Number sense " is a short-hand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence suggesting that number sense constitutes a domain-specific, biologically-determined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence of a homology between the animal, infant, and human adult abilities for number processing ; and the existence of a dedicated cerebral substrate. In adults of all cultures, lesions to the inferior parietal region can specifically impair number sense while leaving the knowledge of other cognitive domains intact. Furthermore, this region is demonstrably activated during number processing. I postulate that higher-level cultural developments in arithmetic emerge through the establishment of linkages between this core analogical representation (the " number line ") and other verbal and visual representations of number notations. The neural and cognitive organization of those representations can explain why some mathematical concepts are intuitive, while others are so difficult to grasp. Thus, the ultimate foundations of mathematics rests on core representations that have been internalized in our brains through evolution.

Did evolution endow the human brain with a predisposition to represent and acquire knowledge about numbers? Although the parietal lobe...

INTRODUCTION How do we go from seeing a word to accessing its meaning? Classical models of word processing postulate that words are initially recognized in modalityspecific input lexicons before contacting a common semantic representation (Caramazza, 1996; Morton, 1979). This predicts that areas which are engaged in semantic-level processing should activate in direct correlation with the amount of semantic manipulation required by the task and do so independent of the modality of presentation of the concept (Chao et al., 2000; Perani et al., 1999; Vandenberghe et al., 1996). Here, we attempt to identify the cerebral areas engaged in the coding and internal manipulation of an abstract semantic content, the meaning of number words. Although numbers can be written in multiple notations, such as words or digits, the parietal lobes are thought to comprise a notation-independent representation of their semantic content as quantities. According to the "triple-code model" of number process

Over the last years evidence has accumulated that shows the possibility to analyze human brain activity on-line and translate brain states into actions such as selecting a letter from a virtual keyboard or moving a robotics device. These initial results have been obtained with either invasive approaches (requiring surgical implantation of electrodes) or synchronous protocols (where brain signals are time-locked to external cues). In this paper we describe a portable noninvasive brain-computer interface that allows the continuous control of a mobile robot in a house-like environment and also the operation of a virtual keyboard. The interface works asynchronously (the person makes selfpaced decisions on when to switch from one mental task to the next) and uses 8 surface electrodes to measure electroencephalogram signals from which a statistical classifier recognizes 3 different mental states. Here we report results with five volunteers during their brain-actuated interaction experiments with the mobile robot and the virtual keyboard. Two of the participants successfully moved the robot between several rooms, while the other three participants managed to write messages with the virtual keyboard. One of the latter volunteers is a physically impaired person suffering from spinal muscular atrophy.

IPS) as playing a special role overlap in the neural substrates of the three compari- in the internal representation of numerical quantities son tasks. Interestingly, the amount of overlap pre- (Dehaene et al., 2003). dicted the amount of cross-dimensional interference: However, it seems unlikely that the many continuous in both behavior and fMRI, number interfered with size, dimensions that we can compare each have a dedicated and size with luminance, but number did not interfere cortical territory. Therefore, another possibility is that with luminance. The results suggest that during com- the intraparietal region is partially involved in generic parative judgments, the relevant continuous quantities processes of comparison and internal transformation are represented in distributed and overlapping neural of quantitative information that can operate on many populations, with number and size engaging a com- different dimensions. Comparative judgements would mon parietal spatial cod

INTRODUCTION The goal of the present work is to examine whether the semantic representations of numbers and body parts are associated with partially distinct cortical territories. Clinical and cognitive neuropsychology studies associate semantic deficits in both domains to lesions coarsely localized to the left parietal lobe (McCarthy and Warrington, 1990). Furthermore, patients with left inferior parietal lesions often exhibit simultaneous deficits for numbers and body parts (Benton, 1992; Gerstmann, 1940). Such an association of neuropsychological deficits is however notoriously ambiguous, and has been the subject of much debate. It might suggest that there is a shared substrate for numbers and body parts in the left parietal region, perhaps based on a common functional system for spatial representation and manipulation (Gerstmann, 1940) or on the crucial role that finger counting plays in numerical development (Butterworth, 1999). However, it might also reflect the existence of dis

