While in society mathematics is often thought of as formal and rigid, mathematicians themselves frequently consider the discipline creative and visual. To challenge stereotypes, we focus on visuo-spatial thinking by research mathematicians (n = 232). Via the Object-Spatial Imagery and Verbal Questionnaire (Blazhenkova & Kozhevnikov, 2009), together with open questions, we ask the following: (1) Are mathematicians visuo-spatial thinkers? (2) Is the degree of visual thinking correlated with mathematical subdiscipline? (3) Which role does visual thinking play in mathematical research? The Object-Spatial Imagery and Verbal Questionnaire results indicate that mathematicians are more strongly visuo-spatial thinkers than scientists, humanities researchers or visual artists. The degree of visuo-spatial thinking does not correlate to how 'visual' the mathematical subdiscipline is as measured by average figure environment per article, obtained through text mining 3,799 arXiv articles. In open questions, two thirds of respondents (n = 222) report using visual mental imagery during mathematical research. Some mathematicians mention metaphors for research that refer to spatial movement, such as rock climbing, moving through a jungle or attacking the problem like an insect. Our study contributes to the research agenda set by Alcock et al. (2016), which aims to improve our understanding of mathematical cognition for the purpose of elucidating the nature of mathematical thinking and inform policymakers to address challenges in mathematics education. We conclude that visualisation plays an important part in the practice of mathematics, contrary to common belief. As Hadamard wrote in 1945: 'deductions in the realm of numbers may be, at least in several mathematical minds, most generally accompanied by images'. (PsycInfo Database Record (c) 2025 APA, all rights reserved).
A common gender stereotype is that men are higher performers than women in math. This stereotype not only affects students' math performance but also influences their interests and vocational options in science, technology, engineering, and mathematics (STEM). The "Draw-a-Mathematician Task" (DAMT) has been used to understand students' perceptions of who is a mathematician. However, the existing studies with DAMT often do not consider the role of other individual traits that are closely associated with gender stereotypes, such as math anxiety. The current study examined how students' math anxiety, gender, and grade level may be associated with their gendered representations of mathematicians and the level of math difficulty included in their drawings. Students (N = 261; 133 girls, 128 boys; 116 fourth graders, 89 sixth graders, 56 eighth graders) completed a math anxiety questionnaire and were then asked to draw a picture of a mathematician and explain where their ideas came from. Overall, girls drew more female mathematicians than boys, and the proportion of students drawing female mathematicians dropped steeply in eighth grade, particularly for girls. Girls showed higher levels of math anxiety than boys, and math anxiety increased across grades. However, math anxiety was unrelated to the content of students' drawings. This study emphasizes the importance of efforts to support girls' sense of belonging in mathematics, especially into secondary grades in which reported levels of math anxiety are higher.
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The "eureka" insights that drive progress in science and mathematics remain shrouded in mystery. Sudden, unexpected, appearing like "flashes of lightning", these insights have the hallmarks of critical transitions in complex systems. Here, zooming in on mathematicians working on proofs in their own departments, we show that sudden insights are anticipated by a system-agnostic, information-theoretic early warning signal. Using dense behavioral recordings of mathematicians' moment-to-moment activity, we find that their blackboard interactions (e.g., writing, gesturing; [Formula: see text]) became increasingly unpredictable before an insight, analogous to the critical fluctuations that anticipate transitions in physical and ecological systems. We explore analytically when this early warning signal applies to varied systems with discrete, symbolic dynamics. While bibliometric analyses offer a zoomed-out perspective on innovation, publications are a coarse-grained record of individuals' insights. Explaining the sudden insights of innovators, from scientists to sculptors, requires attending to the local, distributed systems of their intellectual activity.
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Mapping time and numbers on space is affected by the writing direction. In two experiments, we searched for an explanation of how writing scripts can influence the mental representation of time and number axes. We presented to participants either 2 months (written in their native language) or two numbers (Arabic numerals), one on the left and the other on the right of the screen, and asked them to judge which number is larger or which month comes later in the year. For the months, Arabic speakers responded more accurately and faster when the correct answer was shown on the left, and the pattern was reversed for the Portuguese. However, this effect was not detected when the numbers were compared. We suggest that the observed effect is not rooted in mental mapping of time on space but is accounted for by automatized behavioral patterns related to habitual information processing. We also found that mathematicians performed better with numbers and worse with month names than nonmathematicians, confirming the direct effect of experience on cognitive processing without involving mental representations of number or time axes.
Shape analysis and classification are popular methods for biologists, biophysicists, and mathematicians investigating relationships between function and form. Classic shape descriptors, such as sphericity, can be powerful but may be insufficient for more complex shapes. Here, we present "napari-toska" a topological skeleton-based method to analyze complex shapes by representing their asymmetries as networks. Using global neighborhood principles, classic network science metrics, and spatial feature embedding, we create instance segmentation object profiles for immediate or downstream classification. napari-toska also follows temporal dynamics and identifies network features that differentiate experimental phenotypes. We incorporated absolute spatial feature measurements of objects to retain aspects of scale. Furthermore, napari-toska identifies certain segmentation errors through the emergence or loss of network cycles. Combined, napari-toska functions allow for flexible and in-depth shape profiling of intricate shapes often observed in biological and physical settings where robust, yet precise, system configuration is essential to functionality.
