Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

The neuronal code for number

Key Points

  • In primates, number neurons in a dedicated parieto-frontal network encode the number of elements in a stimulus.

  • Number neurons in the prefrontal cortex respond in an abstract manner, and their responses generalize across spatial, temporal and visuo-auditory item presentations.

  • Number neurons are present in numerically naive monkeys, suggesting that the brain is hard-wired to extract number.

  • Number processing provides mechanistic insight into how relevant information is selected and maintained in working memory.

  • Rule neurons and neuron populations in the frontal lobe guide decisions based on number information.


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 and temporal presentation arrays. After numbers have been extracted from sensory input, they need to be processed to support goal-directed behaviour. Studying number neurons provides insights into how information is maintained in working memory and transformed in tasks that require rule-based decisions. Beyond an understanding of how cardinal numbers are encoded, number processing provides a window into the neuronal mechanisms of high-level brain functions.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Representation of number in the primate brain.
Figure 2: Responses of neuron populations to number.
Figure 3: Microcircuit interactions of number neurons.
Figure 4: Cognitive inhibition of a prefrontal cortex cell during numerical distraction.
Figure 5: Numerical rules.


  1. 1

    Wiese, H. Numbers, Language, and the Human Mind. (Cambridge Univ. Press, 2003).

    Book  Google Scholar 

  2. 2

    Nieder, A. Counting on neurons: the neurobiology of numerical competence. Nat. Rev. Neurosci. 6, 177–190 (2005).

    CAS  Article  Google Scholar 

  3. 3

    Whalen, J., Gallistel, C. R. & Gelman, R. Nonverbal counting in humans: the psychophysics of number representations. Psychol. Sci. 10, 130–137 (1999).

    Article  Google Scholar 

  4. 4

    Merten, K. & Nieder, A. Compressed scaling of abstract numerosity representations in adult humans and monkeys. J. Cogn. Neurosci. 21, 333–346 (2009).

    Article  Google Scholar 

  5. 5

    Gordon, P. Numerical cognition without words: evidence from Amazonia. Science 306, 496–499 (2004).

    CAS  Article  Google Scholar 

  6. 6

    Pica, P., Lemer, C., Izard, V. & Dehaene, S. Exact and approximate arithmetic in an Amazonian indigene group. Science 306, 499–503 (2004).

    CAS  Article  Google Scholar 

  7. 7

    Siegler, R. S. & Opfer, J. E. The development of numerical estimation: evidence for multiple representations of numerical quantity. Psychol. Sci. 14, 237–243 (2003).

    Article  Google Scholar 

  8. 8

    Feigenson, L., Dehaene, S. & Spelke, E. Core systems of number. Trends Cogn. Sci. 8, 307–314 (2004).

    Article  Google Scholar 

  9. 9

    Dacke, M. & Srinivasan, M. V. Evidence for counting in insects. Anim. Cogn. 11, 683–689 (2008).

    Article  Google Scholar 

  10. 10

    Gross, H. J. et al. Number-based visual generalisation in the honeybee. PLoS ONE 4, e4263 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. 11

    Agrillo, C., Piffer, L. & Bisazza, A. Number versus continuous quantity in numerosity judgments by fish. Cognition 119, 281–287 (2011).

    Article  Google Scholar 

  12. 12

    Bisazza, A., Tagliapietra, C., Bertolucci, C., Foà, A. & Agrillo, C. Non-visual numerical discrimination in a blind cavefish (Phreatichthys andruzzii). J. Exp. Biol. 217, 1902–1909 (2014).

    Article  Google Scholar 

  13. 13

    Uller, C., Jaeger, R., Guidry, G. & Martin, C. Salamanders (Plethodon cinereus) go for more: rudiments of number in an amphibian. Anim. Cogn. 6, 105–112 (2003).

    Article  Google Scholar 

  14. 14

    Krusche, P., Uller, C. & Dicke, U. Quantity discrimination in salamanders. J. Exp. Biol. 213, 1822–1828 (2010).

    Article  Google Scholar 

  15. 15

    Koehler, O. Can pigeons “count”? Zeitschrift Tierpsychol. 1, 39–48 (in German) (1937).

    Article  Google Scholar 

  16. 16

    Emmerton, J. in Avian Visual Cognition (ed. Cook, R. G.) [online], (Comparative Cognition Press, 2001).

    Google Scholar 

  17. 17

    McComb, K., Packer, C. & Pusey, A. Roaring and numerical assessment in contests between groups of female lions, Panthera leo. Animal Behav. 47, 379–387 (1994).

    Article  Google Scholar 

  18. 18

    Brannon, E. M. & Terrace, H. S. Ordering of the numerosities 1 to 9 by monkeys. Science 282, 746–749 (1998). Using painstakingly controlled visual stimuli and elegant protocols, this seminal behavioural study showed that monkeys grasp the cardinal and ordinal meaning of numbers.

    CAS  Article  Google Scholar 

  19. 19

    Cantlon, J. F. & Brannon, E. M. How much does number matter to a monkey (Macaca mulatta)? J. Exp. Psychol. Anim. Behav. Process 33, 32–41 (2007).

    Article  Google Scholar 

  20. 20

    Jordan, K. E., Maclean, E. L. & Brannon, E. M. Monkeys match and tally quantities across senses. Cognition 108, 617–625 (2008).

    Article  PubMed  PubMed Central  Google Scholar 

  21. 21

    Beran, M. J. Quantity judgments of auditory and visual stimuli by chimpanzees (Pan troglodytes). J. Exp. Psychol. Anim. Behav. Process 38, 23–29 (2012).

    Article  Google Scholar 

  22. 22

    Wilson, M. L., Kahlenberg, S. M., Wells, M. & Wrangham, R. W. Ecological and social factors affect the occurrence and outcomes of intergroup encounters in chimpanzees. Anim. Behav. 83, 277–291 (2012).

    Article  Google Scholar 

  23. 23

    Kaufman, E. L. & Lord, M. W. The discrimination of visual number. Am. J. Psychol. 62, 498–525 (1949).

