Wild Mathematics: Scientific Evidence of the Numerical Abilities of Animals

By Saulo Silvestre and Mariana Meneses

Mathematics is the science of structure, order, and relation.

Also known as the language of the universe, mathematics provides the most detailed description of the material world available through abstract thought.

There is increasing evidence, however, that humans are not the only animals with mathematical skills. 

Whether aware of it or not, we constantly use mathematics to assess our surroundings and make decisions in our daily lives. It might be for obvious needs, like counting the number of eggs to use in a recipe, but also for intuitive calculations such as estimating when and with what force you should apply your vehicle’s brakes to avoid a collision.

Abilities like counting and performing arithmetic are such fundamental tools for our ability to interact with the world that it should not come as a surprise that we humans are not the only ones to use them.

“[The universe] cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.” Galileo Galilei, Il Saggiatore (1623).

Since the first evidence that humans are not the only animals capable of counting, the scientific community has been consistently surprised by the extent of numerical understanding that other animal species demonstrate.

The ability to count can provide countless advantages to the daily lives of animals. These include managing resources and monitoring changes in their surroundings, like how many nuts were stashed in a tree trunk or if any cubs are missing from the lair. Such advantages factor in evolution, and basic cognitive abilities for numerical abstraction seem to be present in most animals, from insects and cephalopods to birds and mammals.

 

Throughout the history of research on this topic, many examples of animals counting have emerged.

Lionesses decide how to respond to a pride intruding in their territory based on the number of roars they hear. Frogs may be capable of tallying the number of vocalizations performed by competitors of the same species during mating rituals. Honeybees count landmarks to navigate outside the colony. Some ants can keep track of the number of steps they take. Some spiders can calculate the quantity of prey in their web. The list goes on and on.

 

An approximate sense of quantity, and numerosity, which is a mental representation of the size of a collection or set of objects, is the fundamental capacity for any numerical abilities in animals.

Most animals seem to share an ability to approximate numerosity, and some can even perform simple arithmetic such as addition and subtraction. For example, just by watching scientists add and remove pieces of bread from a closed, opaque box, wild monkeys can determine when the box was empty. 

In some cases, arithmetic abilities may be innate to some animals. A group led by Dr. Rosa Rugani at the University of Padua in Italy observed that newly hatched, untrained chicks could keep track of the number of items behind screens based solely on watching them moving from behind one screen to the other.

Dr. Rugani told The Quantum Record that their main finding in this study was that “chicks can distinguish between various numerical comparisons, such as 2 vs. 3, 2 vs. 8, 6 vs. 9, 8 vs. 14, 4 vs. 6, and 4 vs. 8, supporting the hypothesis that a single system process both small and large numerosity. This indicates a continuity in the representation of numbers, challenging the notion of distinct nonverbal numerical systems.”

We asked Dr. Rugani about the next steps in this research, and she explained that they are “currently delving deeper into the mechanisms underlying numerical cognition. For example, we have been focusing on investigating the arithmetic abilities of newborn chicks and exploring strategies to make complex operations, such as 1+1+1 vs. 1+1+1+1, solvable for them. Our research has revealed that timing and cues that emphasize the individuality of each object play crucial roles in enabling the chicks to successfully solve the task. We are also examining the mental number line in chicks, bees, and children. Our research aims to understand the underlying mechanisms and how the spatial representation of numbers can aid numerical estimations. By exploring the neural basis of numerical cognition in both humans and animals, I attempt to shed light on the fundamental processes involved and provide insights that can potentially aid in developing interventions for children struggling with mathematical concepts.”

 

 

But the most shocking discovery was that some animals understand the quantitative concept of zero.

Even though this concept may seem simple, interpreting zero as a quantity carries a deep paradoxical complexity. In our history of mathematics, humans only began to use zero as a value around the sixth century.

As explained by Dr. Brian Butterworth, a cognitive neuroscientist at University College London, all numerosities are abstractions, in the sense that they assess the size of a set, irrespective of its members. Ten can equally refer to a set of apples, clouds, or cars, for example. However, zero is simultaneously an abstraction of perceiving something, and also the absence of the thing. Therefore, when interpreting an empty set (i.e., zero) as a quantity, we are representing nothing as something. The cognitive challenge is illustrated by the way young children struggle to understand zero as a quantity rather than an absence, unrelated to other values. 

In the animal kingdom, monkeys, crows, and even honeybees have demonstrated the ability to interpret zero as numerosity.

The capacity to understand zero can be valuable if, for example, an animal watches a few predators enter a cave, and later has to determine when the predators have left and the cave is safe. As the animal monitors the last predator exiting the cave, it understands zero as a result of subtracting from the number of predators that were initially added to the set of predators in the cave.

Comparing the neural activity of monkeys and crows, a group led by Dr. Andreas Nieder, at the University of Tübingen in Germany, observed the same response patterns in interpreting the numerosity of zero. This similarity among animal species, whose brains and neurological pathways evolved separately for hundreds of millions of years, suggests that some numerical abilities emerged independently many times in the animal kingdom.

 

The neural mechanisms behind the sense of quantity in humans and other animals are similar.

Within a margin of error, specific neurons respond to different numerosities. For example, neurons that respond to the quantity five also show weak responses to the numbers four and six, but not to more distant values. The main difference for humans is the extra step of associating numerosities with specific numerical symbols, such as the digits 5, 4, and 6. Even though animals can learn such associations, there is no evidence that they can understand how they relate to each other.

With this symbolic system, humans developed a more precise and discrete concept of number, which allows us to manipulate quantities according to specific rules.

The similarities imply that all animals share an ancient, evolutionary foundation for a sense of numbers. The next big step for scientists may involve discovery of the genetic mechanisms underlying numerical abilities. 

Dr. Brian Butterworth, Dr. Giorgio Vallortigara, a neuroscientist at the University of Trento in Italy, and Dr. Caroline Brennan, a molecular geneticist at the Queen Mary University of London, are part of a group currently investigating the genetic origins of numeracy. They have already discovered genes that seem to be associated with dyscalculia, a human learning disability in mathematics. Such advances could have substantial consequences for many fields of knowledge, from the evolution of cognition in humans and other animals to the development, to developmental challenges in the numerical abilities of children.

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