Mental calculation in a prodigy is sustained by right prefrontal and medial temporal areas

Temporal-spatial deciphering mental subtraction in the human brain

Mental subtraction, involving numerical processing and operation, requires a complex interplay among several brain regions. Diverse studies have utilized scalp electroencephalograph, electrocorticogram, or functional magnetic resonance imaging to resolve the structure pattern and functional activity during subtraction operation. However, a high resolution of the spatial-temporal understanding of the neural mechanisms involved in mental subtraction is unavailable. Thus, this study obtained intracranial stereoelectroencephalography recordings from 20 patients with pharmacologically resistant epilepsy. Specifically, two sample-delayed mismatch paradigms of numeric comparison and subtracting results comparison were used to help reveal the time frame of mental subtraction. The brain sub-regions were chronologically screened using the stereoelectroencephalography recording for mental subtraction. The results indicated that the anterior cortex, containing the frontal, insular, and parahippocampous, worked for preparing for mental subtraction; moreover, the posterior cortex, such as parietal, occipital, limbic, and temporal regions, cooperated during subtraction. Especially, the gamma band activities in core regions within the parietal-cingulate-temporal cortices mediated the critical mental subtraction. Overall, this research is the first to describe the spatiotemporal activities underlying mental subtraction in the human brain. It provides a comprehensive insight into the cognitive control activity underlying mental arithmetic.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-023-09937-z.

Probing Our Built-in Calculator: A Systematic Narrative Review of Noninvasive Brain Stimulation Studies on Arithmetic Operation-Related Brain Areas

This systematic review presented a comprehensive survey of studies that applied transcranial magnetic stimulation and transcranial electrical stimulation to parietal and nonparietal areas to examine the neural basis of symbolic arithmetic processing. All findings were compiled with regard to the three assumptions of the triple-code model (TCM) of number processing. Thirty-seven eligible manuscripts were identified for review (33 with healthy participants and 4 with patients). Their results are broadly consistent with the first assumption of the TCM that intraparietal sulcus both hold a magnitude code and engage in operations requiring numerical manipulations such as subtraction. However, largely heterogeneous results conflicted with the second assumption of the TCM that the left angular gyrus subserves arithmetic fact retrieval, such as the retrieval of rote-learned multiplication results. Support is also limited for the third assumption of the TCM, namely, that the posterior superior parietal lobule engages in spatial operations on the mental number line. Furthermore, results from the stimulation of brain areas outside of those postulated by the TCM show that the bilateral supramarginal gyrus is involved in online calculation and retrieval, the left temporal cortex in retrieval, and the bilateral dorsolateral prefrontal cortex and cerebellum in online calculation of cognitively demanding arithmetic problems. The overall results indicate that multiple cortical areas subserve arithmetic skills.

Neurobiology of numerical learning

Numerical abilities are complex cognitive skills essential for dealing with requirements of the modern world. Although the brain structures and functions underlying numerical cognition in different species have long been appreciated, genetic and molecular techniques have more recently expanded the knowledge about the mechanisms underlying numerical learning. In this review, we discuss the status of the research related to the neurobiological bases of numerical abilities. We consider how genetic factors have been associated with mathematical capacities and how these link to the current knowledge of brain regions underlying these capacities in human and non-human animals. We further discuss the extent to which significant variations in the levels of specific neurotransmitters may be used as potential markers of individual performance and learning difficulties and take into consideration the therapeutic potential of brain stimulation methods to modulate learning and improve interventional outcomes. The implications of this research for formulating a more comprehensive view of the neural basis of mathematical learning are discussed.

A review and perspective on the neural basis of radiological expertise

Radiological expertise requires tremendous time, effort, and training. While there has been a myriad of studies focusing on radiological expertise and error, the precise underlying neural mechanism still remains largely unexplored. In this article, we review potential neural mechanisms, namely, the fusiform face area, working memory, and predictive coding and propose experiments to test the predictive coding framework.

The predictive role of eye movements in mental arithmetic

Behavioural studies have suggested that number manipulation involves shifting attention along a left-to-right oriented continuum. However, these studies provide little evidence about the time course of attention shifts during number processing. We used an eye-tracker with high spatio-temporal resolution to measure eye movements during the mental solving of addition (e.g., 43 + 4) and subtraction problems (e.g., 53 - 6), as a proxy for the rightward and leftward attention shifts that accompany these operations. A first difference in eye position was observed as soon as the operator was heard: the hearing of "plus" shifted the eye rightward compared to "minus". A second difference was observed later between problem offset and response onset: addition shifted the eye rightward and upward compared to subtraction, suggesting that the space used to represent the problem is bidimensional. Further analyses confirmed the fast deployment of spatial attention and evidenced its relationship with the carrying and borrowing procedures triggered by the problem presentation. The predictive role of horizontal eye movements, in particular, is essential to understand how attention contributes to narrow down the range of plausible answers. We propose that attention illuminates significant portions of the numerical continuum anticipatively to guide the search of the answer and facilitate the implementation of solving procedures in verbal working memory.

Neuroanatomical differences in the memory systems of intellectual giftedness and typical development

INTRODUCTION

Studying neuro-structural markers of intellectual giftedness (IG) will inform scientific understanding of the processes helping children excel academically.

