📐 Our brain may never have had a mathematical module

Since antiquity, thinkers have attributed mathematics, and particularly geometry, to a uniquely human faculty. Yet, a recent analysis reveals a much older and more common root shared by living beings.

For a long time, philosophers like Plato or Kant debated the foundations of geometry. It was only in the 20th century that scientists tested these ideas experimentally. Several theories then emerged, linking this ability to specific mental structures. Some propose the existence of a "language of thought," composed of specialized internal systems.


In this classical approach, geometry would rest on an innate cognitive module. This module would contain notions such as parallelism or perpendicularity. These concepts would then allow for building more complex reasoning. Such a view sets human beings apart, as the only ones capable of manipulating these abstractions.

But Moira Dillon, a psychologist at New York University, offers another interpretation. In an analysis published in Trends in Cognitive Sciences, she challenges the idea of an exclusively human module. According to her, the foundations of geometry would instead come from mechanisms related to navigation.

Work accumulated over several decades shows that many animals orient themselves effectively. Rats, chickens, or fish assess distances and directions without formal learning. They are even capable of anticipating routes by mentally simulating their movements. These abilities mobilize a form of approximate geometry.

This approach, dubbed the "hiker hypothesis," explains that geometric thinking stems from orientation in space. It does not perfectly reproduce Euclidean geometry, but captures some essential aspects of it. Even infants show an early sensitivity to shapes and distances.

Experiments indicate that these skills appear without teaching. They would be inherited from evolution, as they are essential for survival. Moving around, finding shelter or food requires a reliable spatial representation. This foundation would be common to many species.

The question remains of what distinguishes humans. Dillon suggests that the major difference lies in language. Not a specialized mathematical language, but ordinary language. This would allow the mobilization of these spatial intuitions in abstract situations.

Thanks to language, humans can mentally manipulate shapes without moving. They can reason about figures, solve problems, and transmit concepts. This ability would transform a navigation skill into an advanced intellectual tool.

The analysis also relies on cross-cultural studies and artificial intelligence. Systems like AlphaGeometry make attempts to reproduce these mechanisms.

This would therefore indicate that human geometry is an extension of older aptitudes, amplified by language.