For centuries, the nature and origins of geometric understanding have intrigued philosophers and scientists alike, tracing back to the intellectual musings of Plato and permeating through the works of Descartes and Kant. Traditionally, geometry—the study of shapes, lines, points, and spatial relationships—has been viewed as an exclusively human cognitive construct, uniquely embedded in our minds as an intrinsic “math module.” These classical perspectives suggest that humans are born equipped with a mental framework predisposing us to grasp Euclidean principles such as parallelism and perpendicularity from birth, setting us apart from other species. However, a groundbreaking new analysis led by Dr. Moira Dillon, a psychology professor at New York University, challenges this long-standing view by proposing that geometric cognition is not solely the product of an innate human faculty but is instead deeply intertwined with spatial navigation processes shared across a broad spectrum of animals.
Dillon’s work, recently published in the esteemed journal Trends in Cognitive Sciences, introduces what she calls the “Wanderers Hypothesis for Geometry.” This framework postulates that the foundations of geometric understanding stem from navigation-like cognitive mechanisms that evolved to facilitate spatial orientation and route planning in both humans and non-human animals. Unlike the traditional “language-of-thought” hypothesis, which posits that complex mental languages underpin uniquely human faculties like mathematics and music, Dillon argues that the competencies necessary for geometric reasoning are evolutionary products of spatial awareness systems. These systems allow creatures as diverse as rats, chickens, and fish to navigate their environments effectively, demonstrating an awareness of fundamental geometric concepts such as distance, direction, and shape, albeit without full adherence to formal Euclidean rules.
Exploring decades of experimental research, Dillon elucidates how animals engage in mental simulations of navigation, planning routes through spatial landmarks without explicit training in geometry. Such behaviors indicate that an approximate, evolved form of geometric cognition exists beyond the human species. This finding disrupts the conventional assumption that geometry is an exclusive product of human symbolic thought. Humans, she explains, are not unique because they possess a special geometric module; rather, they are distinguished by their capacity to incorporate language into their cognitive toolkit. Language, in Dillon’s view, transforms these spatial navigation processes, enabling humans to manipulate geometric concepts abstractly and solve geometry problems internally, without relying on direct physical exploration.
The hypothesis further gains credence when considering infant cognition. Dillon’s recent studies reveal that even preverbal babies demonstrate an intuitive grasp of spatial parameters, suggesting that fundamental geometric understanding precedes formal education and linguistic development. Intriguingly, these abilities often outstrip current AI systems in tasks requiring commonsense psychological reasoning, highlighting the sophistication and evolutionary depth of these navigation-based cognitive faculties. Thus, the mental operations underlying geometric reasoning appear to be rooted in inherited spatial navigation mechanisms that are both ancient and widely shared among vertebrates.
Dillon’s analysis gains additional power by integrating comparative studies across diverse cultures and developmental stages. Evidence shows that children and adults worldwide engage with geometric concepts in ways that align with navigation-based mental processing, rather than relying solely on abstract mathematical instruction. The cross-cultural consistency of geometric perception and learning undermines the notion that formal Euclidean geometry arises exclusively from culturally transmitted symbolic thought. Instead, it supports the idea that a more primitive, approximate geometric competence grounded in space-finding and route-planning instincts serves as a universal cognitive substrate.
Additionally, Dillon addresses cutting-edge developments in artificial intelligence, particularly efforts like Google DeepMind’s AlphaGeometry project, which attempts to replicate human geometric reasoning. These AI systems, while proficient in many respects, still struggle to emulate the flexible, navigation-based cognitive strategies that animals and humans naturally exhibit. This limitation underscores the significance of evolutionary inherited processes as the foundation rather than formal symbolic geometry alone. Dillon’s synthesis suggests that AI might benefit from models that better mimic biological spatial cognition, rather than relying solely on classical mathematical formalism.
The implications of Dillon’s Wanderers Hypothesis extend beyond cognitive psychology and neuroscience; they resonate within evolutionary biology and philosophy of mind. By framing geometric understanding as an outgrowth of ancient navigation faculties, her work illuminates how complex abstract thinking might arise from more fundamental, embodied cognitive processes. It also invites a reexamination of what truly distinguishes human intelligence—shifting the emphasis from specialized mental modules to the transformative power of language. Language, she argues, uniquely grants humans the ability to mentally traverse geometric space without physical movement, enabling problem solving, abstract thought, and cultural transmission of mathematical knowledge.
Moreover, Dillon’s theory offers a cohesive explanation for how geometry could evolve across species with differing ecological demands and navigational needs. Animals inhabiting environments requiring precise spatial mapping would benefit from refined geometric cognition bolstered by navigation mechanisms. This underlying commonality might explain why diverse vertebrates show remarkable spatial reasoning abilities despite wide variations in sensory modalities and neural architectures. The Wanderers Hypothesis thus bridges gaps between behavioral ecology, cognitive psychology, and linguistics, synthesizing multidisciplinary findings into a unified theoretical framework.
Throughout her article, Dillon carefully situates her perspective within the broader intellectual lineage, acknowledging the insights and limitations of earlier thinkers while pushing the scientific dialogue forward. By focusing on empirical evidence—from animal navigation experiments to infant cognitive assessments and AI benchmarking—she constructs a persuasive case that challenges deeply entrenched assumptions about human exceptionalism in geometric reasoning. Her work underscores the importance of viewing cognition as an adaptive, evolutionary phenomenon that can be profoundly influenced by cross-species shared mechanisms.
In conclusion, Moira Dillon’s research reorients our understanding of the cognitive origins of geometry. Rather than arising from a discrete, innate mental geometry module present only in humans, geometric knowledge appears to be scaffolded upon ancient, evolutionarily conserved navigation processes that permit animals to perceive and mentally simulate spatial relationships. The uniquely human leap emerges from linguistic capabilities, which allow abstract manipulation of these spatial representations independent of immediate environmental interaction. This paradigm not only reshapes theories about geometric cognition but also holds potential to inspire innovations in education, AI development, and understanding of cognitive evolution.
As ongoing research delves deeper into the neural and behavioral bases of spatial reasoning, Dillon’s Wanderers Hypothesis for Geometry stands as a bold and illuminating model. It challenges us to rethink the cognitive architecture from which geometry arises, emphasizing the intertwined roles of biology, environment, and language in shaping one of humanity’s most treasured intellectual achievements. The convergence of psychology, neuroscience, ethology, and AI research in this endeavor exemplifies the dynamic, integrative future of cognitive science.
Subject of Research: Cognitive origins of geometric understanding and its evolutionary and cross-species foundations
Article Title: The cognitive origins of geometry
News Publication Date: 6-Apr-2026
Web References: https://doi.org/10.1016/j.tics.2026.01.005
Image Credits: Jonathan King/NYU
Keywords: Mathematics, Learning processes, Cognitive psychology, Cognitive development
