Geometry’s Hidden Roots: Intuition Persists Into Adulthood and Falters in Dyscalculia

Long before children ever learn to name an angle or prove that two triangles are congruent, they are already fluent in a quieter, older language of geometry. A new study published in iScience by Elisa Castaldi of the University of Florence and colleagues traces that language from early adolescence into adulthood, and in doing so delivers a striking finding: adults with developmental dyscalculia, a disorder typically defined by difficulties with numbers and arithmetic, also show deep and lasting impairments in geometric thinking, even when the tasks they face involve no calculation whatsoever.

The research team set out to answer two questions that have long hovered over the science of mathematical cognition. First, how do geometric abilities mature across development, and does the intuitive, preverbal sense of shape and space that we share with infants and even some animals continue to feed into the formal geometry learned at school? Second, are geometric abilities selectively damaged in people with learning disorders, particularly dyscalculia and dyslexia? To find out, the researchers tested twenty-two neurotypical children aged eleven to fourteen and fifty-seven adults aged twenty to twenty-nine, including university students with dyscalculia, most of whom also had dyslexia, and students with dyslexia but no dyscalculia.

The design was carefully constructed to separate geometry itself from the general cognitive machinery that often muddies such comparisons. Non-symbolic geometry, meaning intuitive geometric competence that does not depend on schooling or vocabulary, was probed with two tasks adapted from landmark studies by Stanislas Dehaene and colleagues and by Marie Amalric and colleagues. In the geometrical odd-one-out task, participants saw arrays of six figures and had to point to the one that violated a geometric principle, testing sensitivity to properties such as topology, symmetry, chirality, metric properties and Euclidean relationships. In the geometrical inference task, a cursor hopped around a circular grid of dots following a hidden geometric rule, from simple repeating sequences to complex structured paths, and participants had to predict where it would go next. Symbolic geometry, the school-learned kind, was measured with the standardized Italian Geometria test, which assesses both declarative knowledge of geometric concepts, such as supplementary angles or the value of pi, and geometry-specific visuospatial skills, such as mentally folding sheets of paper or counting cubes in a structure.

The developmental results were clear. Adults outperformed adolescents on every measure, both intuitive and formal. Children scored around 83 percent on the non-symbolic composite and 66 percent on the symbolic composite, while adults reached 87 percent and 77 percent respectively. Crucially, a statistical model that included verbal reasoning, non-verbal reasoning and visuospatial working memory as covariates still showed a significant effect of age, meaning the improvement was not simply a by-product of sharpened general cognition. The gains were also uneven: the jump in symbolic geometry was large, with a Cohen’s d of nearly two, while the improvement in non-symbolic geometry was smaller, consistent with the idea that intuitive geometric competence is largely in place early and undergoes slower refinement.

Perhaps the most theoretically important finding concerns the bridge between the two kinds of geometry. After statistically removing the contributions of verbal reasoning, non-verbal reasoning, visuospatial working memory and age, the researchers computed residual scores for each participant and found a robust correlation of 0.59 between non-symbolic and symbolic geometric performance. The association held for both intuitive tasks individually, at correlations of 0.46 for the odd-one-out task and 0.51 for the inference task. In other words, a person’s raw, wordless intuition for geometric regularities predicts how well they command the formal geometry of the classroom, independent of how smart they are, how good their working memory is, or how old they are.

Hierarchical regression analyses then revealed that the two components of symbolic geometry draw on different resources. For declarative geometric knowledge, general cognitive abilities accounted for roughly 29 percent of the variance, and non-symbolic geometry added a modest but significant seven percent. Geometry-specific visuospatial ability showed the opposite architecture: general cognition mattered far less, while age and non-symbolic geometry together dominated the picture, with non-symbolic geometry alone contributing an additional 23 percent of explained variance. This suggests that formal geometric competence is not a single skill but a family of skills, some leaning heavily on domain-general intelligence and others rooted firmly in ancient spatial intuitions.

The clinical half of the study is where the findings become genuinely arresting. Adults with dyscalculia performed worse than both neurotypical controls and dyslexic peers on every geometry measure. On the odd-one-out task, the dyscalculia group averaged 77 percent accuracy against 87 percent for controls and 89 percent for the dyslexia group, yielding effect sizes above 1.5. On the inference task they scored 79 percent versus 87 percent for both other groups. Their declarative geometric knowledge, at 44 percent correct, lagged far behind the 63 percent of controls and the 60 percent of dyslexic participants, and their visuospatial geometry scores were similarly depressed. Importantly, every one of these differences survived statistical control of visuospatial working memory, and the deficits were homogeneous across geometric categories rather than confined to one type of problem.

What makes this pattern so remarkable is who the participants were. These were university students, individuals with high education and years of opportunity to develop compensatory strategies, which makes it very unlikely that their geometric difficulties merely reflect delayed development or poor schooling. It also contrasts sharply with other dyscalculia-related impairments, such as reduced precision in perceiving numerosity, which tend to be pronounced in children and fade in adulthood. The persistence of geometric impairment into adulthood, combined with its selectivity, since dyslexic participants without dyscalculia performed indistinguishably from controls on nearly everything, points to geometric processing as a core and enduring feature of dyscalculia rather than a secondary consequence of reading or attention problems.

The findings also carry practical weight. Recent OECD assessments have documented a marked decline in mathematical achievement since 2018, including substantial trouble with geometric concepts, yet geometric learning difficulties remain almost entirely absent from diagnostic batteries. Because geometry assessment is rarely included when dyscalculia is diagnosed, an important dimension of the disorder may be routinely overlooked. The authors argue that understanding the foundations of geometry could inform targeted educational interventions and more sensitive clinical practice, potentially identifying students at risk before formal geometry instruction begins to fail them.

The study is not without limitations. Children and adults took the symbolic test under different conditions, adults had to use a version standardized for adolescents because no adult norms exist, and the researchers did not measure non-geometric magnitude processing such as area discrimination, leaving open the possibility that broader magnitude mechanisms contribute to the observed links. Even so, the overall message stands firm: the geometry we learn from teachers rests on intuitions that predate schooling, language and perhaps even our species, and when those intuitions are compromised, as they appear to be in dyscalculia, the deficit runs deep, lasts a lifetime, and has been hiding in plain sight.

Subject of Research: Development and impairment of symbolic and non-symbolic geometric abilities in dyscalculia and dyslexia

Article Title: Symbolic and non-symbolic geometric abilities across development and in individuals with dyscalculia and dyslexia

Article References: Castaldi, E., Anobile, G., Marazzi, M., Federici, S., Angelelli, P., & Turi, M. (2026). Symbolic and non-symbolic geometric abilities across development and in individuals with dyscalculia and dyslexia. iScience, 29(11), Article 117841. https://doi.org/10.1016/j.isci.2026.117841

Image Credits: AI Generated

DOI: 10.1016/j.isci.2026.117841

Keywords: geometry, dyscalculia, dyslexia, non-symbolic cognition, spatial reasoning, mathematical cognition, development, working memory, learning disabilities, geometric intuition, Symbolic, non-symbolic