    CAS  Article  Google Scholar 

  24. 24

    Anobile, G., Cicchini, G. M. & Burr, D. C. Number as a primary perceptual attribute: a review. Perception 45, 5–31 (2016).

    Article  Google Scholar 

  25. 25

    Dehaene, S., Molko, N., Cohen, L. & Wilson, A. J. Arithmetic and the brain. Curr. Opin. Neurobiol. 14, 218–224 (2004).

    CAS  Article  Google Scholar 

  26. 26

    Nieder, A. & Dehaene, S. Representation of number in the brain. Annu. Rev. Neurosci. 32, 185–208 (2009).

    CAS  Article  Google Scholar 

  27. 27

    Nieder, A., Freedman, D. J. & Miller, E. K. Representation of the quantity of visual items in the primate prefrontal cortex. Science 297, 1708–1711 (2002). This was the first report of neurons in the PFC responding to the number of visual items monkeys were trained to discriminate.

    CAS  Article  Google Scholar 

  28. 28

    Nieder, A. & Miller, E. K. Coding of cognitive magnitude: compressed scaling of numerical information in the primate prefrontal cortex. Neuron 37, 149–157 (2003).

    CAS  Article  Google Scholar 

  29. 29

    Nieder, A. & Miller, E. K. A parieto-frontal network for visual numerical information in the monkey. Proc. Natl Acad. Sci. USA 101, 7457–7462 (2004).

    CAS  Article  Google Scholar 

  30. 30

    Tudusciuc, O. & Nieder, A. Contributions of primate prefrontal and posterior parietal cortices to length and numerosity representation. J. Neurophysiol. 101, 2984–2994 (2009).

    Article  Google Scholar 

  31. 31

    Nieder, A. & Merten, K. A labeled-line code for small and large numerosities in the monkey prefrontal cortex. J. Neurosci. 27, 5986–5993 (2007).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  32. 32

    Okuyama, S., Kuki, T. & Mushiake, H. Representation of the numerosity 'zero' in the parietal cortex of the monkey. Sci. Rep. 5, 10059 (2015).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  33. 33

    Ramirez-Cardenas, A., Moskaleva, M. & Nieder, A. Neuronal representation of numerosity zero in the primate parieto-frontal number network. Curr Biol. (2016).

  34. 34

    Nieder, A., Diester, I. & Tudusciuc, O. Temporal and spatial enumeration processes in the primate parietal cortex. Science 313, 1431–1435 (2006).

    CAS  Article  Google Scholar 

  35. 35

    Castelli, F., Glaser, D. E. & Butterworth, B. Discrete and analogue quantity processing in the parietal lobe: a functional MRI study. Proc. Natl Acad. Sci. USA 103, 4693–4698 (2006).

    CAS  Article  Google Scholar 

  36. 36

    Sawamura, H., Shima, K. & Tanji, J. Numerical representation for action in the parietal cortex of the monkey. Nature 415, 918–922 (2002). This was the first report of neurons in the parietal lobe responding to the number of hand movements that monkeys were trained to perform.

    CAS  Article  Google Scholar 

  37. 37

    Sawamura, H., Shima, K. & Tanji, J. Deficits in action selection based on numerical information after inactivation of the posterior parietal cortex in monkeys. J. Neurophysiol. 104, 902–910 (2010). Transient pharmacological inactivation of neuronal activity in parietal area 5 prevented monkeys from performing the correct number of movements, while sparing general motor functions and action selection. This demonstrates that the activity of number neurons is causally related to number estimation.

    Article  Google Scholar 

  38. 38

    Nieder, A. Supramodal numerosity selectivity of neurons in primate prefrontal and posterior parietal cortices. Proc. Natl Acad. Sci. USA 109, 11860–11865 (2012). Neurons in the PFC encode the same number of visual or auditory events in behaving monkeys.

    CAS  Article  Google Scholar 

  39. 39

    Piazza, M., Mechelli, A., Price, C. J. & Butterworth, B. Exact and approximate judgements of visual and auditory numerosity: an fMRI study. Brain Res. 1106, 177–188 (2006).

    CAS  Article  Google Scholar 

  40. 40

    Ansari, D., Garcia, N., Lucas, E., Hamon, K. & Dhital, B. Neural correlates of symbolic number processing in children and adults. Neuroreport. 16, 1769–1773 (2005).

    Article  Google Scholar 

  41. 41

    Ansari, D. & Dhital, B. Age-related changes in the activation of the intraparietal sulcus during nonsymbolic magnitude processing: an event-related functional magnetic resonance imaging study. J. Cogn. Neurosci. 18, 1820–1828 (2006).

    Article  Google Scholar 

  42. 42

    Eger, E., Sterzer, P., Russ, M. O., Giraud, A. L. & Kleinschmidt, A. A supramodal number representation in human intraparietal cortex. Neuron 37, 719–725 (2003).

    CAS  Article  Google Scholar 

  43. 43

    Cohen Kadosh, R. & Walsh, V. Numerical representation in the parietal lobes: abstract or not abstract? Behav. Brain Sci. 32, 313–328 (2009).

    Article  Google Scholar 

  44. 44

    Nieder, A. The number domain — can we count on parietal cortex? Neuron 44, 407–409 (2004).

    CAS  Article  Google Scholar 

  45. 45

    Diester, I. & Nieder, A. Semantic associations between signs and numerical categories in the prefrontal cortex. PLoS Biol. 5, e294 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  46. 46

    Park, J., DeWind, N. K., Woldorff, M. G. & Brannon, E. M. Rapid and direct encoding of numerosity in the visual stream. Cereb. Cortex 26, 748–763 (2016).

    PubMed  Google Scholar 

  47. 47

    Leibovich, T., Vogel, S. E., Henik, A. & Ansari, D. Asymmetric processing of numerical and nonnumerical magnitudes in the brain: an fMRI study. J. Cogn. Neurosci. 28, 166–176 (2016).

    Article  Google Scholar 

  48. 48

    Dehaene, S. Varieties of numerical abilities. Cognition 44, 1–42 (1992).

