We’ve all heard about ‘clever’ animals. Chimpanzees, elephants, dolphins… there are plenty of examples of animals learning to use tools, communicate complex information and solve problems. But how about maths: can animals count?

A horse is a horse, of course, of course, that is of course unless the horse is the famous Clever Hans! Image: public domain.

Clever Hans and Alex the African Parrot

Clever Hans, an Arabian stallion, was famous for his ability to count. Beginning in 1891, retired high school maths teacher William van Osten wowed European crowds with shows of Hans’ extraordinary abilities. When asked what two plus three equaled, Hans had no trouble giving the correct answer by the number of times he tapped his hoof. Many scientists observed Hans answering maths questions and couldn’t find any evidence of fraud or trickery. It wasn’t until 1907 that the truth was uncovered. Hans’ brilliance didn’t lie with his sums, but rather with his incredible ability to read human body language. Even his trainer wasn’t aware Hans would simply tap until tiny changes in the facial expressions or other body language of his observers indicated he had reached the correct number of taps. When his observers relaxed, Hans stopped tapping.

Unlike Clever Hans, Alex the African Grey Parrot appeared to have genuine mathematical ability. When he died aged 31, Alex could count up to eight and perform a variety of sums. For example, he could tell you that two plus one plus two jellybeans made five. Alex also had a vocabulary of more than 100 English words, which he could use correctly. No, he wasn’t just parroting them. Alex’s trainer says he also had an understanding of zero, which is more impressive than it might sound. Alex’s maths was on par with chimpanzees and other non-human primates and his abilities have been the focus of dozens of scientific papers.

Maths and mammals

It’s not surprising primates have been found to be top maths students in the animal world. Since the 1980s, many researchers have demonstrated the capacity of primates, particularly chimpanzees and rhesus monkeys, to do maths at a similar level to very young kids. This means not only being able to do basic adding up, but also understanding what zero is. Chimpanzees have no trouble learning to match an empty food tray with ‘zero’. Monkeys are also able to match the number of sounds they hear with the right number of objects. More recent research has focused on understanding what is actually going on inside a monkey’s head while doing sums.

What about other mammals; is it only primates who can learn maths? Not at all. Brutus the black bear can discriminate between larger and smaller numbers and dogs can count up to four or five. Like monkeys, elephants can rank small numbers in order and compare the answers of very simple sums. When lions hear the roars of other lions intruding into their territory, they decide to attack only if they outnumber them. Similarly, hyenas can tell the difference between one, two, or three intruders on the basis of calls. And if you’re concerned Clever Hans tarnished the mathematical reputation of all horses, don’t worry. We now know horses really can tell the difference between small numbers.

Counting crows

In the bird world, having some basic maths smarts isn’t limited to Alex the parrot. We’ve known for a long time crows are brainy: they use tools and solve problems. Crows can also learn to count – tell the difference between different numbers of dots. What’s more, researchers have worked out which brain cells are involved in the process. New Zealand robins watch researchers hide tasty beetle larvae in holes in logs and then immediately go to the hole where the largest number of larvae were stashed. If the scientists removed some of the larvae when the robins weren’t looking, the birds got agitated and kept searching: they knew they’d been tricked.

Newborn chicks, without any training, can tell the difference between a small number, and larger number of balls. American coots appear to count the number of eggs in their nest, as well as in the nest of birds around them. Even the humble pigeon can tell the difference between many (six or seven) and few (one or two) dots. In fact, in some maths tasks (like ranking numbers from smallest to largest), pigeons are just as good as monkeys.

Ants on stilts

There’s plenty of evidence you don’t even need a backbone to be able to count: invertebrates can do it too. Honeybees can count up to four objects they encounter while out searching for food. Ingenious experiments making use of tiny stilts showed that desert ants use a perception of number steps to find their way back home to their nest after searching for food. The researchers suggest the ants have something acting like a pedometer in their brains. Recent research showed that cuttlefish can accurately tell the difference between different numbers of tasty shrimp, up to the count of five.

Animals may not be doing long division but in many cases, they can count, or at least tell the difference between bigger and smaller numbers. We shouldn’t be surprised: whether an animal is searching for food, or working out how many enemies are invading, being able to tell the difference between more and less makes a lot of sense.

And hey, even plants can count. Venus flytraps decide whether to snap shut their traps and start producing a cocktail of enzymes to digest their prey on the basis of how many times their trigger hairs get touched. No point wasting energy on a false alarm.

Links and stuff

• Radio National Science Show: counting fish
• New York Times video: how birds count
• Alex the counting parrot
• NPR video: ants that count