The Individual Brain Charting project focuses on collecting functional Magnetic Resonance Imaging data across a large set of cognitive tasks from a fixed cohort of participants, within a standardized environment. This approach seeks to obtain refined cognitive phenotyping of individual brains, uncovering details of their functional organization. We present an extension to the dataset, integrating data from eleven participants obtained at 3T, from a fixed environment to minimize inter-site and inter-subject variability. This release further enriches the cumulative coverage of psychological domains, while introducing new concepts. It includes tasks on mathematical processing, spatial navigation, emotion recognition and memory, proactive control, oddball detection, reward processing, reaction time, biological motion perception, gambling, scene processing and working memory. In total, 18 tasks with 180 contrasts were added, and 54 cognitive components were included in the description of the ensuing contrasts. As the dataset becomes larger, the collection of the corresponding topographies becomes more comprehensive, leading to enhanced brain-atlasing frameworks. Aligned with open-access and data-sharing standards, this dataset emphasizes transparency and collaborative research.

Commutativity—the principle that operand order does not affect the result of an operation—is a core feature of two foundational operations of arithmetic: addition and multiplication. Recent theories propose that such compositional structures emerge from an innate “language of thought” that enables abstract principles to apply flexibly across symbolic and non-symbolic formats. While children possess early intuitions about additive commutativity, less is known about their grasp of the commutativity of multiplication. Here, we ask whether children’s understanding of the commutative principle of multiplication stems from pre-existing intuitions that the order in which sets are grouped does not matter, or whether it instead emerges from reasoning about structural relations among numerical symbols. We tested 8- to 9-year-old children in a number comparison game, probing their understanding of multiplicative commutativity in both symbolic expressions (3x2 = 2x3) and in non-symbolic sets of grouped dots. On average, children performed better with symbolic expressions than with non-symbolic arrays. Moreover, their performance on the arrays of grouped dots was directly linked to their mastery of commutativity in symbolic expressions, and independent of their intuitive, non-symbolic numerosity estimation skills. To probe children’s developing mastery of the commutativity of multiplication, a subset of the children were given brief training on commutativity and played the same game in a second session, 2 to 14 days later. Children who, in the first session, did not master the commutative principle with symbolic stimuli showed improvement on symbolic trials, while improvement on non-symbolic trials lagged for the entire group. These findings suggest that symbolic learning of the principle of commutativity of multiplication comes first, before children can apply it to concrete contexts. Moreover, they provide evidence for format- and operation-specific limits to children’s mastery of the compositional structure of the natural number system.

This chapter presents an overview of current research on geometric cognition. By integrating evidence from diverse methodologies including behavioral experiments, neuroimaging, computational modeling, and cross-cultural studies, it aims to identify some of the core competencies in geometric cognition, and explore both their underpinnings and developmental course.

The ability to compose complex mental representations by recombining simpler primitives is a characteristic of the human brain that manifests itself in a variety of domains such as spoken or written language, mathematics, or social reasoning. While it is known that these domains rest on partially distinct brain networks, they are rarely investigated together in the same paradigm. Here, we present a systematic functional MRI study of written and spoken word and sentence processing in each of these domains. In a true-false judgment task, adult participants were presented with a hierarchy of meaningless and meaningful stimuli bearing on various domains of general semantic knowledge and mathematics. The results show that distinct brain regions are activated by (1) syntax and semantics; (2) math versus non-math knowledge; (3) different domains of mathematics, such as geometry versus arithmetic; (4) social knowledge versus other knowledge. All of these regions are activated essentially identically in the written and spoken modalities. The results were replicated in a group of adolescents. Our experiments show that the human brain comprises distinct amodal networks for various domains of linguistic and semantic knowledge, and provide a simple paradigm to dissect them within a short fMRI session.

Deductive reasoning is essential to most of our scientific and technological achievements and is a crucial component to scientific education. In Western culture, deductive reasoning first emerged as a dedicated mode of thinking in the field of geometry, but the cognitive mechanisms behind this major intellectual achievement remain largely understudied. Here, we report an unexpected cognitive bias in geometric reasoning that challenges existing theories of human deductive reasoning. Over two experiments involving almost 250 participants, we show that educated adults systematically mistook as valid a set of elementary invalid inferences with points and circles in the Euclidean plane. Our results suggest that people got “locked” on unwarranted conclusions because they tended to represent geometric premisses in specific ways and they mainly relied on translating, but not scaling, the circles when searching for possible conclusions. We conducted two further experiments to test these hypotheses and found confirmation for them. Although mathematical reasoning is considered as the hallmark of rational thinking, our findings indicate that it is not exempt from cognitive biases and is subject to fundamental counter-intuitions. Our empirical investigations of the source of this bias provide some insights into the cognitive mechanisms underlying geometric deduction, and thus shed light on the cognitive roots of intuitive mathematical reasoning.