    CAS  Article  Google Scholar 

  49. 49

    Ansari, D. Effects of development and enculturation on number representation in the brain. Nat. Rev. Neurosci. 9, 278–291 (2008).

    CAS  Article  Google Scholar 

  50. 50

    Piazza, M. Neurocognitive start-up tools for symbolic number representations. Trends Cogn. Sci. 14, 542–551 (2010).

    Article  Google Scholar 

  51. 51

    Freedman, D. J., Riesenhuber, M., Poggio, T. & Miller, E. K. Categorical representation of visual stimuli in the primate prefrontal cortex. Science 291, 312–316 (2001).

    CAS  Article  Google Scholar 

  52. 52

    Roy, J. E., Riesenhuber, M., Poggio, T. & Miller, E. K. Prefrontal cortex activity during flexible categorization. J. Neurosci. 30, 8519–8528 (2010).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  53. 53

    Viswanathan, P. & Nieder, A. Neuronal correlates of a visual “sense of number” in primate parietal and prefrontal cortices. Proc. Natl Acad. Sci. USA 110, 11187–11192 (2013). Visual number neurons were spontaneously present in monkeys that had never been trained to judge numerosity, arguing that the primate brain is hard-wired to assess numerical quantity.

    CAS  Article  Google Scholar 

  54. 54

    Burr, D. & Ross, J. A visual sense of number. Curr. Biol. 18, 425–428 (2008).

    CAS  Article  Google Scholar 

  55. 55

    Ross, J. & Burr, D. C. Vision senses number directly. J. Vis. 10, 10.1–10.8 (2010).

    Article  Google Scholar 

  56. 56

    Arrighi, R., Togoli, I. & Burr, D. C. A generalized sense of number. Proc. Biol. Sci. 281, 20141791 (2014). Impressive psychophysical experiments reporting the generalization of number adaptation across modalities and spatio-temporal formats, suggesting a perceptual system to encode an abstract sense of number.

    Article  PubMed  PubMed Central  Google Scholar 

  57. 57

    Roitman, J. D., Brannon, E. M. & Platt, M. L. Monotonic coding of numerosity in macaque lateral intraparietal area. PLoS Biol. 5, e208 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  58. 58

    Colby, C. L., Duhamel, J. R. & Goldberg, M. E. Ventral intraparietal area of the macaque: anatomic location and visual response properties. J. Neurophysiol. 69, 902–914 (1993).

    CAS  Article  Google Scholar 

  59. 59

    Wang, L., Uhrig, L., Jarraya, B. & Dehaene, S. Representation of numerical and sequential patterns in macaque and human brains. Curr. Biol. 25, 1966–1974 (2015).

    CAS  Article  Google Scholar 

  60. 60

    Barbas, H. & Mesulam, M. M. Cortical afferent input to the principalis region of the rhesus monkey. Neuroscience 15, 619–637 (1985).

    CAS  Article  Google Scholar 

  61. 61

    Petrides, M. & Pandya, D. N. Projections to the frontal cortex from the posterior parietal region in the rhesus monkey. J. Comp. Neurol. 228, 105–116 (1984).

    CAS  Article  Google Scholar 

  62. 62

    Cavada, C. & Goldman-Rakic, P. S. Posterior parietal cortex in rhesus monkey: II. Evidence for segregated corticocortical networks linking sensory and limbic areas with the frontal lobe. J. Comp. Neurol. 287, 422–445 (1989).

    CAS  Article  Google Scholar 

  63. 63

    Lewis, J. W. & Van Essen, D. C. Corticocortical connections of visual, sensorimotor, and multimodal processing areas in the parietal lobe of the macaque monkey. J. Comp. Neurol. 428, 112–137 (2000).

    CAS  Article  Google Scholar 

  64. 64

    Quintana, J., Fuster, J. M. & Yajeya, J. Effects of cooling parietal cortex on prefrontal units in delay tasks. Brain Res. 503, 100–110 (1989).

    CAS  Article  Google Scholar 

  65. 65

    Chafee, M. V. & Goldman-Rakic, P. S. Inactivation of parietal and prefrontal cortex reveals interdependence of neural activity during memory-guided saccades. J. Neurophysiol. 83, 1550–1566 (2000).

    CAS  Article  Google Scholar 

  66. 66

    Miller, E. K. & Cohen, J. D. An integrative theory of prefrontal cortex function. Annu. Rev. Neurosci. 24, 167–202 (2001).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  67. 67

    Vallentin, D. & Nieder, A. Representations of visual proportions in the primate posterior parietal and prefrontal cortices. Eur. J. Neurosci. 32, 1380–1387 (2010).

    Article  Google Scholar 

  68. 68

    Berger, H. Über Rechenstörungen bei Herderkrankungen des Großhirns. Archiv. Psychiatrie Nervenkrankheiten 78, 238–263 (in German) (1926).

    Article  Google Scholar 

  69. 69

    Hécaen, H., Angelergues, R. & Houillier, S. Les variétes cliniques de acalculies au cours de lesions retrorolandiques: approche statistique du problème. Revue Neurol. 105, 85–103 (in French) (1961).

    Google Scholar 

  70. 70

    Lemer, C., Dehaene, S., Spelke, E. & Cohen, L. Approximate quantities and exact number words: dissociable systems. Neuropsychologia 41, 1942–1958 (2003).

    Article  Google Scholar 

  71. 71

    Lewandowsky, M. & Stadelmann, E. Über einen bemerkenswerten Fall von Hirnblutung und über Rechenstörungen bei Herderkrankung des Gehirns. J. Psychol. Neurol. 11, 249–265 (in German) (1908).

    Google Scholar 

  72. 72

    Henschen, S. E. Über Sprach-, Musik-und Rechenmechanismen und ihre Lokalisation im Großhirn. Zeitschrift Gesamte Neurol. Psychiatrie 52, 273–298 (in German) (1919).

    Article  Google Scholar 

  73. 73

    Ashkenazi, S., Henik, A., Ifergane, G. & Shelef, I. Basic numerical processing in left intraparietal sulcus (IPS) acalculia. Cortex 44, 439–448 (2008).

