A new study suggests that the intuitive understanding of shapes and geometric relationships may have evolved long before humans began studying mathematics.
Humans often think of mathematics as one of the clearest examples of what makes our species unique. We build complex equations, design bridges, calculate trajectories, and develop entire scientific disciplines around numbers and geometry.
But some of the mental abilities behind mathematics may be much older than human civilization β and perhaps much older than humanity itself. New research from Carnegie Mellon University suggests that basic geometric intuition is shared by humans and other primates. In experiments involving rhesus macaques, olive baboons, young children, and adults, researchers found striking similarities in how participants recognized relationships between geometric shapes.
The finding doesn’t mean monkeys can do geometry homework. It suggests something more fundamental: the brain may have an intuitive understanding of shape and spatial relationships that existed before formal mathematics was ever invented.
What Did the Study Actually Find?
The study’s main result wasn’t that monkeys can “do geometry” the way humans do. Instead, researchers found evidence that monkeys and humans rely on surprisingly similar mental representations when deciding whether two shapes are alike.
The team tested eight monkeys β rhesus macaques and olive baboons β alongside preschool children and adults, using shape-matching tasks on a touchscreen. Participants had to pick the correct target shape from several alternatives, with the shapes manipulated in ways designed to reveal exactly which geometric properties each participant was actually paying attention to, according to a study published on PubMed Central.
The key finding was that the monkeys didn’t rely exclusively on simple visual details, like the exact outline or overall appearance of a shape. Their responses showed they could also track more abstract properties and relationships β symmetry, parallelism, angles, proportions, and broader patterns β much like the human participants did.
The Most Interesting Result: Rotation
One of the strongest findings in the study involved rotated shapes. When shapes were rotated, the monkeys showed a notably strong reliance on representations that stayed stable despite the rotation β in some conditions, even more so than the preschool children did when viewing shapes that hadn’t been rotated at all.
That matters because it suggests the monkeys weren’t simply memorizing what each shape looked like. Instead, they appeared able to recognize a shape based on relationships that hold steady even when its orientation changes. A triangle, after all, doesn’t stop being a triangle just because someone turns it sideways β and the monkeys seemed to understand that on some level, without ever being taught the word “triangle.”
Humans Still Have Far More Advanced Mathematical Abilities
None of this means monkeys understand geometry at anything close to the human level. The researchers tested relatively basic geometric intuition β not mathematical proofs, calculations, coordinate geometry, or the ability to combine geometric principles into more sophisticated arguments.
The study’s actual conclusion is more specific and, in some ways, more interesting: there appears to be a gradual evolutionary continuity between humans and other primates in basic geometric representation, rather than a sharp divide where humans suddenly developed an entirely different kind of geometric thinking from scratch.
A Geometry Test Without Numbers
The broader experimental design behind these results was, on its surface, simple. Participants were shown a geometric shape on a touchscreen and asked to identify the matching shape among several alternatives. The catch was that the correct answer couldn’t always be identified just by looking at color, size, or superficial appearance β participants had to attend to relationships like angles, symmetry, proportions, and overall geometric structure instead.
Alongside the macaques and baboons, the researchers tested preschool children between 3 and 6 years old, as well as adults β including people from Bolivia’s Tsimane’ community, where formal schooling looks very different from that of the American participants. That range let the researchers ask an important question: is geometric intuition something humans learn through education, or does it appear much earlier, independent of schooling?
The results pointed toward the latter.
Why the Youngest Humans Matter So Much
The preschool participants are an especially important piece of the puzzle. If adults alone outperformed the monkeys, researchers could chalk the gap up to years of schooling and mathematical experience. But young children have had far less formal instruction β so if children and monkeys show similar patterns when solving basic geometric problems, that suggests at least part of the ability doesn’t depend on classroom mathematics at all.
Including adults from very different educational backgrounds helped the researchers separate the effects of age from the effects of schooling. What emerged was broad continuity across every group tested. That doesn’t make education unimportant β it suggests education builds sophisticated mathematics on top of cognitive abilities that were already there to begin with.
Geometry May Be Older Than Mathematics
That points to a fascinating evolutionary question. Humans eventually turned geometric intuition into formal mathematics β angles, ratios, symmetry, measurement, proof. But the underlying ability to recognize spatial relationships likely served a much more basic purpose long before any of that existed.
Animals constantly interact with physical environments. They need to navigate around objects, judge distances, recognize familiar structures, and understand how things relate to one another in space. Seen that way, basic geometry isn’t fundamentally a classroom skill β it’s an environmental survival skill. A bird navigating a landscape, a monkey moving through branches, and a human walking around obstacles all rely on some understanding of spatial relationships. The mathematics came later.
Humans May Not Be as Cognitively Unique as We Think
This study adds to a growing body of research showing that abilities once considered uniquely human turn up in other animals too β sophisticated memory, navigation, object recognition, quantity sense, and problem-solving have all been documented elsewhere in the animal kingdom. The geometry findings add another piece to that puzzle.
Carnegie Mellon researchers suggest these geometric intuitions may be part of a basic cognitive architecture shared across primates. That doesn’t diminish human intelligence β humans remain extraordinarily unusual in our ability to turn basic intuitions into elaborate systems of mathematics, science, and engineering. The real distinction may simply be that humans took an ancient cognitive ability and pushed it to an extraordinary extreme.
What This Could Teach Us About the Human Brain
The most important lesson here may not be about monkeys at all β it may be about us. Humans often imagine mathematics as an abstract invention that lives almost entirely inside culture and education. But the ability to recognize patterns, relationships, and spatial structures may be far more deeply rooted in biology than that picture suggests.
Long before anyone wrote a geometry textbook, animals were already navigating three-dimensional environments. Long before humans developed mathematical notation, our ancestors had to recognize objects, distances, and spatial relationships just to get through the day. This research suggests that some of the mental machinery required for geometry may have been inherited from that much older evolutionary history β humans later built language, symbols, education, and formal mathematics on top of it.
So the discovery here isn’t that monkeys are secretly mathematicians. It’s that the cognitive building blocks that eventually helped humans invent mathematics may be far older than mathematics itself β a finding that matters for understanding not just animal intelligence, but where human mathematical thinking actually came from.
The Next Question Is Much Harder
Researchers now want to determine which geometric relationships are easiest and hardest for monkeys and humans alike to recognize, which could reveal exactly where the similarities between species end. Basic shape matching may be evolutionarily ancient, for instance, while combining multiple geometric elements into increasingly complex structures may demand cognitive abilities that are far more developed in humans.
Understanding that progression could also help scientists study how children acquire mathematical concepts in the first place. If children arrive at school already equipped with an intuitive sense of space and shape, teaching methods could potentially be designed to build on those existing mental structures β rather than treating geometry as something entirely unfamiliar that has to be built from zero.
From Monkey Shapes to Human Mathematics
There’s a huge distance between recognizing a triangle and proving a mathematical theorem. But the two abilities may share part of the same foundation, and that’s what makes this research so interesting. Humans likely didn’t invent geometric intuition out of nothing β we may have inherited basic ways of understanding shape and space from ancestors who lived long before mathematics became a formal discipline. Education then transformed those intuitions into something vastly more powerful.
The next time a student struggles with geometry, it may be worth remembering that the underlying ability isn’t entirely foreign to the brain. In some form, it may have been with primates for millions of years. The remarkable part of human mathematics, then, may not be that we can see geometric relationships at all β it may be how far we’ve learned to take them.
Sources: PubMed Central (study on shape representation in monkeys, children, and adults); EurekAlert (Carnegie Mellon University research summary).
