Guess what? Fish can do basic math! Children’s news article

Researchers from the University of Bonn taught fish to do basic math. (Dr. Vera Schlüssel/University of Bonn)

Your quiet, expressionless goldfish may appear unconscious to you and its environment. But the aquatic vertebrates are smarter than they look. Previous studies have shown that fish learn quickly, can to hold onto information for up to five months, and even recognize their owner from a group of humans.

Some fish species even have mastered tool use – a skill previously believed to be possesses only by humans and primates like chimpanzees. Now a new study affirms that fish can be trained to do basic calculations.

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

The rules were simple. If the pictures contained blue shapes, the fish was rewarded with food tablet if they swam towards the five-formed one. This indicated that they knew an additional shape had been added to the original image. Conversely, if the pictures contained yellow shapes, the fish received a reward for choosing the three-shape picture. The researchers say that over time, six of eight zebrafish and four of 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 hard.

The blue images represented addition and the yellow represented subtraction. (Esther Schmidt/University of Bonn)

The researchers then tested to see if the fish could apply their newly acquired math skills to new tasks to which they had not been exposed. “To verify this, we deliberately omitted certain calculations during the training”, explains Vera Schluessel, responsible for the study. “Namely, 3 + 1 and 3 -1. After the learning phase, the animals were able to see these two tasks for the first time. But even in these tests, they significantly often chose the correct answer.”

To make sure fish didn’t simply associate blue with plus and yellow with minus, the researchers set a new challenge. They introduced the animals to the option add one or two shapes if blue images are displayed and subtract one or two shapes if yellow images are displayed. Again, the fish largely chose the image with a plus or minus shape. This proved that they had learned the rule of adding or subtracting one.

“Then the animals had to recognize the number of objects represented and at the same time deduct the slide rule from their color,” explains Schluessel. “They had to keep both in working memory when the original image was swapped for the two resulting images. And they had to decide the correct outcome afterwards. Overall it’s a feat it requires complex thinking skills.”

The fish were rewarded with food if they picked the correct number. (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 have no cerebral cortex. It is the part of the brain that is responsible for complex cognitive tasks in mammals.

But not everyone is convinced fish math skills. Rafael Núñez, a cognitive scientist from the University of California, San Diego, argues that fish neither add nor subtract. Instead, they select the image that most closely resembles the one they saw previously. He says, “In the case of blue, the most similar but more, and in the case of yellow, the most similar but less. There is no arithmetic here, just more and less and similar.”

However, Schluessel and his team maintain their interpretation. They believe the complexity of the tasks that the fish had to solve is a clear indication they had mastered basic math. Schluessel states: “It is very clearly the plus one or the minus one decisioninstead of just choosing based on more or less.” She hopes the results encourage “humans see fish as sentient creatures like us [who] deserve to be treated with more respect.”


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