    Article  Google Scholar 

  74. 74

    Cohen, L. & Dehaene, S. in The Behavioral and Cognitive Neurology of Stroke. 2nd edn (ed. Godefroy, O.) 101–113 (Cambridge University Press, 2013).

    Book  Google Scholar 

  75. 75

    Cipolotti, L. & van Harskamp, N. Handbook of Neuropsychology. 2nd edn Vol. 3 (ed. Berndt, R.S.) 305–334 (Elsevier Science, 2001).

    Google Scholar 

  76. 76

    Cappelletti, M. The Oxford Handbook of Numerical Cognition (ed. Cohen Kadosh, R. & Dowker, A.) 808–836 (Oxford University Press, 2015).

    Google Scholar 

  77. 77

    Butterworth, B., Varma, S. & Laurillard, D. Dyscalculia: from brain to education. Science 332, 1049–1053 (2011).

    CAS  Article  Google Scholar 

  78. 78

    Isaacs, E. B., Edmonds, C. J., Lucas, A. & Gadian, D. G. Calculation difficulties in children of very low birthweight: a neural correlate. Brain 124, 1701–1707 (2001).

    CAS  Article  Google Scholar 

  79. 79

    Rotzer, S. et al. Optimized voxel-based morphometry in children with developmental dyscalculia. Neuroimage 39, 417–422 (2008).

    CAS  Article  Google Scholar 

  80. 80

    Piazza, M., Pinel, P., Le Bihan, D. & Dehaene, S. A magnitude code common to numerosities and number symbols in human intraparietal cortex. Neuron 53, 293–305 (2007).

    CAS  Article  Google Scholar 

  81. 81

    Harvey, B. M., Klein, B. P., Petridou, N. & Dumoulin, S. O. Topographic representation of numerosity in the human parietal cortex. Science 341, 1123–1126 (2013).

    CAS  Article  Google Scholar 

  82. 82

    Arsalidou, M. & Taylor, M. J. Is 2 + 2=4? Meta-analyses of brain areas needed for numbers and calculations. Neuroimage 54, 2382–2393 (2011).

    Article  Google Scholar 

  83. 83

    Nieder, A. Coding of abstract quantity by 'number neurons' of the primate brain. J. Comp. Physiol. A Neuroethol. Sens. Neural Behav. Physiol. 199, 1–16 (2013).

    Article  Google Scholar 

  84. 84

    Viswanathan, P. & Nieder, A. Differential impact of behavioral relevance on quantity coding in primate frontal and parietal neurons. Curr. Biol. 25, 1259–1269 (2015).

    CAS  Article  Google Scholar 

  85. 85

    Dehaene, S., Izard, V., Spelke, E. & Pica, P. Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures. Science 320, 1217–1220 (2008).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  86. 86

    Pouget, A., Dayan, P. & Zemel, R. Information processing with population codes. Nat. Rev. Neurosci. 1, 125–132 (2000).

    CAS  Article  Google Scholar 

  87. 87

    Piazza, M., Izard, V., Pinel, P., Le Bihan, D. & Dehaene, S. Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron 44, 547–555 (2004). Using fMRI adaptation, the authors retrace logarithmically scaled number-tuning functions in the human parietal lobe.

    CAS  Article  Google Scholar 

  88. 88

    Jacob, S. N. & Nieder, A. Tuning to non-symbolic proportions in the human frontoparietal cortex. Eur. J. Neurosci. 30, 1432–1442 (2009).

    Article  Google Scholar 

  89. 89

    Dehaene, S. & Changeux, J. P. Development of elementary numerical abilities: a neural model. J. Cogn. Neurosci. 5, 390–407 (1993).

    CAS  Article  Google Scholar 

  90. 90

    Verguts, T. & Fias, W. Representation of number in animals and humans: a neural model. J. Cogn. Neurosci. 16, 1493–1504 (2004).

    Article  Google Scholar 

  91. 91

    Stoianov, I. & Zorzi, M. Emergence of a 'visual number sense' in hierarchical generative models. Nat. Neurosci. 15, 194–196 (2012).

    CAS  Article  Google Scholar 

  92. 92

    Meck, W. H. & Church, R. M. A mode control model of counting and timing processes. J. Exp. Psychol. Anim. Behav. Process 9, 320–334 (1983).

    CAS  Article  Google Scholar 

  93. 93

    Gallistel, C. R. & Gelman, R. Preverbal and verbal counting and computation. Cognition 44, 43–74 (1992).

    CAS  Article  Google Scholar 

  94. 94

    DeCharms, R. C. & Zador, A. Neural representation and the cortical code. Annu. Rev. Neurosci. 23, 613–647 (2000).

    CAS  Article  Google Scholar 

  95. 95

    Georgopoulos, A., Kalaska, J. & Caminiti, R. On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex. J. Neurosci. 2, 1527–1537 (1982).

    CAS  Article  Google Scholar 

  96. 96

    Salinas, E. & Abbot, L. Vector reconstruction from firing rate. J. Comput. Neurosci. 1, 89–108 (1994).

    CAS  Article  Google Scholar 

  97. 97

    Sanger, T. Probability density estimation for the interpretation of neural population codes. J. Neurophysiol. 76, 2790–2793 (1996).

    CAS  Article  Google Scholar 

  98. 98

    Deneve, S., Latham, P. E. & Pouget, A. Reading population codes: a neural implementation of ideal observers. Nat. Neurosci. 2, 740–745 (1999).

    CAS  Article  Google Scholar 

  99. 99

    Stokes, M. G. 'Activity-silent' working memory in prefrontal cortex: a dynamic coding framework. Trends Cogn. Sci. 19, 394–405 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  100. 100

    Crowe, D. A., Averbeck, B. B. & Chafee, M. V. Rapid sequences of population activity patterns dynamically encode task-critical spatial information in parietal cortex. J. Neurosci. 30, 11640–11653 (2010).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  101. 101

    Meyers, E. M., Freedman, D. J., Kreiman, G., Miller, E. K. & Poggio, T. Dynamic population coding of category information in inferior temporal and prefrontal cortex. J. Neurophysiol. 100, 1407–1419 (2008).

