The ability to recognize geometrically identical shapes, even when rotated, often proves useful for humans, but, as it turns out, we are not the only animals capable of this. When it comes to grasping geometry, a lack of formal training may be one of the few factors holding back our primate relatives.
Scientists from Carnegie Mellon University led a team of researchers to determine how our understanding of shapes differs from that of other primates. The study’s findings were published in the journal Proceedings of the National Academy of Sciences.
The results are based on experiments involving eight adult monkeys—four rhesus macaques (Macaca mulatta) and four olive baboons (Papio anubis)—55 preschool children (3-6 years old) from the United States, and 77 adult volunteers from the indigenous Tsimane population, who have minimal formal education.
They also used a subset of data from a prior study, which included baboons, French preschoolers and first-graders, as well as French adults and indigenous Himba people, and analyzed it in parallel.
“By studying adults with informal geometry education, alongside adults who have formalized geometry training (as in the US), as well as children and monkeys, we could determine which aspects of geometric thinking arise naturally and which are strengthened specifically through education,” said neuroscientist Jessica Cantlon.
Monkeys may not possess the same symbolic understanding of geometric shapes as we do, but their ability to recognize rotated triangles, rectangles, trapezoids, and other figures in a row is nearly on par with the human mind.
Participants of all ages and species were asked to complete a matching task using a touchscreen. The goal was to find pairs of shapes with identical geometry (e.g., two right triangles) among a set of geometric figures, which could be slightly rotated or scaled to different sizes.
Participants received minimal instructions on the task and were asked to “figure it out” through trial and error. Correct answers were followed by a pleasant “bing” sound, after which primates and children received a reward. For monkeys, this was a breakfast cereal; for children, a sticker.
“The most surprising finding is that young children, who have not yet received formal math education, struggle with this task just like monkeys do,” said co-author Jialin Li. “We found that the degree of overlap between children and monkeys is almost as strong as that between children and adults.”
Successfully solving such a task requires an abstract understanding of geometric features, once thought unique to humans—but that is no longer the case.
“When you and I look at these shapes, the matches seem obvious, but young children and monkeys have to seriously think about geometric properties because the matching shapes have different sizes and orientations,” explained Cantlon. “The results show that abstract thinking is not an ‘all-or-nothing’ ability that suddenly appeared in humans. Instead, some cognitive foundations of mathematical thinking appear to be shared across primates, and human education and culture build on these ancient biological abilities.”
For adults, this task was much easier, likely due to their greater ability to rely on symbolic features of each shape, such as symmetry, side length, parallelism, and angle measures.
Indeed, data analysis showed that children and monkeys tended to rely more on intuitive processing, while adults leaned more on a symbolic approach, unconsciously abstracting the core geometric rules that define similar shapes.
This suggests, the authors write, that greater use of symbolic representations is learned, possibly through formal education, rather than being an innate quality of human intelligence.
Scientists may need to start enrolling monkeys in geometry lessons to unlock their true potential.
“Our study shows that formal education strengthens symbolic geometric representation, but humans already have abstract geometric intuitions—intuitions about metric properties and angles—that are shared with other primates,” said Cantlon. “Rather than creating mathematical thinking from scratch, schooling may refine and expand ancient cognitive abilities that evolution has shaped over millions of years.”
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