University of Bonn researchers taught fish to do basic math (Credit: Dr. Vera Schlüssel/University of Bonn)

Your silent, expressionless pet goldfish may appear oblivious to you and its surroundings. But the aquatic vertebrates are smarter than they seem. Previous studies have shown that fish are quick learners, can retain information for up to five months, and even recognize their owner from a group of humans.

Some fish species have even mastered tool use — a skill previously believed to be possessed only by humans and primates like chimpanzees. Now, a new study asserts that fish can be trained to do basic math.

The team at Germany's University of Bonn focused on the colorful zebrafish and the freshwater stingrays for their study. The animals were shown two images, each with four squares, circles, or triangles. They were given five seconds to memorize the number and color of the shapes, which were either all blue or all yellow. The fish were then shown two new images — one with five and one with three squares.

The rules were simple. If the images contained blue shapes, the fish was rewarded with a food pellet if they swam towards the one with five shapes. This indicated they knew one extra shape had been added to the original image. Conversely, if the images contained yellow shapes, the fish received a treat for choosing the image with three shapes. The researchers say over time, six of the eight zebrafish and four of the eight stingrays learned to pick the right color, especially when it came to addition. Like most young children, both species found subtraction to be more challenging.

Blue images stood for addition and yellow for subtraction (Credit: Esther Schmidt/University of Bonn)

The researchers then tested to see if the fish could apply their newly-learned math skills to new tasks they had not been exposed to. "To check this, we deliberately omitted some calculations during training," explains study leader Vera Schluessel. "Namely, 3+1 and 3 -1. After the learning phase, the animals got to see these two tasks for the first time. But even in those tests, they significantly often chose the correct answer."

To make sure the fish were not simply associating blue with more and yellow with less, the researchers set up a new challenge. They presented the animals with the option of adding one or two shapes if shown the blue images and subtracting one or two shapes if shown yellow images. Once again, the fish largely chose the image with one more or one less shape. This proved they had learned the rule of adding or subtracting one.

"So the animals had to recognize the number of objects depicted and at the same time infer the calculation rule from their color," Schluessel says. "They had to keep both in working memory when the original picture was exchanged for the two result pictures. And they had to decide on the correct result afterwards. Overall, it's a feat that requires complex thinking skills."

The fish were rewarded with food if they picked the correct number (Credit: Prof. Vera Schlüsse Et/Al/

The results of the study, published in the journal Nature on March 31, 2022, are particularly surprising given that fish don't have a cerebral cortex. This is the part of the brain that is responsible for complex cognitive tasks in mammals.

But not everyone is convinced of the fishes' math skills. Rafael Núñez, a cognitive scientist at the University of California, San Diego, argues that the fish are not adding or subtracting. Instead, they are selecting the image that looks the most similar to the one they had previously seen. He says, "In the case of blue, the most similar but more, and in the case of yellow, the most similar but less. There's no arithmetic here, just more and less and similar."

However, Schluessel and her team stand by their interpretation. They believe the complexity of the tasks the fish had to solve is a clear indication that they had mastered basic math. Schluessel states, "It's very clearly the plus one or minus one decision, as opposed to just choosing based on more or less." She hopes the findings will encourage "humans to see fish as sentient creatures like us [who] deserve to be treated with more respect."