THE people of an isolated tribe in the Amazonian rainforest can understand geometry as well as American schoolchildren, according to research that suggests the branch of mathematics is deeply ingrained in human nature.

Though they have never been taught about triangles, symmetry or right angles, the Munduruku people have an intuitive grasp of these concepts that shows basic geometry to be part of humanity’s innate intellectual tool kit, scientists believe. In a series of geometrical tests devised by French and American researchers, Munduruku children and adults achieved similar scores to schoolchildren from the US who had learnt the subject in maths classes for several years.

The findings offer strong evidence that the human mind has evolved a fundamental ability to understand geometrical forms and principles.

“The spontaneous understanding of geometrical concepts and maps by this remote human community provides evidence that core geometrical knowledge is a universal constituent of the human mind,” said Elizabeth Spelke, Professor of Psychology at Harvard University in Cambridge, Massachusetts, a lead author of the study.

The experiments confirm the conclusions reached by the Greek philosopher Socrates, who is described by Plato as testing an uneducated slave to determine if he understood geometry. The slave’s answers so impressed Socrates that he concluded that “his soul must have always possessed this knowledge”, Plato wrote in the Meno, in the 4th century BC.

If geometry is not learnt simply from culture, but rather rests on the architecture of the brain, geometrical skills can be improved by formal education in the subject. Though the abilities of American children were comparable with those of Munduruku of all ages, the Amazonians were easily outshone on the tests by American adults.

“While geometrical concepts can be enriched by culturespecific devices like maps, or the terms of a natural language, underneath this variability lies a shared set of geometrical concepts,” Professor Spelke said. “These concepts allow adults and children with no formal education, and minimal spatial language, to categorise geometrical forms and to use geometrical relationships to represent the surrounding spatial layout.”

The study, published today in the journal Science, involved the researchers travelling to Brazil before seeking out the Munduruku, who live along the Cururu river, deep in the rainforest.

They were chosen for their remoteness from Western culture, and because their language and culture does not include geometrical concepts such as symmetry or parallelism. They have no tradition of using maps, which relies on geometry and spatial reasoning.

In one of the tests, the researchers showed Munduruku children and adults a set of 45 slides, each of which contained six images of shapes or lines. In each case, five of the images demonstrated the same geometrical concept, such as parallel lines, symmetry or right angled triangles, while one was an odd one out.

The tribespeople, the youngest of whom was aged 6, were asked to say which of the images were “weird” or “ugly”.

They scored an average of 66.8 per cent; significantly higher than the 16.6 per cent that would be expected if they were guessing. There was no difference in performance between adults and children.

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