Many teaching websites, such as the Khan Academy, propose vivid videos illustrating a mathematical concept. Using functional magnetic resonance imaging, we asked whether watching such a video suffices to rapidly change the brain networks for mathematical knowledge. We capitalized on the finding that, when judging the truth of short spoken statements, distinct semantic regions activate depending on whether the statements bear on mathematical knowledge or on other domains of semantic knowledge. Here, participants answered such questions before and after watching a lively 5-min video, which taught them the rudiments of a new domain. During the video, a distinct math-responsive network, comprising anterior intraparietal and inferior temporal nodes, showed intersubject synchrony when viewing mathematics course rather than control courses in biology or law. However, this experience led to minimal subsequent changes in the activity of those domain-specific areas when answering questions on the same topics a few minutes later. All taught facts, whether mathematical or not, led to domain-general repetition enhancement, particularly prominent in the cuneus, posterior cingulate, and posterior parietal cortices. We conclude that short videos do not suffice to induce a meaningful lasting change in the brain's math-responsive network, but merely engage domain-general regions possibly involved in episodic short-term memory.

Temporal characteristics of neural signals are often overlooked in traditional fMRI developmental studies but are critical to studying brain functions in ecologically valid settings. In the present study, we explore the temporal properties of children's neural responses during naturalistic mathematics and grammar tasks. To do so, we introduce a novel measure in developmental fMRI: neural entropy, which indicates temporal complexity of BOLD signals. We show that temporal patterns of neural activity have lower complexity and greater variability in children than in adults in the association cortex but not in the sensory-motor cortex. We also show that neural entropy is associated with both child-adult similarity in functional connectivity and neural synchrony, and that neural entropy increases with the size of functionally connected networks in the association cortex. In addition, neural entropy increases with functional maturity (i.e., child-adult neural synchrony) in content-specific regions. These exploratory findings suggest the hypothesis that neural entropy indexes the increasing breadth and diversity of neural processes available to children for analyzing mathematical information over development.

Two major goals of human neuroscience are to understand how the brain functions in the real world and to measure neural processes under conditions that are ecologically valid. A critical step toward these goals is understanding how brain activity during naturalistic tasks that mimic the real world relates to brain activity in more traditional laboratory tasks. In this study, we used intersubject correlations to locate reliable stimulus-driven cerebral processes among children and adults in a naturalistic video lesson and a laboratory forced-choice task that shared the same arithmetic concept. We show that relative to a control condition with grammatical content, naturalistic and laboratory arithmetic tasks evoked overlapping activation within brain regions previously associated with math semantics. The regions of specific functional overlap between the naturalistic mathematics lesson and laboratory mathematics task included bilateral intraparietal cortex, which confirms that this region processes mathematical content independently of differences in task mode. These findings suggest that regions of the intraparietal cortex process mathematical content when children are learning about mathematics in a naturalistic setting.

A major goal of human neuroscience is to understand how the brain functions in the real world, and to measure neural processes under conditions that are ecologically valid. A critical step toward this goal is understanding how brain activity during naturalistic tasks that mimic the real world, relates to brain activity in more traditional laboratory tasks. In the present study, we used intersubject correlations to locate reliable stimulus-driven cerebral processes among children and adults in a naturalistic video lesson and a laboratory forced-choice task that shared the same arithmetic concept. We show that relative to a control condition with grammatical content, naturalistic and laboratory arithmetic tasks evoked overlapping activation within brain regions previously associated with math semantics. The regions of specific functional overlap between the naturalistic mathematics lesson and laboratory mathematics task included bilateral intraparietal cortex, which confirms that this region processes mathematical content independently of differences in task mode. These findings suggest that regions of the intraparietal cortex process mathematical content when children are learning about mathematics in the real world.

Many teaching websites, such as the Khan Academy, propose vivid videos illustrating a mathematical concept. Using fMRI, we asked whether watching such a video suffices to rapidly change the brain networks for mathematical knowledge. We capitalized on the finding that, when judging the truth of short spoken statements, distinct semantic regions activate depending on whether the statements bear on mathematical knowledge or on other domains of semantic knowledge. Here, participants answered such questions before and after watching a lively five-minute video which taught them the rudiments of a new domain. During the video, a distinct math-responsive network, comprising anterior intraparietal and inferior temporal nodes, showed inter-subject synchrony when viewing mathematics course rather than control courses in biology or law. However, this experience led to minimal subsequent changes in the activity of those domain-specific areas when answering questions on the same topics a few minutes later. All taught facts, whether mathematical or not, led to domain-general repetition enhancement, particularly prominent in the cuneus, posterior cingulate and posterior parietal cortices. We conclude that short videos do not suffice to induce a meaningful lasting change in the brain’s math-responsive network, but merely engage domain-general regions possibly involved in episodic short-term memory. Significance Statement Teaching mathematical concepts is difficult. To facilitate the comprehension and appeal of mathematics, several teaching websites provide vivid videos illustrating math concepts. Here, however, we show that merely watching such videos fails to improve the brain networks for mathematics. During the video itself, these networks are transiently engaged – but a few minutes later, when we ask questions about the taught concepts, performance is only minimally improved, and the participants engage generic regions thought to be involved in short-memory and language, rather than the targeted math-responsive regions. Brief video watching is therefore insufficient as a pedagogical device, probably because it misses ingredients such as teacher-pupil interactions, explicit teaching, active engagement, retrieval practice, repetition, and sleep.