    Article  PubMed  PubMed Central  Google Scholar 

  102. 102

    Stokes, M. G. et al. Dynamic coding for cognitive control in prefrontal cortex. Neuron 78, 364–375 (2013). Population activity of PFC neurons experiences dynamic neuronal state transitions during the course of a cognitive task, indicating that neural tuning profiles adapt to accommodate changes in behavioural context.

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  103. 103

    Averbeck, B. B., Latham, P. E. & Pouget, A. Neural correlations, population coding and computation. Nat. Rev. Neurosci. 7, 358–366 (2006).

    CAS  Article  Google Scholar 

  104. 104

    Kohonen, T. Self-Organizing Maps (Springer-Verlag Berlin Heidelberg, 1997).

    Book  Google Scholar 

  105. 105

    Tudusciuc, O. & Nieder, A. Neuronal population coding of continuous and discrete quantity in the primate posterior parietal cortex. Proc. Natl Acad. Sci. USA 104, 14513–14518 (2007).

    CAS  Article  Google Scholar 

  106. 106

    Genovesio, A., Tsujimoto, S. & Wise, S. P. Prefrontal cortex activity during the discrimination of relative distance. J. Neurosci. 31, 3968–3980 (2011).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  107. 107

    Leon, M. I. & Shadlen, M. N. Representation of time by neurons in the posterior parietal cortex of the macaque. Neuron 38, 317–327 (2003).

    CAS  Article  Google Scholar 

  108. 108

    Mita, A., Mushiake, H., Shima, K., Matsuzaka, Y. & Tanji, J. Interval time coding by neurons in the presupplementary and supplementary motor areas. Nat. Neurosci. 12, 502–507 (2009).

    CAS  Article  Google Scholar 

  109. 109

    Eiselt, A. K. & Nieder, A. Single-cell coding of sensory, spatial and numerical magnitudes in primate prefrontal, premotor and cingulate motor cortices. Exp. Brain Res. 234, 241–254 (2016).

    Article  Google Scholar 

  110. 110

    Pinel, P., Piazza, M., Le Bihan, D. & Dehaene, S. Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments. Neuron 41, 983–993 (2004).

    CAS  Article  Google Scholar 

  111. 111

    Kaufmann, L. et al. A developmental fMRI study of nonsymbolic numerical and spatial processing. Cortex 44, 376–385 (2008).

    Article  Google Scholar 

  112. 112

    Walsh, V. A theory of magnitude: common cortical metrics of time, space and quantity. Trends Cogn. Sci. 7, 483–488 (2003).

    Article  Google Scholar 

  113. 113

    Markram, H. et al. Interneurons of the neocortical inhibitory system. Nat. Rev. Neurosci. 5, 793–807 (2004).

    CAS  Article  Google Scholar 

  114. 114

    Wonders, C. P. & Anderson, S. A. The origin and specification of cortical interneurons. Nat. Rev. Neurosci. 7, 687–696 (2006).

    CAS  Article  Google Scholar 

  115. 115

    Wilson, F. A., O'Scalaidhe, S. P. & Goldman-Rakic, P. S. Functional synergism between putative γ-aminobutyrate-containing neurons and pyramidal neurons in prefrontal cortex. Proc. Natl Acad. Sci. USA 91, 4009–4013 (1994).

    CAS  Article  Google Scholar 

  116. 116

    Rao, S. G., Williams, G. V. & Goldman-Rakic, P. S. Isodirectional tuning of adjacent interneurons and pyramidal cells during working memory: evidence for microcolumnar organization in PFC. J. Neurophysiol. 81, 1903–1916 (1999).

    CAS  Article  Google Scholar 

  117. 117

    Constantinidis, C. & Goldman-Rakic, P. S. Correlated discharges among putative pyramidal neurons and interneurons in the primate prefrontal cortex. J. Neurophysiol. 88, 3487–3497 (2002).

    Article  Google Scholar 

  118. 118

    Johnston, K. & Everling, S. Task-relevant output signals are sent from monkey dorsolateral prefrontal cortex to the superior colliculus during a visuospatial working memory task. J. Cogn. Neurosci. 21, 1023–1038 (2009).

    Article  Google Scholar 

  119. 119

    Merchant, H., de Lafuente, V., Peña-Ortega, F. & Larriva-Sahd, J. Functional impact of interneuronal inhibition in the cerebral cortex of behaving animals. Prog. Neurobiol. 99, 163–178 (2012).

    Article  Google Scholar 

  120. 120

    Epping, W. J. & Eggermont, J. J. Coherent neural activity in the auditory midbrain of the grassfrog. J. Neurophysiol. 57, 1464–1483 (1987).

    CAS  Article  Google Scholar 

  121. 121

    Diester, I. & Nieder, A. Complementary contributions of prefrontal neuron classes in abstract numerical categorization. J. Neurosci. 28, 7737–7747 (2008).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  122. 122

    Rao, S. G., Williams, G. V. & Goldman-Rakic, P. S. Destruction and creation of spatial tuning by disinhibition: GABAA blockade of prefrontal cortical neurons engaged by working memory. J. Neurosci. 20, 485–494 (2000).

    CAS  Article  Google Scholar 

  123. 123

    Compte, A., Brunel, N., Goldman-Rakic, P. S. & Wang, X.-J. Synaptic mechanisms and network dynamics underlying spatial working memory in a cortical network model. Cerebral Cortex 10, 910–923 (2000).

    CAS  Article  Google Scholar 

  124. 124

    Durstewitz, D., Seamans, J. K. & Sejnowski, T. J. Neurocomputational models of working memory. Nat. Neurosci. 3, S1184–S1191 (2000).

    Article  Google Scholar 

  125. 125

    Selemon, L. D. & Goldman-Rakic, P. S. Common cortical and subcortical targets of the dorsolateral prefrontal and posterior parietal cortices in the rhesus monkey: evidence for a distributed neural network subserving spatially guided behavior. J. Neurosci. 8, 4049–4068 (1988).

