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What are the brain and cognitive systems that allow humans to play baseball, compute square roots, cook soufflés, or navigate the Tokyo subways? It may seem that studies of human infants and of non-human animals will tell us little about these abilities, because only educated, enculturated human adults engage in organized games, formal mathematics, gourmet cooking, or map-reading. In this chapter, we argue against this seemingly sensible conclusion. When human adults exhibit complex, uniquely human, culture-specific skills, they draw on a set of psychological and neural mechanisms with two distinctive properties: they evolved before humanity and thus are shared with other animals, and they emerge early in human development and thus are common to infants, children, and adults. These core knowledge systems form the building blocks for uniquely human skills. Without them we wouldn’t be able to learn about different kinds of games, mathematics, cooking, or maps. To understand what is special about human intelligence, therefore, we must study both the core knowledge systems on which it rests and the mechanisms by which these systems are orchestrated to permit new kinds of concepts and cognitive processes. What is core knowledge? A wealth of research on non-human primates and on human

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

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.

Current theories of number processing postulate that the human abilities for arithmetic are based on cerebral circuits that are partially laid down under genetic control and later modified by schooling and education. This view predicts the existence of genetic diseases that interfere specifically with components of the number system. Here, we investigate whether Turner syndrome (TS) corresponds to this definition. TS is a genetic disorder which affects one woman in 2500 and is characterized by partial or complete absence of one X chromosome. In addition to well-characterized physical and hormonal dysfunction, TS patients exhibit cognitive deficits including dyscalculia. We tested 12 women with Turner syndrome and 13 control subjects on a cognitive battery including arithmetical tests (addition, subtraction, multiplication, division) as well as tests of the understanding of numerosity and quantity (cognitive estimation, estimation, comparison, bisection, subitizing/counting). Impairments were observed in cognitive estimation, subitizing, and calculation. We examine whether these deficits can be attributed to a single source, and discuss the possible implications of hormonal and genetic factors in the neuropsychological profile of TS patients.

Encoding the serial order of events is an essential function of working memory, but one whose neural basis is not yet well understood. In the present work, we advance a new model of how serial order is represented in working memory. Our approach is predicated on three key findings from neurophysiological research: (1) prefrontal neurons that code conjunctively for item and order, (2) parietal neurons that represent count information through a graded and compressive code, and (3) multiplicative gain modulation as a mechanism for information integration. We used an artificial neural network, integrating across these three findings, to simulate human immediate serial recall performance. The model reproduced a core set of benchmark empirical findings, including primacy and recency effects, transposition gradients, effects of interitem similarity, and developmental effects. The model moves beyond previous accounts by bridging between neuroscientific findings and detailed behavioral data, and gives rise to several testable predictions. Key words: prefrontal cortex; parietal cortex; working memory; serial order; computational models; numerosity

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Numerical abilities are thought to rest on the integration of two distinct systems, a verbal system of number words and a non-symbolic representation of approximate quantities. This view has lead to the classification of acalculias into two broad categories depending on whether the deficit affects the verbal or the quantity system. Here, we test the association of deficits predicted by this theory, and particularly the presence or absence of impairments in non-symbolic quantity processing. We describe two acalculic patients, one with a focal lesion of the left parietal lobe and Gerstmann's syndrome and another with semantic dementia with predominantly left temporal hypometabolism. As predicted by a quantity deficit, the first patient was more impaired in subtraction than in multiplication, showed a severe slowness in approximation, and exhibited associated impairments in subitizing and numerical comparison tasks, both with Arabic digits and with arrays of dots. As predicted by a verbal deficit, the second patient was more impaired in multiplication than in subtraction, had intact approximation abilities, and showed preserved processing of non-symbolic numerosities.

INTRODUCTION Consider a lioness in her pride in the Serengeti National park, Tanzania. One night she is all alone and hears a roar from an intruder lioness. Should she try to drive the intruder off? That would be an even match, thus ending in a possibly fatal fight. She decides not to act. The following night she is with four sisters, when they hear the roars of three intruder lionesses. This time it is three versus five. The lionesses peer into each others eyes and then launch the attack. But by the time they reach the expected location, they find no intruder, and that is because the sounds were actually coming from loudspeakers set up by a researcher investigating the numerical capacity of animals. This research shows that generally, animals decide to attack back only when the number of defenders is superior to the number of intruders (McComb, Packer, & Pusey, 1994). The process of "decision making" of these animals seems to be based on a multimodal comparison between the number of

are distributed on a logarithmic scale, thus permitting a wide range of quantities to be encoded with a small population of cells. This compressive property implies 1Unité INSERM 562 “Cognitive Neuroimaging ” an increasingly coarser encoding of larger numbers. 2Unité de Neuroimagerie Anatomo-Fonctionnelle Thus, it can explain the behavioral observation that, as