METHODS

Structural and diffusion-weighted MRI was used to compare regional brain shape and connectivity of 12 children with average to high average IQ and 18 IG children, defined as having IQ greater than 145.

RESULTS

IG had larger subcortical structures and more robust white matter microstructural organization between those structures in regions associated with explicit memory. TD had more connected, larger subcortical structures in regions associated with implicit memory.

CONCLUSIONS

It was found that the memory systems within brains of children with exceptional intellectual abilities are differently sized and connected compared to the brains of typically developing children. These different neurodevelopmental trajectories suggest different learning strategies. A spectrum of intelligence types is envisioned, facilitated by different ratios of implicit and explicit system, which was validated using a large external dataset.

Magnetoencephalography reveals differences in brain activations for fast and slow responses to simple multiplications

Despite decades of studies, it is still an open question on how and where simple multiplications are solved by the brain. This fragmented picture is mostly related to the different tasks employed. While in neuropsychological studies patients are asked to perform and report simple oral calculations, neuroimaging and neurophysiological studies often use verification tasks, in which the result is shown, and the participant must verify the correctness. This MEG study aims to unify the sources of evidence, investigating how brain activation unfolds in time using a single-digit multiplication production task. We compared the participants' brain activity-focusing on the parietal lobes-based on response efficiency, dividing their responses in fast and slow. Results showed higher activation for fast, as compared to slow, responses in the left angular gyrus starting after the first operand, and in the right supramarginal gyrus only after the second operand. A whole-brain analysis showed that fast responses had higher activation in the right dorsolateral prefrontal cortex. We show a timing difference of both hemispheres during simple multiplications. Results suggest that while the left parietal lobe may allow an initial retrieval of several possible solutions, the right one may be engaged later, helping to identify the solution based on magnitude checking.

Directed Connectivity Analysis of the Brain Network in Mathematically Gifted Adolescents

The neurocognitive characteristics of mathematically gifted adolescents are characterized by highly developed functional interactions between the right hemisphere and excellent cognitive control of the prefrontal cortex, enhanced frontoparietal cortex, and posterior parietal cortex. However, it is still unclear when and how these cortical interactions occur. In this paper, we used directional coherence analysis based on Granger causality to study the interactions between the frontal brain area and the posterior brain area in the mathematical frontoparietal network system during deductive reasoning tasks. Specifically, the scalp electroencephalography (EEG) signal was first converted into a cortical dipole source signal to construct a Granger causality network over the θ-band and γ-band ranges. We constructed the binary Granger causality network at the 40 pairs of cortical nodes in the frontal lobe and parietal lobe across the θ-band and the γ-band, which were selected as regions of interest (ROI). We then used graph theory to analyze the network differences. It was found that, in the process of reasoning tasks, the frontoparietal regions of the mathematically gifted show stronger working memory information processing at the θ-band. Additionally, in the middle and late stages of the conclusion period, the mathematically talented individuals have less information flow in the anterior and posterior parietal regions of the brain than the normal subjects. We draw the conclusion that the mathematically gifted brain frontoparietal network appears to have more “automated” information processing during reasoning tasks.

Can the interference effect in multiplication fact retrieval be modulated by an arithmetic training? An fMRI study

Single-digit multiplications are thought to be associated with different levels of interference because they show different degrees of feature overlap (i.e., digits) with previously learnt problems. Recent behavioral and neuroimaging studies provided evidence for this interference effect and showed that individual differences in arithmetic fact retrieval are related to differences in sensitivity to interference (STI). The present study investigated whether and to what extent competence-related differences in STI and its neurophysiological correlates can be modulated by a multiplication facts training. Participants were 23 adults with high and 23 adults with low arithmetic competencies who underwent a five-day multiplication facts training in which they intensively practiced sets of low- and high-interfering multiplication problems. In a functional magnetic resonance imaging (fMRI) test session after the training, participants worked on a multiplication verification task that comprised trained and untrained problems. Analyses of the behavioral data revealed an interference effect only in the low competence group, which could be reduced but not resolved by training. On the neural level, competence-related differences in the interference effect were observed in the left supramarginal gyrus (SMG), showing activation differences between low- and high-interfering problems only in the low competent group. These findings support the idea that individuals' low arithmetic skills are related to the development of insufficient memory representations because of STI. Further, our results indicate that a short training by drill (i.e., learning associations between operands and solutions) was not fully effective to resolve existing interference effects in arithmetic fact knowledge.

Neural Evidence of Superior Memory: How to Capture Brain Activities of Encoding Processes Underlying Superior Memory

Relatively little attention has been paid to the neural basis of superior memory despite its potential in providing important insight into efforts to improve memory in the general population or to offset age-related cognitive decline. The current study reports a rare opportunity to reproduce and isolate specific neural activities directly associated with exceptional memory. To capture the brain processes responsible for superior memory, we returned to a laboratory task and analytic approach used to explore the nature of exceptional memory, namely, digit-span task combined with verbal protocol analysis. One participant with average memory received approximately 50 h of digit-span training and the participant's digit-span increased from normative (8 digits) to exceptional (30 digits). Event-related potentials were recorded while the participant's digit span increased from 19 to 30 digits. Protocol analysis allowed us to identify direct behavioral indices of idiosyncratic encoding processes underlying the superior memory performance. EEG indices directly corresponding to the behavioral indices of encoding processes were identified. The results suggest that the early attention-related encoding processes were reflected in theta and delta whereas the later attention-independent encoding processes were reflected in time-domain slow-wave. This fine-grained approach offers new insights into studying neural mechanism mediating superior memory and the cognitive effort necessary to develop it.

