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Fish don’t learn it in schools, but they can do math

Many animals know how to count and add — which tells us something about our own numerical skills.

Fish know there's safety in numbers — and they're not the only animal that can count.Jacob Asher/Associated Press

“Do you know much about the mating habits of the tungara frog?” Brian Butterworth asks eagerly.

The tiny tungara lives in swamps from Mexico to South America. To impress females, males make a call with a series of quick croaks at the end. Females prefer males who can squeeze more croaks into one breath. So males listen to their nearby rivals and try to outcroak them by one. This means both sexes must be able to count to between 4 and 6.

The tungara is one of many animals with surprising numerical abilities that Butterworth discusses in his new book “Can Fish Count? What Animals Reveal About Our Uniquely Mathematical Minds.”


From amphibians to apes to ants, numerical prowess is widespread across species. “It is something innate,” says Butterworth, a cognitive neuroscientist at University College London. And by giving readers a tour of mathematical minds across the animal kingdom, he aims to offer hope for humans who struggle with math.

To answer the question posed by the book’s title: Yes, fish can count. For example, when a fish in the lab sees two groups of its own kind nearby, it will choose the larger group to swim with (safety in numbers!). Many other animals ace laboratory math exams. Mice, for instance, can learn to press a lever at least 40 times before pressing a second lever to get a reward.

Some early research in animal arithmetic took place in the 1940s, when German scientist Otto Koehler studied the numerical abilities of birds. He found that jackdaws could look at a picture of a number of ink blobs and then find a container with the same number of dots on its lid — up to seven — to get a reward. The birds could also retrieve objects from a series of boxes until they added up to the number of ink blobs.


Other animals use math to find their way around. Honeybees can count the number of landmarks they pass while they’re out foraging. Desert ants have been shown to count their steps when they’re searching for food and use that calculation to navigate their way home. When scientists waited until the ants reached food and then gave them “stilts” by gluing a tiny bit of hair to each leg, the step-counting ants overshot their nests on their return trips.

In his own research, Butterworth has used brain scans to better understand the mathematical skills of humans. By studying patients who lost the ability to do math after experiencing brain damage, he and others have seen that a certain part of the brain within a region called the neocortex handles human number-crunching.

These studies originally led Butterworth to think “you need a neocortex — you need quite a lot of it — and that’s how you can count,” he says.

But the findings from the animal kingdom changed his understanding of the brain. “Apart from mammals, other animals don’t have a neocortex,” Butterworth says. So how do they count? “We’re not really sure.”

“What we’ve learned in the last few years is that you don’t need a lot of neurons to do the counting,” Butterworth says. Animals like ants and bees manage their impressive mathematical feats with vastly smaller brains than humans have.

In other research, Butterworth focuses on humans who have an innate difficulty with basic math, a condition called dyscalculia. Just as some people are born color-blind, Butterworth says, “there are also a small proportion, about 5 percent of humans, who don’t really see the world in numbers.” He’s been working to make society more aware of dyscalculia and also developing tests that can diagnose it and tools to help kids with the condition.


Butterworth believes that if people realize that numerical skill is inherited and necessary across many species, they’ll understand that dyscalculia is also inborn, like color blindness — and not a personal failing.

“The universe is actually mathematical in its structure,” Butterworth says. Whether we’re in a classroom or a swamp, understanding numbers helps us and other animals navigate our own corners of that universe.

Elizabeth Preston is a science journalist in the Boston area.