Geometry may come from navigation skills shared with animals, while human language allows those spatial abilities to become abstract mathematical reasoning.

Discussions about how humans learn and understand geometry go back to ancient Greece and the time of Plato. In recent decades, some researchers have argued that only humans possess the mental foundations needed for geometric thinking.

But a new analysis from New York University psychology professor Moira Dillon challenges that idea, concluding that the roots of geometry are shared across many species, including rats, chickens, and fish.

“Our ability to think geometrically may not come from a built-in, uniquely human ‘math module’ in the brain, but rather from the same cognitive systems that help humans, as well as animals, find their way home,” explains Dillon, whose work appears in the journal Trends in Cognitive Sciences. “Put another way, our understanding of geometry may very well come from wandering rather than from worksheets.”

Philosophers, including Plato, Descartes, and Kant, all explored the origins of geometry and the role of human thought in shaping it. However, scientists did not begin experimentally studying how geometry is learned until the second half of the 20th century.

The “Language-of-Thought” Theory

One leading explanation links geometric thinking to the “language-of-thought” hypothesis. According to this view, the mind contains multiple formal systems, or mental “languages,” that support uniquely human abilities such as mathematics and music.

Supporters of this theory argue that humans build complex ideas from simpler concepts through these mental systems. In geometry, this proposed mental language is based on Euclidean geometry, which describes the properties of lines, shapes, and points on flat surfaces. The theory suggests that concepts such as “parallelism” and “perpendicularity” are built into the human mind from birth.

Dillon, however, points to decades of research suggesting that geometric thinking instead grows out of navigation-related mental abilities shared by both humans and animals. These systems only approximate Euclidean geometry rather than reproducing it perfectly. She refers to this idea as the Wanderers Hypothesis for Geometry.

The Wanderers Hypothesis Explained

“Animals that have never studied angles or triangles can navigate efficiently and simulate that navigation in their minds to plan their routes—and even babies seem to understand something about distance, direction, and shape,” adds Dillon, whose 2023 study found that infants could outperform AI in certain cognitive tasks. “These abilities rely on geometry that captures some, but not all, of the properties of Euclidean geometry.”

So what separates humans from other animals?

According to Dillon, the key difference is not a specialized geometry language but ordinary human language itself.

“Language allows humans to call upon the geometry used for navigation and use it in new ways, for example, to solve geometry problems in our minds without actually going anywhere,” she explains. “Language allows us to mentally wander unlike any other animal can.”

Reference: “The cognitive origins of geometry” by Moira R. Dillon, 6 April 2026, Trends in Cognitive Sciences.
DOI: 10.1016/j.tics.2026.01.005

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