New Analysis Gives Geometry an Evolutionary Shape

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A new analysis by NYU psychology professor Moira Dillon proposes that the foundations of human geometric thinking may be much older and more evolutionarily widespread than traditionally assumed. Rather than originating from a uniquely human, innate “geometry module,” our basic geometric abilities may have developed from cognitive systems used for navigation and spatial reasoning. Research involving humans and animals—including rats, chickens, and fish—shows that non-human animals can represent distance, direction, location, and spatial relationships without formal knowledge of geometry.

The proposal, called the “Wanderers Hypothesis for Geometry,” challenges theories that place Euclidean concepts such as parallelism and perpendicularity directly into the human mind from birth. According to Dillon's analysis, navigation provides a more fundamental form of geometry: organisms construct approximate representations of space that allow them to move efficiently and plan routes. This geometry does not reproduce Euclidean mathematics exactly, but it captures enough spatial structure to support practical reasoning about position, distance, direction, and shape.

The distinctive human contribution, according to Dillon, may therefore be language rather than a specialized mathematical faculty. Animals can use spatial representations to navigate, while humans can describe, manipulate, and recombine those representations symbolically. Language effectively allows humans to “wander” mentally without physically moving, transforming navigation-based spatial cognition into more abstract reasoning. This could help explain how humans progress from practical spatial experience to formal concepts such as geometric figures, relations, proofs, and mathematical problem-solving.

The analysis brings together evidence from developmental psychology, comparative cognition, cross-cultural studies of geometry learning, animal navigation, and artificial intelligence—including systems such as Google DeepMind's AlphaGeometry. It suggests an evolutionary pathway from embodied spatial behavior to increasingly abstract mathematical thought: navigation provides primitive geometric representations, human cognition reorganizes them, and language enables symbolic manipulation. The paper, “The cognitive origins of geometry,” was published in Trends in Cognitive Sciences on April 6, 2026, and is a peer-reviewed publication.

Key takeaways

• Geometry may have evolutionary roots: basic spatial reasoning appears to be shared with other animals rather than being exclusively human.
  
• Navigation may precede formal geometry: organisms can reason about distance, direction, and spatial relationships without knowing mathematical definitions.
  
• The Wanderers Hypothesis proposes that geometric cognition evolved from navigation-like mental processes.
  
• Euclidean geometry may be an abstraction: practical spatial cognition approximates mathematical geometry rather than implementing it exactly.
  
• Language may be the crucial human advantage: language lets humans manipulate spatial representations without physically navigating.
  
• From movement to mathematics: an evolutionary chain can be envisioned as
  navigation→spatial representation→language→abstract geometry.\text{navigation} \rightarrow \text{spatial representation} \rightarrow \text{language} \rightarrow \text{abstract geometry}.
  
• Educational implication: learning geometry might be connected to intuitive experiences involving movement, maps, shapes, distance, and spatial exploration—not only symbolic exercises.
  
• AI connection: the analysis also raises questions about whether systems such as AlphaGeometry acquire geometric reasoning through mechanisms analogous to human spatial abstraction.
  
• Central conceptual shift: instead of asking “Why are humans born knowing geometry?”, the research asks how evolutionary spatial cognition could have been transformed into formal mathematical reasoning.
  

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