The human brain is especially unique within the animal kingdom in its understanding of abstract mathematical concepts. We are able to conceive irrational numbers, idealized geometrical shapes, abstract topological properties, and so on without ever perceiving them. How, then, do such concepts develop in the human mind? And what is the neural basis underlying the manipulation of high-level math concepts? While previous work mainly focused on arithmetic processing, the work reported in the present chapter focuses on more advanced math knowledge. This gives better account for the diversity of math domains such as analysis, algebra, topology, geometry, and so on that could call upon very different skills. One way to assess the brain mechanisms underlying advanced mathematical concepts' ontogeny is to use functional MRI and study various mathematically skilled populations such as math professors or researchers, math students, or more generally math learners. The present chapter offers an overview of various neuroimaging studies assessing the cerebral underpinnings of advanced mathematical reflection and logical reasoning, as well as the effect of mathematical expertise on the brain. In professional mathematicians, including the exceptional cases of three blind mathematicians, these studies revealed that mathematical concepts are encoded in a very abstract manner. Notably, a set of brain areas including the bilateral intraparietal sulci and bilateral inferior-temporal regions appears to be systematically involved in mathematical activity. I then discuss the relation of this math-related network with language vs numerical-spatial processing in the brain, as well as its potential link to visual processes. I also discuss the potential overlap of the math-related network with the neural correlates of deductive reasoning, a process that is at the heart of the modern mathematical practice of proofs. Finally, this chapter briefly reviews the main brain markers that have been found to accompany mathematical expertise or giftedness.

Topological relations such as inside, outside, or intersection are ubiquitous to our spatial thinking. Here, we examined how people reason deductively with topological relations between points, lines, and circles in geometric diagrams. We hypothesized in particular that a counterexample search generally underlies this type of reasoning. We first verified that educated adults without specific math training were able to produce correct diagrammatic representations contained in the premisses of an inference. Our first experiment then revealed that subjects who correctly judged an inference as invalid almost always produced a counterexample to support their answer. Noticeably, even if the counterexample always bore a certain level of similarity to the initial diagram, we observed that an object was more likely to be varied between the two drawings if it was present in the conclusion of the inference. Experiments 2 and 3 then directly probed counterexample search. While participants were asked to evaluate a conclusion on the basis of a given diagram and some premisses, we modulated the difficulty of reaching a counterexample from the diagram. Our results indicate that both decreasing the counterexample density and increasing the counterexample distance impaired reasoning performance. Taken together, our results suggest that a search procedure for counterexamples, which proceeds object-wise, could underlie diagram-based geometric reasoning. Transposing points, lines, and circles to our spatial environment, the present study may ultimately provide insights on how humans reason about topological relations between positions, paths, and regions.

How does the human brain store sequences of spatial locations? We propose that each sequence is internally compressed using an abstract, language-like code that captures its numerical and geometrical regularities. We exposed participants to spatial sequences of fixed length but variable regularity while their brain activity was recorded using magneto-encephalography. Using multivariate decoders, each successive location could be decoded from brain signals, and upcoming locations were anticipated prior to their actual onset. Crucially, sequences with lower complexity, defined as the minimal description length provided by the formal language, led to lower error rates and to increased anticipations. Furthermore, neural codes specific to the numerical and geometrical primitives of the postulated language could be detected, both in isolation and within the sequences. These results suggest that the human brain detects sequence regularities at multiple nested levels and uses them to compress long sequences in working memory.

Among primates, humans are special in their ability to create and manipulate highly elaborate structures of language, mathematics or music. Here, we show that this sensitivity to abstract structure is already present in a much simpler domain: the visual perception of regular geometric shapes such as squares, rectangles or parallelograms. We asked human subjects to detect an intruder shape among six quadrilaterals. Although the intruder was always defined by an identical amount of displacement of a single vertex, the results revealed a geometric regularity effect: detection was considerably easier when either the base shape or the intruder was a regular figure comprising right angles, parallelism or symmetry, than a more irregular shape. This effect was replicated in several tasks and in all human populations tested, including uneducated Himba adults and French preschoolers. Baboons, however, showed no such geometric regularity effect, even after extensive training. Baboon behavior was captured by convolutional neural networks (CNNs), but neither CNNs nor a variational auto-encoder captured the human geometric regularity effect. However, a symbolic model, based on exact properties of Euclidean geometry, closely fitted human behavior. Our results indicate that the human propensity for symbolic abstraction permeates even elementary shape perception. They suggest a new putative signature of human singularity, and provide a novel challenge for non-symbolic models of human shape perception.