Neuroenhancement of High-Level Cognition: Evidence for Homeostatic Constraints of Non-invasive Brain Stimulation

Neuroenhancement aims to improve cognitive performance in typically and atypically functioning populations. However, it is currently debated whether it is also effective in exceptionally high-functioning individuals. Present theories suggest that homeostatic set points for learning and cortical plasticity limit the beneficial effects of neuroenhancement. To examine this possibility, we used transcranial random noise stimulation (tRNS) to non-invasively stimulate bilateral dorsolateral prefrontal cortices (DLPFC) of the world champion in mental calculation, G.M. TRNS did not change G.M.’s calculation performance compared to sham stimulation on an exceptionally complex arithmetic task. However, a sample of mathematicians who were not calculation prodigies (N = 6) showed reduced accuracy on a complex multiplication task in response to tRNS, relative to sham. Our findings suggest that there may be an upper limit for cognitive enhancement and that further attempts to enhance performance using tRNS (at least with the current parameters) may impair optimal functioning. The discussion of potential negative effects of brain stimulation for cognitive enhancement is critical, as it may lead to unintended impairments in different subgroups of the population.

Electrophysiological markers of poor versus superior math abilities in healthy individuals

Interindividual differences in the numerical ability of healthy adults have been previously demonstrated, mainly with tasks involving mental number line or size representation. However, electrophysiological correlates of superior versus poor arithmetic ability (in the healthy population) have been scarcely investigated. We correlated electric potentials with math performance in 13 skilled and 13 poor calculators selected from a sample of 41 graduate students on the basis of their poor or superior math abilities assessed through a timed test. EEG was recorded from 128 channels while participants solved 352 arithmetical operations (additions, subtractions, multiplications, divisions) and decided whether the provided solution was correct or incorrect. Overall skilled individuals correctly solved a higher number of operations than poor calculators and had faster response times. Consistently, the latency of fronto-central P300 component of event-related potentials (ERPs) peaked earlier in the skilled than poor group. The P300 was larger in amplitude to correct than incorrect solutions, but just in the skilled group, with a tendency found in poor calculators. Spearman's ρ correlation coefficient analyses showed that the larger P300 response was to correct arithmetic solutions, the better the performance; conversely, the larger the P300 amplitude was to incorrect solutions, the worse the performance. The results suggest that poor calculators had a less clear representation of arithmetic solutions and difficulty in quickly accessing it. This study provides a standard method for directly investigating math abilities throughout ERP recordings that could be useful for assessing acalculia/dyscalculia in the clinical population (children, elderly, brain-damaged patients).

The contributions of executive functions to mathematical learning difficulties and mathematical talent during adolescence

Are mathematical learning difficulties caused by impairment of the abilities that underlie mathematical talent? Or are mathematical difficulties and talent qualitatively different? The main goal of this study was to determine whether mathematical learning difficulties are explained by the same executive functions as mathematical talent. We screened a pool of 2,682 first-year high school students and selected 48 for evaluation, dividing them into three groups: those with mathematical learning difficulties (n = 16), those with typical performance (n = 16), and those with mathematical talent (n = 16). Adolescents from the learning difficulties and talented groups had age, reading skills, and verbal and non-verbal intelligence that were similar to those of the typical performance group. Participants were administered a suite of tasks to evaluate verbal and visual short-term memory and executive functions of inhibition, shifting, and updating. Different executive functions showed different contributions at the two ends of the math ability continuum: lower levels of performance in updating visual information were related to mathematical learning difficulties, while greater shifting abilities were related to mathematical talent. Effect sizes for the differences in performance between groups were large (Hedges' g > 0.8). These results suggest that different executive functions are associated with mathematical learning difficulties and mathematical talent. We discuss how these differences in executive functions could be related to the different types of mathematical abilities that distinguish the three groups.

The Double Take of Expertise: Neural Expansion Is Associated With Outstanding Performance

The performance of experts seems almost effortless. The neural-efficiency hypothesis takes this into account, suggesting that because of practice and automatization of procedures, experts require fewer brain resources. Here, I argue that the way the brain accommodates complex skills does indeed have to do with the nature of experts’ performance. However, instead of exhibiting less brain activation, experts’ performance actually engages more brain areas. Behind the seemingly effortless performance of experts lies a complex cognitive system that relies on knowledge about the domain of expertise. Unlike novices, who need to execute one process at a time, experts are able to recognize an object, retrieve its function, and connect it to another object simultaneously. The expert brain deals with this computational burden by engaging not only specific brain areas in one hemisphere but also the same (homologous) area in the opposite hemisphere. This phenomenon, which I call the double take of expertise, has been observed in a number of expertise domains. I describe it here in object- and pattern-recognition tasks in the domain of chess. I also discuss the importance of the study of expertise for our understanding of the human brain in general.

