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Two stingrays are swimming on the blue sea near the underwater rocks and white sand.
Two stingrays are swimming on the blue sea near the underwater rocks and white sand.

Did Researchers Teach Fish To “Do Math”?

Some test fish learned how to how to get food pellets but the difficulty, as so often, lies with interpretation

University of Bonn researchers think that they may have taught fish to count. They tested the fact that many life forms can note the difference in small quantities between “one more” and “one less,” at least up to five items. Not much work had been done on fish in this area so they decided to test eight freshwater stingrays and eight cichlids:

All of the fish were taught to recognize blue as corresponding to “more” and yellow to “less.” The fish or stingrays entered an experimental arena where they saw a test stimulus: a card showing a set of geometric shapes (square, circle, triangle) in either yellow or blue. In a separate compartment of the tank, the fish were then presented with a choice stimulus: two gates showing different numbers of shapes in the same color. When the fish were presented with blue shapes, they were supposed to swim toward the gate with one more shape than the test stimulus image. When presented yellow shapes, the animals were supposed to choose the gate with one less. Correct choices were rewarded with a food pellet. Three of the eight stingrays and six cichlids successfully learned to complete this task.

Sophie Fessl, “Scientists find that two species can be trained to distinguish quantities that vary by one.” at The Scientist (March 31, 2022) The paper is open access.

But were the fish really counting?

Rafael Núñez, a cognitive scientist at the University of California, San Diego, who was not involved in the study, regards the study as “well conducted,” adding that “the problem is the interpretation.” For him, the paper provides information about what he termed “quantical cognition”—the ability to differentiate between quantities—in a 2017 paper. According to Núñez, arithmetic or counting doesn’t have to be invoked to explain the results in the present paper. “I could explain this result by . . . a fish or stingray having the perceptual ability to discriminate quantities: in this case, this will be to learn how to pick, 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.”

Sophie Fessl, “Scientists find that two species can be trained to distinguish quantities that vary by one.” at The Scientist (March 31, 2022) The paper is open access.

The problem, as Núñez says, is with interpretation. Animal cognition researcher Silke Goebel points out that many life forms can distinguish between “more” and “less” in large numbers. Researchers have also found that, so far, infants, fish, and bees can recognize changes in number between 1 and 3. But they don’t get much beyond that.

To say seriously that fish “do math” would, of course, be misleading. Mathematics is an abstract enterprise. The same operations that work for single digits work for arbitrarily large numbers. It is possible to calculate using infinite (hyperreal) numbers. There are imaginary numbers, unexplained/unexplainable numbers, and at least one unknowable number. But we are stepping out into territory here that will not get a fish its food pellet.

Still, it’s a remarkable discovery that many life forms can manipulate quantities in a practical way. Here are some other recent highlights:

● Pigeons can solve the Monty Hall problem. But can you? The dilemma pits human folk intuition against actual probability theory, with surprising results. In one 2010 study, pigeons outperformed humans in the three-doors test but in a second 2012 study, they only beat preschoolers, not college kids.

● The mystery of numeracy: How DID we learn to count? Some animals do rough figuring but only humans actually count.


● Polly wants a… statistician? Michael Egnor: Ethology, the science of animal behavior, offers interesting data but the interpretations are too often witless. Can birds really do statistics? A reporter writing up the results of a study for a popular science magazine seems to think so. The researchers are (appropriately) more cautious. But what are the issues here?

You may also wish to read: Why animals can count but can’t do math. A numerical cognition researcher outlines the differences between recognizing numbers and doing math. Psychologist Silke Goebel says that the cardinality principle — the highest number in a series sums the numbers, takes children some time to learn.

Denyse O'Leary

Denyse O'Leary is a freelance journalist based in Victoria, Canada. Specializing in faith and science issues, she is co-author, with neuroscientist Mario Beauregard, of The Spiritual Brain: A Neuroscientist's Case for the Existence of the Soul; and with neurosurgeon Michael Egnor of the forthcoming The Human Soul: What Neuroscience Shows Us about the Brain, the Mind, and the Difference Between the Two (Worthy, 2025). She received her degree in honors English language and literature.

Did Researchers Teach Fish To “Do Math”?