Arithmetic and the brain

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Abstract

Recent studies in human neuroimaging, primate neurophysiology, and developmental neuropsychology indicate that the human ability for arithmetic has a tangible cerebral substrate. The human intraparietal sulcus is systematically activated in all number tasks and could host a central amodal representation of quantity. Areas of the precentral and inferior prefrontal cortex also activate when subjects engage in mental calculation. A monkey analogue of these parieto-frontal regions has recently been identified, and a neuronal population code for number has been characterized. Finally, pathologies of this system, leading to acalculia in adults or to developmental dyscalculia in children, are beginning to be understood, thus paving the way for brain-oriented intervention studies.

Introduction

Number theory is a complex achievement of the human mind. However, the core concept of arithmetic number is simple, and all human cultures have at least a few words for numbers. Seven years ago, I proposed the hypothesis that ‘number sense’ is a basic capacity of the human brain [1]: dedicated brain circuits, inherited from our evolutionary history, are engaged in recognizing numerosity (the number of objects in a set), and provide us with a basic intuition that guides the acquisition of formal arithmetic.

The purpose of the present review is to re-evaluate this hypothesis in the light of recent findings in cognitive neuroscience. Progress has been fast in several domains, which are each reviewed in turn: neuroimaging of number processing in humans, animal models of the cerebral bases of number sense and developmental psychology of basic numerical abilities and their disorders.

Section snippets

The intraparietal sulcus and number sense

Which brain areas are engaged when we compute 7−4 or 3×7? Modern neuroimaging confirms that a reproducible set of parietal, prefrontal and cingulate areas is systematically activated (over and above the activations related to stimulus identification and response output) whenever subjects are asked to perform a calculation 2., 3.••, 4., 5., 6., 7., 8.. A recent meta-analysis indicates that the horizontal segment of the bilateral intraparietal sulcus (HIPS), in particular, is implicated in most

Number sense in the animal brain

The human number sense has roots in evolution. It has long been known that many animal species can discriminate stimuli that differ only in numerosity. Considering only recent work, dolphins [37] and salamanders [38] have joined macaques 39., 40., tamarin monkeys 41.•, 42., and lions [43] in the list of number-competent species, which suggests that number sense is widespread. Importantly, several of these studies observed untrained behavior, for instance showing that animals spontaneously

Development and pathologies of number sense

Adult human arithmetic also has its roots in development. In recent years, claims of numerical competence in infants have received important qualifications. First, some tasks previously thought to tap numerical competence have been shown to engage a representation of physical amount rather than number 50., 51.. Second, many tasks are now known to depend on a special object-file system limited to representing up to three objects 52., 53.. Nevertheless, other studies have conclusively

Conclusions

The present review suggests that quantity-related brain regions including the IPS are present early in evolution, are laid down under partial genetic control, and play a significant role in early numerical development, to the extent that their disorganization can create a lifelong impairment in arithmetic. The challenges for the future involve first, understanding the homologies, but also the differences, between the human and the macaque number-related areas; second, understanding the global

References and recommended reading

Papers of particular interest, published within the annual period of review, have been highlighted as:

  • of special interest

  • ••

    of outstanding interest

Acknowledgements

The authors are supported by Institut National de la Santé et de la Recherche Médicale, Commissariat à l’énergie atomique, a centennial fellowship of the McDonnell Foundation to S Dehaene and a Fyssen Foundation fellowship to A Wilson.

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