The question of whether animals can “do math” explores the cognitive capabilities of diverse species. Unlike human mathematics, which relies on abstract symbols and language, animal numerical abilities typically involve a “number sense” or “numerosity.” This refers to an innate capacity to perceive, represent, and discriminate quantities without formal counting systems. Researchers use “numerosity” to describe this approximate estimation, distinguishing it from the exact, symbolic number systems of humans.
Recognizing Quantities
At the most fundamental level, animals recognize and distinguish between different quantities. This involves two primary systems: the approximate number system (ANS) and the parallel individuation system. The parallel individuation system allows for the exact representation of very small numbers, up to four. Beyond this range, the ANS provides an imprecise estimation of larger quantities, with accuracy decreasing as numbers grow larger.
Mosquitofish, for instance, distinguish between shoals containing one or two fish, two or three fish, and three or four fish, choosing the larger group. Fruit flies demonstrate numerical sensitivity by preferring larger quantities and distinguishing quantities based on clear ratios. Honeybees also perceive and discriminate numerical quantities, showing a limit around four items.
Counting and Basic Arithmetic
Beyond simple quantity discrimination, some animals engage in more advanced numerical operations, including what resembles counting and basic arithmetic. This involves tracking sequences or combining and separating groups of objects. While not “counting” in the human sense of associating symbols with numbers, these behaviors indicate a sophisticated understanding of quantity changes.
Chimpanzees, for example, can add quantities of objects and select the correct sum. Monkeys have mentally added numerical values of two object sets and chosen a visual array corresponding to the sum. African Grey parrots, like Alex, have counted objects up to six and comprehended simple addition. Fish, including cichlids and stingrays, have even been trained to perform basic addition and subtraction of one, associating blue shapes with adding one and yellow shapes with subtracting one.
Abstract Numerical Concepts
Some research indicates that animals grasp more abstract numerical concepts, extending beyond practical counting or quantity discrimination. One such concept is “zero” as a numerical quantity. Honeybees have demonstrated an understanding of zero, treating an empty set as quantitatively less than one or more objects. Crows have also shown an understanding of the empty set, placing it in numerical order.
Monkeys have neurons in their prefrontal cortex that respond specifically to the concept of zero, suggesting a neural basis for this abstract understanding. Ring-tailed lemurs have demonstrated an ability to order groups of objects by size, indicating a grasp of numerical ordering. These findings suggest that abstract numerical reasoning may be more widespread in the animal kingdom than once thought.
Studying Animal Math
Scientists employ various methodologies to investigate numerical cognition in animals, carefully designing experiments to isolate numerical abilities from other cues. Operant conditioning is a common technique, where animals learn to associate specific actions with rewards based on numerical outcomes. For example, rats have been trained to press a lever a specified number of times to receive food.
Choice experiments, such as preferential looking or selecting between visual arrays, are also widely used. Researchers might present an animal with two options, each displaying a different number of items, and observe which option the animal chooses. Fish, for instance, are often tested by presenting them with shoals of varying sizes and observing their preference for larger groups. A challenge in these studies is ensuring animals respond to the numerical quantity itself, rather than non-numerical factors like total area, density, or perimeter. Researchers control these variables to prevent the “Clever Hans phenomenon,” where an animal appears to perform a task but responds to subtle, unintentional cues from its handler.
Why Numerical Skills Matter
Numerical abilities offer evolutionary and ecological advantages, contributing to an animal’s survival and reproductive success. These skills aid in behaviors like foraging, navigating, social interactions, and avoiding predators. Foraging animals use numerical competence to assess food abundance, choosing areas with more resources. Golden orb weaver spiders, for example, track the number of insects caught in their webs.
Navigation also benefits from numerical tracking; honeybees count landmarks to find their way between food sources and their hive. In social contexts, numerical assessment is important. Lionesses decide how to respond to an encroaching pride by estimating the number of roars they hear. Wolves adjust their hunting party size based on prey numbers, optimizing their chances of success. This widespread numerical competence across diverse animal groups suggests it is an adaptive trait.