& Language and arithmetic are both lateralized to the left hemisphere in the majority of right-handed adults. Yet, does this similar lateralization reflect a single overall constraint of brain organization, such an overall ‘‘dominance’ ’ of the left hemisphere for all linguistic and symbolic operations? Is it related to the lateralization of specific cerebral subregions? Or is it merely coincidental? To shed light on this issue, we performed a ‘‘colateralization analysis’ ’ over 209 healthy subjects: We investigated whether normal variations in the degree of left hemispheric asymmetry in areas involved in sentence listening and reading are mirrored in the asymmetry of areas involved in mental arithmetic. Within the language network, a region-of-interest analysis disclosed partially dissociated patterns of lateralization, inconsistent with an overall ‘‘dominance’’ model. Only two of these areas presented a lateralization during sentence listening and reading which correlated strongly with the lateralization of two regions active during calculation. Specifically, the profile of asymmetry in the posterior superior temporal sulcus during sentence processing covaried with the asymmetry of calculation-induced activation in the intraparietal sulcus, and a similar colateralization linked the middle frontal gyrus with the superior posterior parietal lobule. Given recent neuroimaging results suggesting a late emergence of hemispheric asymmetries for symbolic arithmetic during childhood, we speculate that these colateralizations might constitute developmental traces of how the acquisition of linguistic symbols affects the cerebral organization of the arithmetic network. &

SUMMARY—Amid ongoing public speculation about the reasons for sex differences in careers in science and mathematics, we present a consensus statement that is based on the best available scientific evidence. Sex differences in science and math achievement and ability are smaller for the mid-range of the abilities distribution than they are for those with the highest levels of achievement and ability. Males are more variable on most measures of quantitative and visuospatial ability, which necessarily results in more males at both high- and low-ability extremes; the reasons why males are often more variable remain elusive. Successful careers in math and science require many types of cognitive abilities. Females tend to excel in verbal abilities, with large differences between females and males found when assessments include writing

The SNARC effect specifically relates small magnitudes to the left hand side and larger magnitudes to the right hand side (e.g. Dehaene et al., 1990; Dehaene et al., 1993). It is certain that cultural characteristics define the SNARC effect: In western cultures small and large numbers are coded in a left-right direction while in Arabic countries magnitude information is coded from right to left (Dehaene et al., 1993; Zebian, in press). In this sense, reading and writing direction have been considered to be the main determinants of the SNARC effect. Indeed, a number of recent studies support the idea that the mastering of a language (and thus reading and writing direction) biases scanning habit in a favourable direction (e.g. Chatterjee et al., 1999; Padakanaya et al., 2002). If this is indeed the case, it is not surprising that the SNARC effect has been found with stimuli other than numbers (Gevers et al., 2004). Related to this, future research could address the question if magnitude and ordinal information are processed by the same mechanism or by different mechanisms with similar properties. However, reading and writing direction alone are not sufficient to explain all SNARC related findings. For instance, it does not allow for an explanation of a

Mathematicians frequently evoke their “intuition” when they are able to quickly and automatically solve a problem, with little introspection into their insight. Cognitive neuroscience research shows that mathematical intuition is a valid concept that can be studied in the laboratory in reduced paradigms, and that relates to the availability of “core knowledge” associated with evolutionarily ancient and specialized cerebral subsystems. As an illustration, I discuss the case of elementary arithmetic. Intuitions of numbers and their elementary transformations by addition and subtraction are present in all human cultures. They relate to a brain system, located in the intraparietal sulcus of both hemispheres, which extracts numerosity of sets and, in educated adults, maps back and forth between numerical symbols and the corresponding quantities. This system is available to animal species and to preverbal human infants. Its neuronal organization is increasingly being uncovered, leading to a precise mathematical theory of how we perform tasks of number comparison or number naming. The next challenge will be to understand how education changes our core intuitions of number.