    CAS  Article  Google Scholar 

  126. 126

    Grieve, K. L., Acuña, C. & Cudeiro, J. The primate pulvinar nuclei: vision and action. Trends Neurosci. 23, 35–39 (2000).

    CAS  Article  Google Scholar 

  127. 127

    Goldman-Rakic, P. S. Topography of cognition: parallel distributed networks in primate association cortex. Annu. Rev. Neurosci. 11, 137–156 (1988).

    CAS  Article  Google Scholar 

  128. 128

    Baars, B. J. A cognitive theory of consciousness. (Cambridge Univ. Press, 1989).

    Google Scholar 

  129. 129

    Dehaene, S. & Changeux, J. P. Experimental and theoretical approaches to conscious processing. Neuron 70, 200–227 (2011).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  130. 130

    Fuster, J. M. & Alexander, G. E. Neuron activity related to short-term memory. Science 173, 652–654 (1971).

    CAS  Article  Google Scholar 

  131. 131

    Kubota, K. & Niki, H. Prefrontal cortical unit activity and delayed alternation performance in monkeys. J. Neurophysiol. 34, 337–347 (1971).

    CAS  Article  Google Scholar 

  132. 132

    Merten, K. & Nieder, A. Active encoding of decisions about stimulus absence in primate prefrontal cortex neurons. Proc. Natl Acad. Sci. USA 109, 6289–6294 (2012).

    CAS  Article  Google Scholar 

  133. 133

    Shadlen, M. N. & Gold, J. I. in The Cognitive Neurosciences. 3rd edn (ed. Gazzaniga, M. S.) 1229–1241 (MIT Press, 2004).

    Google Scholar 

  134. 134

    MacLeod, C. M. Inhibition in cognition. (eds Gorfein, D. S. & MacLeod, C. M.) 3–23 (American Psychological Association, 2007).

    Book  Google Scholar 

  135. 135

    Jacob, S. N. & Nieder, A. Complementary roles for primate frontal and parietal cortex in guarding working memory from distractor stimuli. Neuron 83, 226–237 (2014). This single-cell study points to the PFC as a selection stage for goal-directed number processing that represents behaviourally relevant as well as transiently irrelevant numerical information, whereas distractor-resistant working memory representations seem to be maintained in parietal VIP.

    CAS  Article  Google Scholar 

  136. 136

    Anderson, M. C. & Green, C. Suppressing unwanted memories by executive control. Nature 410, 366–369 (2001).

    CAS  Article  Google Scholar 

  137. 137

    McNab, F. & Klingberg, T. Prefrontal cortex and basal ganglia control access to working memory. Nat. Neurosci. 11, 103–107 (2008).

    CAS  Article  Google Scholar 

  138. 138

    Feredoes, E., Heinen, K., Weiskopf, N., Ruff, C. & Driver, J. Causal evidence for frontal involvement in memory target maintenance by posterior brain areas during distracter interference of visual working memory. Proc. Natl Acad. Sci. USA 108, 17510–17515 (2011).

    CAS  Article  Google Scholar 

  139. 139

    Suzuki, M. & Gottlieb, J. Distinct neural mechanisms of distractor suppression in the frontal and parietal lobe. Nat. Neurosci. 16, 98–104 (2013).

    CAS  Article  Google Scholar 

  140. 140

    Constantinidis, C. & Steinmetz, M. A. Neuronal activity in posterior parietal area 7a during the delay periods of a spatial memory task. J. Neurophysiol. 76, 1352–1355 (1996).

    CAS  Article  Google Scholar 

  141. 141

    Bisley, J. & Goldberg, M. Neural correlates of attention and distractibility in the lateral intraparietal area. J. Neurophysiol. 95, 1696–1717 (2006).

    Article  Google Scholar 

  142. 142

    Postle, B. R. Working memory as an emergent property of the mind and brain. Neuroscience 139, 23–38 (2006).

    CAS  Article  Google Scholar 

  143. 143

    Lara, A. H. & Wallis, J. D. The role of prefrontal cortex in working memory: a mini review. Front. Syst. Neurosci. 9, 173 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  144. 144

    Lennert, T. & Martinez-Trujillo, J. Strength of response suppression to distracter stimuli determines attentional-filtering performance in primate prefrontal neurons. Neuron 70, 141–152 (2011).

    CAS  Article  Google Scholar 

  145. 145

    Malmo, R. B. Interference factors in delayed response in monkeys after removal of frontal lobes. J. Neurophysiol. 5, 295–308 (1942).

    Article  Google Scholar 

  146. 146

    Chao, L. L. & Knight, R. T. Contribution of human prefrontal cortex to delay performance. J. Cogn. Neurosci. 10, 167–177 (1998).

    CAS  Article  Google Scholar 

  147. 147

    Cantlon, J. F. & Brannon, E. M. Semantic congruity affects numerical judgments similarly in monkeys and humans. Proc. Natl Acad. Sci. USA 102, 16507–16511 (2005).

    CAS  Article  Google Scholar 

  148. 148

    Bongard, S. & Nieder, A. Basic mathematical rules are encoded by primate prefrontal cortex neurons. Proc. Natl Acad. Sci. USA 107, 2277–2282 (2010). Populations of rule-selective neurons in the PFC of behaving monkeys signal abstract 'greater-than' or 'fewer-than' rules applied to numbers.

    CAS  Article  Google Scholar 

  149. 149

    Okuyama, S., Iwata, J., Tanji, J. & Mushiake, H. Goal-oriented, flexible use of numerical operations by monkeys. Anim. Cogn. 16, 509–518 (2013).

    Article  Google Scholar 

  150. 150

    Vallentin, D., Bongard, S. & Nieder, A. Numerical rule coding in the prefrontal, premotor, and posterior parietal cortices of macaques. J. Neurosci. 32, 6621–6630 (2012).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  151. 151

    Eiselt, A. K. & Nieder, A. Representation of abstract quantitative rules applied to spatial and numerical magnitudes in primate prefrontal cortex. J. Neurosci. 33, 7526–7534 (2013).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  152. 152

    Wallis, J. D., Anderson, K. C. & Miller, E. K. Single neurons in prefrontal cortex encode abstract rules. Nature 411, 953–956 (2001).

