Does your dog understand mathematics?


Dogs may have more in common with us than we thought when it comes to quantitative thinking.

An eminent visiting professor at a talk I attended stated categorically that it’s not the ability to fashion and use tools that sets humans apart from lower animals, but rather our ability to do mathematics — even simple arithmetic. A colleague of mine leaned over and whispered “Do you think that’s true?”

I replied, in what I hoped was a light-hearted manner, “You know, they say that there’s a test for this. Try letting your dog see you put three dog biscuits in your pocket. Then give him only two of them and see what happens.”


Scientifically speaking, some people doubt that dogs are capable of even the most rudimentary form of quantitative thinking. What do we mean by this? In its most basic form, analyzing the world in a quantitative way involves the judgment of size — being able to determine if one thing is larger than another. Early researchers tested this on dogs by putting out two balls of hamburger, one large and the other small. When they found that dogs were as likely to choose the small one as the large, they concluded that dogs could not estimate size. But there is a flaw in this test. Dogs think opportunistically, with “a bird in the hand is worth two in the bush” mentality. If the two plates of meat were at different distances, the dog would always grab the closest. BUT, if they were at equal distances, the dog would go after the larger portion, demonstrating that he did understand the notion of size.

Norton Milgram, at the University of Toronto, used a different test to confirm that dogs can judge size accurately. He placed two objects of different sizes on a tray. If the dog pushed the correct object, he would find a food treat underneath. The dogs could be taught to always choose the larger (or smaller) of two objects, regardless of the shape or identity of the objects, and they learned this quite easily.


Judging numerosity is a slightly more difficult aspect of quantitative reasoning. Numerosity simply refers to the ability to compare two groups of items. As humans, we do this when we judge which of two crowds contains more people, for example. We don’t need to count or have any idea of the specific number of people in either group in order to know. So what about a dog who runs to a pile that contains ten pieces of kibble, rather than to the pile next to it that contains only four pieces? Is she making her decision based upon her ability to judge the number of kibbles in each pile? It appears so! In the laboratory, dogs show they can judge numerosity by learning to press a panel that has more (or fewer) dots painted on it in order to get a food reward.

The next level up is simple counting, and this is an ability that dogs — especially work and sporting dogs — frequently demonstrate. For example, in field trials for retrievers, higher level tasks require dogs to be able to count to at least three. This is because, if three ducks have been dropped, and the dog has already retrieved two, he must know that there is still one more out in the field to retrieve.

What about simple math?

So if dogs can count, it seems natural to ask whether they can do simple arithmetic. Robert Young of the Pontifical Catholic University in Brazil, and Rebecca West of the University of Lincoln in the UK, attempted to demonstrate this idea by modifying a test that has been used to prove that human infants have the ability to count. The procedure involves something called “preferential viewing”, which simply measures the length of time that infants spend looking at things. Research confirms that infants (just like adults) will stare at something unexpected or unusual for a longer time. The human test is quite simple.

mathematicsFirst, the experimenter shows the child a small doll on a table. Then a low screen is put in front of the doll to block the child from seeing it. While the child watches, the experimenter takes another doll, shows it to the child and then puts it behind the screen. If the child can count, she should expect that when the screen is raised she should see two dolls — and sometimes she does.

However, other times, the experimenter secretly removes one of the dolls so that now when the screen is raised, only one doll is visible. When this occurs, the babies stare at what is on the table for much longer after the screen has been raised. Psychologists believe that this confirms that infants have made the mental calculation and are now surprised to find that the number of dolls they see is different from what they expected.

In the canine version of this test, the experimenter showed the dog a single large treat and then put a low screen in front of it. Next, the dog watched as the experimenter obviously placed another treat behind the screen. If the dog can do the math, he knows that 1 + 1 = 2, and he should expect to see two treats when the screen is raised. However, just as in the case of the infants, sometimes the experimenters secretly removed the second treat, so that when the screen was raised, the dog saw only one. As in the case of the babies, the dogs stared at this unexpected outcome for a longer time than they did when the arithmetic came out correctly, apparently “surprised” at what they saw. Similarly, if an extra treat was secretly added so that the dogs saw three instead of the expected two, the dogs appeared to be equally surprised. This suggests that dogs can not only count, but can also do simple addition and subtraction.


The ability to count and do simple arithmetic might seem to be a superfluous skill for dogs, but it is a useful ability that could have been vital to dog’s wild ancestors. For example, it would be useful for a female to know if all of her pups were present in the den or if one of them had somehow gone astray and required rescuing.

Despite this display of arithmetic ability in dogs, I wouldn’t give one my pocket calculator quite yet, since she is still more apt to view it as a chew toy rather than a mathematical tool!


Stanley Coren is professor Emeritus in the Department of Psychology at the University of British Columbia. He is also an award winning behavioural researcher, a Fellow of the Royal Society of Canada, and was named as one of the 2,000 outstanding scientists of the 20th century. His many books on dog behaviour and human-canine interactions have been international bestsellers. His awards include the prestigious Maxwell Medal of Excellence from The Dog Writers Association of America for his book Born to Bark. Coren has been featured on Oprah, Larry King, and can be heard broadcasting a radio column on CBC. His newest book is Do Dogs Dream.