Vitruvian Man, the iconic drawing by Leonardo Da Vinci, has long been regarded as a representation of the divine perfection of the human form. This emblematic drawing, inspired by the architectural treatise of Vitruvius, reflects the belief in the symmetry and proportionality of the human body. Influenced by the works of other artists and mathematicians of the Renaissance period, including Luca Pacioli and Albrecht Dürer, Leonardo da Vinci's depiction of the ideal human proportions has had a lasting impact on our concepts of beauty and functionality. While modern scientific understanding of human evolution and variation may challenge some aspects of Leonardo's portrayal, the Vitruvian Man continues to be relevant in contemporary discussions of stature and proportionality. The influence of this drawing on our perception of health, beauty, and therapeutic goals, particularly in the management of short stature, remains significant in the medical community.
The heart undergoes substantial structural changes in response to new physiological demands, which occur with the rapid opening of pulmonary circulation immediately after birth. The dependence on pulmonary circulation causes an immediate increase in ventricular workload, resulting in microstructural changes that serve to maintain overall physiological homeostasis. Ageing continues to evolve the heart's structure due to increased myocardial tissue stress and strain, initiating the formation of a new extracellular matrix to facilitate the physiology of an adult. Quantifying the region-specific and age-dependent microstructural changes in tissue due to ageing is pivotal for the development of constitutive models for computational simulations. This study aimed to determine the microstructure of porcine ventricles at four time points from neonatal to adulthood. The three-dimensional microstructure was investigated using diffusion-tensor magnetic resonance imaging, two-photon excited fluorescence and second-harmonic generation microscopy to quantify fibre tractography, fractional anisotropy (FA), spherical measure, rotation and dispersion of cardiomyocytes and collagen fibrils. The results revealed that the left ventricle possessed greater FA than the right. Adult hearts demonstrated smaller FA than the young. The anterior left and right ventricles exhibited greater cardiomyocyte and collagen fibril rotation and dispersion than the posterior. The adult hearts possessed greater cardiomyocyte and collagen fibril rotation and dispersion than young hearts. The right ventricle demonstrated greater cardiomyocyte rotation in the younger hearts, and the Left in the adult. This study provides baseline data that should prove useful to bioengineers, researchers, and mathematicians in developing region-specific and age-dependent constitutive models to enhance the accuracy and bio-fidelity of computational simulations.
Fractals are formed by patterns that repeat across multiple size scales. They are found in natural structures (for example, trees, clouds, and mountains) and have also been generated by artists and mathematicians. Previously, the authors have shown that pupil size oscillates over time in a fractal manner when people view mathematically-generated fractal images. However, it was unclear if these fractal oscillations were induced by fractal variations in luminance as the eye scanned the fractal images or if these oscillations were instead a signature of a more general physiological response to viewing fractal patterns. In particular, pupil size is a well-established measure of relaxation, and previous skin conductance and EEG measurements have shown that specific fractal images induce relaxation. Here, we expand on the original study by including a larger range of types of viewed images, including distorted fractal images, non-fractal images, and uniform grayscale images. We show that fractal pupil oscillations are not limited to images displaying fractal luminance variations. We observe small changes in the oscillations' fractal dimension when the fractal dimension of the image is varied and identify a relationship between these two fractal dimensions and pupil size that is consistent with the oscillations serving as a novel indicator of viewer relaxation.
I pose the epistemological question of what makes the transfer of statistical approaches across disciplines, specifically between physics and biology, legitimate and fruitful despite intrinsic differences in their objects of study - a problem that resurfaces in contemporary interdisciplinary research relying on machine learning for statistical model building. I address it through the historical reconstruction of pivotal steps in the development of statistical thinking in the 19th century, where the appeal to the mathematical formalism of the Gaussian distribution acted as the visible trace of the diffusion of statistical approaches from astronomy to biological and social sciences. My analysis positions the wide-reaching, nowadays accepted applicability of statistics as something historically acquired through gradual conceptual and technical elaboration. It expounds the forms of re-sanctioning that accompanied and enabled the cross-domain transfer of the statistical approach, articulating them in terms of re-interpretation of the mathematical descriptions involved, re-formulation of the underlying assumptions, and re-conceptualization of their theoretical status and foundations from theory-related abstractions to approximations. The latter culminated in a shift of attitude that led to perceiving, as is standard nowadays, statistical mathematical descriptions as convenient tools for quantitative analysis, further legitimating and accelerating their interdisciplinary transfer. This work aims to familiarize historians and philosophers of science, as well as physicists, mathematicians and biologists with an interest in the history of their discipline, with these key episodes, and to dissect the epistemological assumptions and implications, as well as the interpretive frameworks, at stake in the application of a statistical approach across disciplines.
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