietal area (VIP) and the prefrontal cortex (PFC) of monkeys performing a matching task including empty sets and countable numer...