    CAS  Article  Google Scholar 

  153. 153

    Genovesio, A., Brasted, P. J., Mitz, A. R. & Wise, S. P. Prefrontal cortex activity related to abstract response strategies. Neuron 47, 307–320 (2005).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  154. 154

    Mansouri, F. A., Buckley, M. J. & Tanaka, K. Mnemonic function of the dorsolateral prefrontal cortex in conflict-induced behavioral adjustment. Science 318, 987–990 (2007).

    CAS  Article  Google Scholar 

  155. 155

    Rigotti, M. et al. The importance of mixed selectivity in complex cognitive tasks. Nature. 497, 585–590 (2013).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  156. 156

    Dehaene, S. & Changeux, J. P. The Wisconsin Card Sorting Test: theoretical analysis and modeling in a neuronal network. Cereb. Cortex 1, 62–79 (1991).

    CAS  Article  Google Scholar 

  157. 157

    Duncan, J. The structure of cognition: attentional episodes in mind and brain. Neuron 80, 35–50 (2013).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  158. 158

    Seamans, J. K. & Yang, C. R. The principal features and mechanisms of dopamine modulation in the prefrontal cortex. Prog. Neurobiol. 74, 1–58 (2004).

    CAS  Article  Google Scholar 

  159. 159

    Jacob, S. N., Ott, T. & Nieder, A. Dopamine regulates two classes of primate prefrontal neurons that represent sensory signals. J. Neurosci. 33, 13724–13734 (2013).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  160. 160

    Ott, T., Jacob, S. N. & Nieder, A. Dopamine receptors differentially enhance rule coding in primate prefrontal cortex neurons. Neuron 84, 1317–1328 (2014).

    CAS  Article  Google Scholar 

  161. 161

    Dehaene, S., Spelke, E., Pinel, P., Stanescu, R. & Tsivkin, S. Sources of mathematical thinking: behavioral and brain-imaging evidence. Science 284, 970–974 (1999).

    CAS  Article  Google Scholar 

  162. 162

    Gruber, O., Indefrey, P., Steinmetz, H. & Kleinschmidt, A. Dissociating neural correlates of cognitive components in mental calculation. Cereb. Cortex 11, 350–359 (2001).

    CAS  Article  Google Scholar 

  163. 163

    Rivera, S. M., Reiss, A. L., Eckert, M. A. & Menon, V. Developmental changes in mental arithmetic: evidence for increased functional specialization in the left inferior parietal cortex. Cereb. Cortex 15, 1779–1790 (2005).

    CAS  Article  Google Scholar 

  164. 164

    Luria, A. R. Higher Cortical Functions in Man. (Tavistock, 1966).

    Google Scholar 

  165. 165

    Shallice, T. & Evans, M. E. The involvement of the frontal lobes in cognitive estimation. Cortex 14, 294–303 (1978).

    CAS  Article  Google Scholar 

  166. 166

    Smith, M. L. & Milner, B. Differential effects of frontal-lobe lesions on cognitive estimation and spatial memory. Neuropsychologia 22, 697–705 (1984).

    CAS  Article  Google Scholar 

  167. 167

    Della Sala, S., MacPherson, S. E., Phillips, L. H., Sacco, L. & Spinnler, H. The role of semantic knowledge on the cognitive estimation task — evidence from Alzheimer's disease and healthy adult aging. J. Neurol. 251, 156–164 (2004).

    Article  Google Scholar 

  168. 168

    Revkin, S. K. et al. Verbal numerosity estimation deficit in the context of spared semantic representation of numbers: a neuropsychological study of a patient with frontal lesions. Neuropsychologia 46, 2463–2475 (2008).

    Article  Google Scholar 

  169. 169

    Domahs, F., Benke, T. & Delazer, M. A case of 'task-switching acalculia'. Neurocase 17, 24–40 (2011).

    Article  Google Scholar 

  170. 170

    Vallentin, D. & Nieder, A. Behavioural and prefrontal representation of spatial proportions in the monkey. Curr. Biol. 18, 1420–1425 (2008).

    CAS  Article  Google Scholar 

  171. 171

    Tudusciuc, O. & Nieder, A. Comparison of length judgments and the Müller-Lyer illusion in monkeys and humans. Exp. Brain Res. 207, 221–231 (2010).

    Article  Google Scholar 

  172. 172

    Dehaene, S. & Brannon, E. M. Space, Time and Number in the Brain: Searching for the Foundations of Mathematical Thought (Academic Press, 2011).

    Google Scholar 

  173. 173

    Jacob, S. N. & Vallentin, D. & Nieder, A. Relating magnitudes: the brain's code for proportions. Trends Cogn. Sci. 16, 157–166 (2012).

    Article  Google Scholar 

  174. 174

    Genovesio, A., Wise, S. P. & Passingham, R. E. Prefrontal-parietal function: from foraging to foresight. Trends Cogn. Sci. 18, 72–81 (2014).

    Article  Google Scholar 

  175. 175

    Bulthé, J., De Smedt, B. & Op de Beeck, H. P. Format-dependent representations of symbolic and non-symbolic numbers in the human cortex as revealed by multi-voxel pattern analyses. Neuroimage 87, 311–322 (2014).

    Article  Google Scholar 

  176. 176

    Bulthé, J., De Smedt, B. & Op de Beeck, H. P. Visual number beats abstract numerical magnitude: format-dependent representation of Arabic digits and dot patterns in human parietal cortex. J. Cogn. Neurosci. 27, 1376–1387 (2015).

    Article  Google Scholar 

  177. 177

    Lyons, I. M., Ansari, D. & Beilock, S. L. Qualitatively different coding of symbolic and nonsymbolic numbers in the human brain. Hum. Brain Mapp. 36, 475–488 (2015).

    Article  Google Scholar 

  178. 178

    Dehaene, S. & Cohen, L. Cultural recycling of cortical maps. Neuron 56, 384–398 (2007).