Marie Amalric studies the localization of cognitive processes linked to mathematical activities.According to certain hypotheses, these processes are close to those concerned with language, while other hypotheses make them processes related to visuospatial processes.Marie Amalric first recalls previous work showing that we have from birth a minimal nucleus giving an intuitive approach to quantity, number, and positioning in space.These studies suggest that there is an innate proto-mathematical capacity, which then increases by learning.Then she presents experiments carried out comparatively with mathematician and non-mathematician subjects, submitting to them exercises in understanding statements of different types, mathematical and non-mathematical, and observing what is happening in the brain using fMRI imaging.The fMRI tests show that the areas involved in solving mathematical questions are different from those involved in the syntactic and semantic understanding of ordinary language.This is what is observed, as much with professional mathematicians as with non-mathematicians.They also show that at the level at which they can be observed, the same areas of the brain are called upon by mathematical questions, whatever their level and whatever the mathematical discipline concerned.Marie Amalric finally exposes additional investigations and their conclusions, concerning the localization of logical reasoning and the links with visuo-spatial processes.All of the experiments carried out would seem to indicate that the initial nucleus, which hosts proto-mathematical capacities from birth, then remains involved in the exercise of mathematics within a large sector which would grow around this initial nucleus.

A bstract A major goal of human neuroscience is to understand how the brain functions in the real world, and to measure neural processes under naturalistic conditions that are more ecologically valid than traditional laboratory tasks. A critical step toward this goal is understanding how neural activity during real world naturalistic tasks relates to neural activity in more traditional laboratory tasks. In the present study, we used intersubject correlations to locate reliable stimulus-driven neural processes among children and adults in naturalistic and laboratory versions of a mathematics task that shared the same content. We show that relative to a control condition with grammatical content, naturalistic and simplified mathematics tasks evoked overlapping activation within brain regions previously associated with math semantics. We further examined the temporal properties of children’s neural responses during the naturalistic and laboratory tasks to determine whether temporal patterns of neural activity change over development, or dissociate based on semantic or task content. We introduce a rather novel measure, not yet used in fMRI studies of child learning: neural multiscale entropy. In addition to showing new evidence of naturalistic mathematics processing in the developing brain, we show that neural maturity and neural entropy are two independent but complementary markers of functional brain development. We discuss the implications of these results for the development of neural complexity in children.

How does the brain represent and manipulate abstract mathematical concepts? Recent evidence suggests that mathematical processing relies on specific brain areas and dissociates from language. Here, we investigate this dissociation in two fMRI experiments in which professional mathematicians had to judge the truth value of mathematical and nonmathematical spoken statements. Sentences with mathematical content systematically activated bilateral intraparietal sulci and inferior temporal regions, regardless of math domain, problem difficulty, and strategy for judging truth value (memory retrieval, calculation or mental imagery). Second, classical language areas were only involved in the parsing of both nonmathematical and mathematical statements, and their activation correlated with syntactic complexity, not mathematical content. Third, the mere presence, within a sentence, of elementary logical operators such as quantifiers or negation did not suffice to activate math-responsive areas. Instead, quantifiers and negation impacted on activity in right angular gyrus and left inferior frontal gyrus, respectively. Overall, these results support the existence of a distinct, non-linguistic cortical network for mathematical knowledge in the human brain.

At the scale in which we live, space is continuous. Nevertheless, our perception and cognition parse the world into categories, whether physical, like scene or object. or abstract, like infinitesimal point or 7. The present study focuses on 2 categories of special angles in planar geometry. parallels and perpendiculars, and we evaluate how these categories might be reflected in adults' basic angle discrimination. In the first experiment, participants were most precise when detecting 2 parallel or perpendicular lines among other pairs of lines at different relative orientations. Detection was also enhanced for 2 connected lines whose angle approached 90 degrees, with precision peaking at 90 degrees. These patterns emerged despite large variations in the scales and orientations of the angle exemplars. In the second experiment, the enhanced detection of perpendiculars persisted when stimuli were rotated in depth. indicating a capacity to discriminate shapes based on perpendicularity in 3 dimensions despite large variation in angles' 2-dimensional projections. The results suggest that 2 categorical concepts which lie at the foundation of Euclidean geometry, parallelism and perpendicularity, are reflected in our discrimination of simple visual forms. and they pave the way for future studies exploring the developmental and evolutionary origins of these cognitive categories.