The brain-structural correlates of mathematical expertise

Studies in several domains of expertise have established that experience-dependent plasticity brings about both functional and anatomical changes. However, little is known about how such changes come to shape the brain in the case of expertise acquired by professional mathematicians. Here, we aimed to identify cognitive and brain-structural (grey and white matter) characteristics of mathematicians as compared to non-mathematicians. Mathematicians and non-mathematician academics from the University of Oxford underwent structural and diffusion MRI scans, and were tested on a cognitive battery assessing working memory, attention, IQ, numerical and social skills. At the behavioural level, mathematical expertise was associated with better performance in domain-general and domain-specific dimensions. At the grey matter level, in a whole-brain analysis, behavioural performance correlated with grey matter density in left superior frontal gyrus – positively for mathematicians but negatively for non-mathematicians; in a region of interest analysis, we found in mathematicians higher grey matter density in the right superior parietal lobule, but lower grey matter density in the right intraparietal sulcus and in the left inferior frontal gyrus. In terms of white matter, there were no significant group differences in fractional anisotropy or mean diffusivity. These results reveal new insights into the relationship between mathematical expertise and grey matter metrics in brain regions previously implicated in numerical cognition, as well as in regions that have so far received less attention in this field. Further studies, based on longitudinal designs and cognitive training, could examine the conjecture that such cross-sectional findings arise from a bidirectional link between experience and structural brain changes that is itself subject to change across the lifespan.

A network view on brain regions involved in experts' object and pattern recognition: Implications for the neural mechanisms of skilled visual perception

Skilled visual object and pattern recognition form the basis of many everyday behaviours. The game of chess has often been used as a model case for studying how long-term experience aides in perceiving objects and their spatio-functional interrelations. Earlier research revealed two brain regions, posterior middle temporal gyrus (pMTG) and collateral sulcus (CoS), to be linked to chess experts' superior object and pattern recognition, respectively. Here we elucidated the brain networks these two expertise-related regions are embedded in, employing resting-state functional connectivity analysis and meta-analytic connectivity modelling with the BrainMap database. pMTG was preferentially connected with dorsal visual stream areas and a parieto-prefrontal network for action planning, while CoS was preferentially connected with posterior medial cortex and hippocampus, linked to scene perception, perspective-taking and navigation. Functional profiling using BrainMap meta-data revealed that pMTG was linked to semantic processing as well as inhibition and attention, while CoS was linked to face and shape perception as well as passive viewing. Our findings suggest that pMTG subserves skilled object recognition by mediating the link between object identity and object affordances, while CoS subserves skilled pattern recognition by linking the position of individual objects with typical spatio-functional layouts of their environment stored in memory.

What Does "Being an Expert" Mean to the Brain? Functional Specificity and Connectivity in Expertise

To what extent is varying cognitive expertise reflected in the brain's functional specificity and connectivity? We addressed this question by examining expertise in mathematics based on the fact that mathematical skills are one of the most critical cognitive abilities known to be a good predictor of academic achievement. We investigated processing of hierarchical structures, which is a fundamental process for building complex cognitive architecture. Experts and nonexperts in mathematics participated in processing hierarchical structures using algebraic expressions. Results showed that a modulating effect depending on expertise was observed specifically in nonexperts in the left inferior frontal gyrus around pars triangularis and frontal sulcus, the left intraparietal sulcus, and the right inferior parietal lobule. This expertise-dependent pattern of activation led to a crucial dissociation within the left prefrontal cortex. More interestingly, task-related functional networks were also modulated differently in the frontoparietal network for relatively good performance and in the frontostriatal network for poor performance. The present study indicates that a high level of expertise is evident in a small number of specific brain regions, whereas a low level of expertise is reflected by broadly distributed brain areas, along with divergent functional connectivity between experts and nonexperts.

Finger–digit compatibility in Arabic numeral processing

Finger–digit response compatibility was tested by asking participants to identify Arabic digits by pressing 1 of 10 keys with all 10 fingers. The direction of the finger–digit mapping was varied by manipulating the global direction of the hand–digit mapping as well as the direction of the finger–digit mapping within each hand (in each case, from small to large digits, or the reverse). The hypothesis of a left-to-right mental number line predicted that a complete left-to-right mapping should be easier whereas the hypothesis of a representation based on finger counting predicted that a counting-congruent mapping should be easier. The results show that when all 10 fingers are used to answer, a mapping congruent with the prototypical finger-counting strategy reported by the participants leads to better performance than does a mapping congruent with a left-to-right oriented mental number line, both in palm-down and palm-up postures of the hands, and they demonstrate that finger-counting strategies influence the way that numerical information is mentally represented and processed.

Cognitive and Neural Correlates of Mathematical Giftedness in Adults and Children: A Review

Most mathematical cognition research has focused on understanding normal adult function and child development as well as mildly and moderately impaired mathematical skill, often labeled developmental dyscalculia and/or mathematical learning disability. In contrast, much less research is available on cognitive and neural correlates of gifted/excellent mathematical knowledge in adults and children. In order to facilitate further inquiry into this area, here we review 40 available studies, which examine the cognitive and neural basis of gifted mathematics. Studies associated a large number of cognitive factors with gifted mathematics, with spatial processing and working memory being the most frequently identified contributors. However, the current literature suffers from low statistical power, which most probably contributes to variability across findings. Other major shortcomings include failing to establish domain and stimulus specificity of findings, suggesting causation without sufficient evidence and the frequent use of invalid backward inference in neuro-imaging studies. Future studies must increase statistical power and neuro-imaging studies must rely on supporting behavioral data when interpreting findings. Studies should investigate the factors shown to correlate with math giftedness in a more specific manner and determine exactly how individual factors may contribute to gifted math ability.

Becoming an expert: Ontogeny of expertise as an example of neural reuse

In this commentary, we discuss an important pattern of results in the literature on the neural basis of expertise: (a) decrease of cerebral activation at the beginning of acquisition of expertise and (b) functional cerebral reorganization as a consequence of years of practice. We show how these two results can be integrated with the neural reuse framework.

Persistent perceptual grouping effects in the evaluation of simple arithmetic expressions

Landy and Goldstone (2007a, 2010) demonstrated that an explicit rule, operator precedence for simple arithmetic expressions, is enforced in part by perceptual processes like unit formation and attention. When perceptual grouping competes with operator precedence, errors increase. We replicated this result (Exp. 1) and investigated whether perceptual grouping effects persist when the visual stimulus is presented briefly and then masked (Exp. 2) and when verbal recoding is encouraged through vocal expression (Exp. 3). We found that perceptual-grouping effects persisted in the masking condition, suggesting that the mental representations of arithmetic expressions retain visuospatial characteristics. Similarly, verbalization of the expressions did not eliminate perceptual-grouping effects, suggesting that participants were not verbally recoding. In sum, the persistent effects of unit formation and spatial attention emphasize the importance of perceptual processing in the development of human expertise in this domain.

Transcranial random noise stimulation mitigates increased difficulty in an arithmetic learning task

Proficiency in arithmetic learning can be achieved by using a multitude of strategies, the most salient of which are procedural learning (applying a certain set of computations) and rote learning (direct retrieval from long-term memory). Here we investigated the effect of transcranial random noise stimulation (tRNS), a non-invasive brain stimulation method previously shown to enhance cognitive training, on both types of learning in a 5-day sham-controlled training study, under two conditions of task difficulty, defined in terms of item repetition. On the basis of previous research implicating the prefrontal and posterior parietal cortex in early and late stages of arithmetic learning, respectively, sham-controlled tRNS was applied to bilateral prefrontal cortex for the first 3 days and to the posterior parietal cortex for the last 2 days of a 5-day training phase. The training involved learning to solve arithmetic problems by applying a calculation algorithm; both trained and untrained problems were used in a brief testing phase at the end of the training phase. Task difficulty was manipulated between subjects by using either a large ("easy" condition) or a small ("difficult" condition) number of repetition of problems during training. Measures of attention and working memory were acquired before and after the training phase. As compared to sham, participants in the tRNS condition displayed faster reaction times and increased learning rate during the training phase; as well as faster reaction times for both trained and untrained (new) problems, which indicated a transfer effect after the end of training. All stimulation effects reached significance only in the "difficult" condition when number of repetition was lower. There were no transfer effects of tRNS on attention or working memory. The results support the view that tRNS can produce specific facilitative effects on numerical cognition--specifically, on arithmetic learning. They also highlight the importance of task difficulty in the neuromodulation of learning, which in the current study due to the manipulation of item repetition might have being mediated by the memory system.

Cognitive Expertise: An ALE Meta-Analysis

Expert performance constitutes the endpoint of skill acquisition and is accompanied by widespread neuroplastic changes. To reveal common mechanisms of reorganization associated with long-term expertise in a cognitive domain (mental calculation, chess, language, memory, music without motor involvement), we used activation likelihood estimation meta-analysis and compared brain activation of experts to nonexperts. Twenty-six studies matched inclusion criteria, most of which reported an increase and not a decrease of activation foci in experts. Increased activation occurred in the left rolandic operculum (OP 4) and left primary auditory cortex and in bilateral premotor cortex in studies that used auditory stimulation. In studies with visual stimulation, experts showed enhanced activation in the right inferior parietal cortex (area PGp) and the right lingual gyrus. Experts' brain activation patterns seem to be characterized by enhanced or additional activity in domain-specific primary, association, and motor structures, confirming that learning is localized and very specialized.

Processes in arithmetic strategy selection: a fMRI study

This neuroimaging (functional magnetic resonance imaging) study investigated neural correlates of strategy selection. Young adults performed an arithmetic task in two different conditions. In both conditions, participants had to provide estimates of two-digit multiplication problems like 54 × 78. In the choice condition, participants had to select the better of two available rounding strategies, rounding-up (RU) strategy (i.e., doing 60 × 80 = 4,800) or rounding-down (RD) strategy (i.e., doing 50 × 70 = 3,500 to estimate product of 54 × 78). In the no-choice condition, participants did not have to select strategy on each problem but were told which strategy to use; they executed RU and RD strategies each on a series of problems. Participants also had a control task (i.e., providing correct products of multiplication problems like 40 × 50). Brain activations and performance were analyzed as a function of these conditions. Participants were able to frequently choose the better strategy in the choice condition; they were also slower when they executed the difficult RU than the easier RD. Neuroimaging data showed greater brain activations in right anterior cingulate cortex (ACC), dorso-lateral prefrontal cortex (DLPFC), and angular gyrus (ANG), when selecting (relative to executing) the better strategy on each problem. Moreover, RU was associated with more parietal cortex activation than RD. These results suggest an important role of fronto-parietal network in strategy selection and have important implications for our further understanding and modeling cognitive processes underlying strategy selection.

Neural mechanisms of savant calendar calculating in autism: an MEG-study of few single cases

This study contrasted the neurological correlates of calendar calculating (CC) between those individuals with autism spectrum disorder (ASD) and typically developing individuals. CC is the ability to correctly and quickly state the day of the week of a given date. Using magnetoencephalography (MEG), we presented 126 calendar tasks with dates of the present, past, and future. Event-related magnetic fields (ERF) of 3000ms duration and brain activation patterns were compared in three savant calendar calculators with ASD (ASDCC) and three typically developing calendar calculators (TYPCC). ASDCC outperformed TYPCC in correct responses, but not in answering speed. Comparing amplitudes of their ERFs, there was a main effect of group between 1000 and 3000ms, but no further effects of hemisphere or sensor location. We conducted CLARA source analysis across the entire CC period in each individual. Both ASDCC and TYPCC exhibited activation maxima in prefrontal areas including the insulae and the left superior temporal gyrus. This is in accordance with verbal fact retrieval and working memory as well as monitoring and coordination processes. In ASDCC, additional activation sites at the right superior occipital gyrus, the right precuneus, and the right putamen point to visual-spatial strategies and are in line with the preference of autistic individuals for engaging posterior regions relatively more strongly in various reasoning and problem solving tasks.

Broca and Charcot's research on Jacques Inaudi: the psychological and anthropological study of a mental calculator

In the nineteenth century, French scientific institutions became interested in young "mental calculators," arithmetical prodigies able to quickly and accurately perform complex mental calculations. The first scientists to study mental calculators were phrenologists who sought to prove the existence of a calculating organ in the frontal lobe. Paul Broca introduced one such mental calculator, Jacques Inaudi, to the Anthropological Society of Paris in 1880. Broca attributed extraordinary faculty for mental calculation to memory functioning (the psychological hypothesis) rather than physiological difference (the phrenological hypothesis). In 1892, prominent French Academy of Sciences member Jean-Martin Charcot produced a noteworthy study of Inaudi on the organization's behalf. Charcot observed that Inaudi called upon auditory memory rather than visual memory in his mental calculations, unlike most mental calculators who preceded him. Like Broca, Charcot was skeptical of the phrenological hypothesis, though he noted that Inaudi's skull was markedly plagiocephalic. Interestingly, anthropological examination of Inaudi is consistent with the themes of modern cognitive neuroscience. Thus, Charcot seems to have anticipated present research on the localization of mental calculation and memory for numbers. 1. (1)The Academy of Sciences, founded in 1666 by Louis XIV (1638-1715) with the goal of contributing to the advancement and application of the sciences in France, was one of the earliest European scientific institutions. As a prestigious society, it played an active role in defining scientific and technological research policy as well as drafting and publishing official reports.

Serotonergic hyperactivity as a potential factor in developmental, acquired and drug-induced synesthesia

Though synesthesia research has seen a huge growth in recent decades, and tremendous progress has been made in terms of understanding the mechanism and cause of synesthesia, we are still left mostly in the dark when it comes to the mechanistic commonalities (if any) among developmental, acquired and drug-induced synesthesia. We know that many forms of synesthesia involve aberrant structural or functional brain connectivity. Proposed mechanisms include direct projection and disinhibited feedback mechanisms, in which information from two otherwise structurally or functionally separate brain regions mix. We also know that synesthesia sometimes runs in families. However, it is unclear what causes its onset. Studies of psychedelic drugs, such as psilocybin, LSD and mescaline, reveal that exposure to these drugs can induce synesthesia. One neurotransmitter suspected to be central to the perceptual changes is serotonin. Excessive serotonin in the brain may cause many of the characteristics of psychedelic intoxication. Excessive serotonin levels may also play a role in synesthesia acquired after brain injury. In brain injury sudden cell death floods local brain regions with serotonin and glutamate. This neurotransmitter flooding could perhaps result in unusual feature binding. Finally, developmental synesthesia that occurs in individuals with autism may be a result of alterations in the serotonergic system, leading to a blockage of regular gating mechanisms. I conclude on these grounds that one commonality among at least some cases of acquired, developmental and drug-induced synesthesia may be the presence of excessive levels of serotonin, which increases the excitability and connectedness of sensory brain regions.

Effective connectivity reveals strategy differences in an expert calculator

Mathematical reasoning is a core component of cognition and the study of experts defines the upper limits of human cognitive abilities, which is why we are fascinated by peak performers, such as chess masters and mental calculators. Here, we investigated the neural bases of calendrical skills, i.e. the ability to rapidly identify the weekday of a particular date, in a gifted mental calculator who does not fall in the autistic spectrum, using functional MRI. Graph-based mapping of effective connectivity, but not univariate analysis, revealed distinct anatomical location of "cortical hubs" supporting the processing of well-practiced close dates and less-practiced remote dates: the former engaged predominantly occipital and medial temporal areas, whereas the latter were associated mainly with prefrontal, orbitofrontal and anterior cingulate connectivity. These results point to the effect of extensive practice on the development of expertise and long term working memory, and demonstrate the role of frontal networks in supporting performance on less practiced calculations, which incur additional processing demands. Through the example of calendrical skills, our results demonstrate that the ability to perform complex calculations is initially supported by extensive attentional and strategic resources, which, as expertise develops, are gradually replaced by access to long term working memory for familiar material.

Seeing mathematics: perceptual experience and brain activity in acquired synesthesia

We studied the patient JP who has exceptional abilities to draw complex geometrical images by hand and a form of acquired synesthesia for mathematical formulas and objects, which he perceives as geometrical figures. JP sees all smooth curvatures as discrete lines, similarly regardless of scale. We carried out two preliminary investigations to establish the perceptual nature of synesthetic experience and to investigate the neural basis of this phenomenon. In a functional magnetic resonance imaging (fMRI) study, image-inducing formulas produced larger fMRI responses than non-image inducing formulas in the left temporal, parietal and frontal lobes. Thus our main finding is that the activation associated with his experience of complex geometrical images emerging from mathematical formulas is restricted to the left hemisphere.

The approximate number system and its relation to early math achievement: evidence from the preschool years

Humans rely on two main systems of quantification; one is nonsymbolic and involves approximate number representations (known as the approximate number system or ANS), and the other is symbolic and allows for exact calculations of number. Despite the pervasiveness of the ANS across development, recent studies with adolescents and school-aged children point to individual differences in the precision of these representations that, importantly, have been shown to relate to symbolic math competence even after controlling for general aspects of intelligence. Such findings suggest that the ANS, which humans share with nonhuman animals, interfaces specifically with a uniquely human system of formal mathematics. Other findings, however, point to a less straightforward picture, leaving open questions about the nature and ontogenetic origins of the relation between these two systems. Testing children across the preschool period, we found that ANS precision correlated with early math achievement but, critically, that this relation was nonlinear. More specifically, the correlation between ANS precision and math competence was stronger for children with lower math scores than for children with higher math scores. Taken together, our findings suggest that early-developing connections between the ANS and mathematics may be fundamentally discontinuous. Possible mechanisms underlying such nonlinearity are discussed.

Neuroimaging during trance state: a contribution to the study of dissociation

Despite increasing interest in pathological and non-pathological dissociation, few researchers have focused on the spiritual experiences involving dissociative states such as mediumship, in which an individual (the medium) claims to be in communication with, or under the control of, the mind of a deceased person. Our preliminary study investigated psychography – in which allegedly “the spirit writes through the medium's hand” – for potential associations with specific alterations in cerebral activity. We examined ten healthy psychographers – five less expert mediums and five with substantial experience, ranging from 15 to 47 years of automatic writing and 2 to 18 psychographies per month – using single photon emission computed tomography to scan activity as subjects were writing, in both dissociative trance and non-trance states. The complexity of the original written content they produced was analyzed for each individual and for the sample as a whole. The experienced psychographers showed lower levels of activity in the left culmen, left hippocampus, left inferior occipital gyrus, left anterior cingulate, right superior temporal gyrus and right precentral gyrus during psychography compared to their normal (non-trance) writing. The average complexity scores for psychographed content were higher than those for control writing, for both the whole sample and for experienced mediums. The fact that subjects produced complex content in a trance dissociative state suggests they were not merely relaxed, and relaxation seems an unlikely explanation for the underactivation of brain areas specifically related to the cognitive processing being carried out. This finding deserves further investigation both in terms of replication and explanatory hypotheses.

Neural basis of mathematical cognition

The human brain has remarkable capabilities for encoding and manipulating information about quantities. Understanding how the brain carries out such number and quantity processing is a problem not just for those interested in numerical cognition: it raises important questions that are relevant to understanding development, action, vision, language, executive function and cortical organisation. It is also a clear case of research into a core human psychological function having indisputable everyday relevance; hence the emphasis in early education on numeracy and later on mathematics.

Investigating paranormal phenomena: Functional brain imaging of telepathy

Aim:

“Telepathy” is defined as “the communication of impressions of any kind from one mind to another, independently of the recognized channels of sense”. Meta-analyses of “ganzfield” studies as well as “card-guessing task” studies provide compelling evidence for the existence of telepathic phenomena. The aim of this study was to elucidate the neural basis of telepathy by examining an individual with this special ability.

Materials and Methods:

Using functional MRI, we examined a famous “mentalist” while he was performing a telepathic task in a 1.5 T scanner. A matched control subject without this special ability was also examined under similar conditions.

Results:

The mentalist demonstrated significant activation of the right parahippocampal gyrus after successful performance of a telepathic task. The comparison subject, who did not show any telepathic ability, demonstrated significant activation of the left inferior frontal gyrus.

Conclusions:

The findings of this study are suggestive of a limbic basis for telepathy and warrant further systematic research.

The neural architecture of expert calendar calculation: a matter of strategy?

Savants and prodigies are individuals with exceptional skills in particular mental domains. In the present study we used functional magnetic resonance imaging to examine neural correlates of calendar calculation in two individuals, a savant with Asperger's disorder and a self-taught mathematical prodigy. If there is a modular neural organization of exceptional performance in a specific mental domain, calendar calculation should be reflected in a considerable overlap in the recruitment of brain circuits across expert individuals. However, considerable individual differences in activation patterns during calendar calculation were noted. The present results indicate that activation patterns produced by complex mental processing, such as calendar calculation, seem to be influenced strongly by learning history and idiosyncratic strategy usage rather than a modular neural organization. Thus, well-known individual differences in complex cognition play a major role even in experts with exceptional abilities in a particular mental domain and should in particular be considered when examining the neural architecture of complex mental processes and skills.

Dyscalculia: from brain to education

Recent research in cognitive and developmental neuroscience is providing a new approach to the understanding of dyscalculia that emphasizes a core deficit in understanding sets and their numerosities, which is fundamental to all aspects of elementary school mathematics. The neural bases of numerosity processing have been investigated in structural and functional neuroimaging studies of adults and children, and neural markers of its impairment in dyscalculia have been identified. New interventions to strengthen numerosity processing, including adaptive software, promise effective evidence-based education for dyscalculic learners.

Mathematically gifted adolescents use more extensive and more bilateral areas of the fronto-parietal network than controls during executive functioning and fluid reasoning tasks

The main goal of this study was to investigate the neural substrates of fluid reasoning and visuospatial working memory in adolescents with precocious mathematical ability. The study population comprised two groups of adolescents: 13 math-gifted adolescents and 14 controls with average mathematical skills. Patterns of activation specific to reasoning tasks in math-gifted subjects were examined using functional magnetic resonance images acquired while the subjects were performing Raven's Advanced Progressive Matrices (RAPM) and the Tower of London (TOL) tasks. During the tasks, both groups showed significant activations in the frontoparietal network. In the math-gifted group, clusters of activation were always bilateral and more regions were recruited, especially in the right hemisphere. In the TOL task, math-gifted adolescents showed significant hyper-activations relative to controls in the precuneus, superior occipital lobe (BA 19), and medial temporal lobe (BA 39). The maximum differences between the groups were detected during RAPM tasks at the highest level of difficulty, where math-gifted subjects showed significant activations relative to controls in the right inferior parietal lobule (BA 40), anterior cingulated gyrus (BA 32), and frontal (BA 9, and BA 6) areas. Our results support the hypothesis that greater ability for complex mathematical reasoning may be related to more bilateral patterns of activation and that increased activation in the parietal and frontal regions of math-gifted adolescents is associated with enhanced skills in visuospatial processing and logical reasoning.

Rostral premotor cortex as a gateway between motor and cognitive networks

This article presents a hypothesis that the rostral premotor-subcortical networks may serve as a gateway between the cognitive and motor networks. Accumulating evidence has propelled an idea that motor and cognitive behaviors considerably share neural substrates and probably computational principles regardless of the species. Here I conducted a meta-analysis of previous neuroimaging studies on motor planning and different cognitive tasks (mental calculation, visuospatial processing and cognitive control), which showed overlap of all activations in the rostral premotor cortex, with a possible rostro-caudal functional gradient. It was also suggested that the rostral premotor areas might form circuits with specific portions of the cerebellum and the basal ganglia. The rostral premotor areas may provide context-dependent connectivity and mediate information flow between the cognitive and motor networks, thereby making the two networks operating interactively or independently.

It takes two-skilled recognition of objects engages lateral areas in both hemispheres

Our object recognition abilities, a direct product of our experience with objects, are fine-tuned to perfection. Left temporal and lateral areas along the dorsal, action related stream, as well as left infero-temporal areas along the ventral, object related stream are engaged in object recognition. Here we show that expertise modulates the activity of dorsal areas in the recognition of man-made objects with clearly specified functions. Expert chess players were faster than chess novices in identifying chess objects and their functional relations. Experts' advantage was domain-specific as there were no differences between groups in a control task featuring geometrical shapes. The pattern of eye movements supported the notion that experts' extensive knowledge about domain objects and their functions enabled superior recognition even when experts were not directly fixating the objects of interest. Functional magnetic resonance imaging (fMRI) related exclusively the areas along the dorsal stream to chess specific object recognition. Besides the commonly involved left temporal and parietal lateral brain areas, we found that only in experts homologous areas on the right hemisphere were also engaged in chess specific object recognition. Based on these results, we discuss whether skilled object recognition does not only involve a more efficient version of the processes found in non-skilled recognition, but also qualitatively different cognitive processes which engage additional brain areas.