    CAS  Article  Google Scholar 

  179. 179

    Danzig, T. Number — The Language of Science (The Free Press, 1930).

    Google Scholar 

  180. 180

    Dehaene, S. The Number Sense. 2nd edn (Oxford University Press, 2011).

    Google Scholar 

  181. 181

    Evans, S. E. in Evolutionary Developmental Biology of the Cerebral Cortex (eds Bock, G. & Cardew, G.) 109–113 (Wiley, 2000).

    Google Scholar 

  182. 182

    Dugas-Ford, J., Rowell, J. J. & Ragsdale, C. W. Cell-type homologies and the origins of the neocortex. Proc. Natl Acad. Sci. USA 109, 16974–16979 (2012).

    CAS  Article  Google Scholar 

  183. 183

    Dugas-Ford, J. & Ragsdale, C. W. Levels of homology and the problem of neocortex. Annu. Rev. Neurosci. 38, 351–368 (2015).

    CAS  Article  Google Scholar 

  184. 184

    Jarvis, E. D. et al. Avian brains and a new understanding of vertebrate brain evolution. Nat. Rev. Neurosci. 6, 151–159 (2005).

    CAS  Article  Google Scholar 

  185. 185

    Butler, A., Reiner, A. & Karten, H. J. Evolution of the amniote pallium and the origins of mammalian neocortex. Ann. NY Acad. Sci. 1225, 14–27 (2011).

    Article  Google Scholar 

  186. 186

    Scarf, D., Hayne, H. & Colombo, M. Pigeons on par with primates in numerical competence. Science 334, 1664 (2011).

    CAS  Article  Google Scholar 

  187. 187

    Bogale, B. A., Kamata, N., Mioko, K. & Sugita, S. Quantity discrimination in jungle crows, Corvus macrorhynchos. Anim. Behav. 82, 635–641 (2011).

    Article  Google Scholar 

  188. 188

    Moll, F. W. & Nieder, A. The long and the short of it: rule-based relative length discrimination in carrion crows, Corvus corone. Behav. Processes 107, 142–149 (2014).

    Article  Google Scholar 

  189. 189

    Lyon, B. E. Egg recognition and counting reduce costs of avian conspecific brood parasitism. Nature 422, 495–499 (2003).

    CAS  Article  Google Scholar 

  190. 190

    Templeton, C. N., Greene, E. & Davis, K. Allometry of alarm calls: black-capped chickadees encode information about predator size. Science 308, 1934–1937 (2005).

    CAS  Article  Google Scholar 

  191. 191

    Hunt, S., Low, J. & Burns, K. C. Adaptive numerical competency in a food-hoarding songbird. Proc. Roy. Soc. B 275, 2373–2379 (2008).

    Article  Google Scholar 

  192. 192

    Ditz, H. M. & Nieder, A. Numerosity representations in crows obey the Weber–Fechner law. Proc. R. Soc. B 283, 20160083 (2016).

    Article  Google Scholar 

  193. 193

    Ditz, H. M. & Nieder, A. Neurons selective to the number of visual items in the corvid songbird endbrain. Proc. Natl Acad. Sci. USA 112, 7827–7832 (2015). This was the first study reporting number neurons in a non-mammalian species, and a species without a neocortex: the crow.

    CAS  Article  Google Scholar 

  194. 194

    Divac, I., Mogensen, J. & Björklund, A. The prefrontal “cortex” in the pigeon. Biochemical evidence. Brain Res. 332, 365–368 (1985).

    CAS  Article  Google Scholar 

  195. 195

    Güntürkün, O. The avian “prefrontal cortex” and cognition. Curr. Opin. Neurobiol. 15, 686–693 (2005).

    Article  CAS  Google Scholar 

  196. 196

    Veit, L. & Nieder, A. Abstract rule neurons in the endbrain support intelligent behaviour in corvid songbirds. Nat. Commun. 4, 2878 (2013).

    Article  CAS  Google Scholar 

Download references


The author thanks H. Ditz, T. Ott, L. Veit and S. Westendorff for valuable comments on the manuscript. H. Ditz helped with Figures 1b and 1c, and T. Ott provided Figure 5d.

Author information



Corresponding author

Correspondence to Andreas Nieder.

Ethics declarations

Competing interests

The author declares no competing financial interests.

PowerPoint slides


Ordinal numbers

Numbers that relate to the empirical property of 'rank' in a sequence (for example, 'fifth place').

Nominal numbers

Strictly linguistic labels to identify objects (for example, 'Bus number 5').

Number estimation

(Also known as the analogue magnitude system and the analogue number system). A process of representing small and large set sizes that becomes systematically less precise with increasing numbers. Thus, number estimation obeys Weber's law.


(Also known as object file representation or object tracking system). The rapid tracking for up to approximately four items by assigning 'files' or 'pointers' to individual items.

Texture-like mechanism

A mechanism that allows the representation of very many and densely packed items and does not obey Weber's law.


A trait that serves a different purpose from the one for which it evolved.

Labelled-line rate code

Relates to the discharge rates of neurons that belong to dedicated processing pathways and that convey information about specific stimulus parameters (it is a variation of a rate code).

Weber–Fechner law

Classic psychophysical law about the perception of magnitudes in relation to the physical intensity of a stimulus; it states that linear increments in sensation S are proportional to the logarithm of stimulus magnitude I (S = k * log(I)).

Rate code

Relates to the information encoded by the number of spikes during an interval.

Time code

Relates to the information encoded by temporal patterns of action potentials within an interval.

Global neuronal workspace

(GNW). A framework for the mechanism of consciousness. It consists of a network of distributed neurons with long-distance connectivity constituting a 'global workspace' that can potentially interconnect multiple specialized brain areas in a coordinated manner to give rise to a subjective feeling of conscious effort.


Refers to traits that share a common ancestry but may have different functions.


Refers to traits with common functions but that are associated with different underlying structures and origins, and have evolved by convergent evolution.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Nieder, A. The neuronal code for number. Nat Rev Neurosci 17, 366–382 (2016).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing