A numerical cognition researcher outlines the differences between recognizing numbers and doing math:
It was the development of symbol systems such as the decimal system that enabled the development of complex mathematical theories but they were thousands of years in the making. And they have led us into some remarkable abstract worlds.
There is a current conflict among researchers as to whether our number sense is biological or cultural (nature or nurture). But the conflict appears to miss the point: Elaborate number sense depends on the ability to abstract. If that ability is biological, where exactly is it? If it is cultural, it is an iteration of the ability to abstract.
When comparing the way animals and small children handle numbers, we should keep in mind that animals do not have the ability to abstract. Children do have the ability to abstract but it is latent. Language skills (and the attendant math skills) take years to acquire from nothing. The remarkable thing is that almost all children do it and no animals do.News, “Why animals can count but can’t do math” at Mind Matters News (August 4, 2021)
Note: Psychologist Silke Goebel says that the cardinality principle — the highest number in a series sums the numbers, takes children some time to learn.
You may also wish to read: Is our “number sense” biology, culture — or something else? It’s a surprisingly controversial question with a — perhaps unsettling — answer. Mathematics supports a dualist view of the universe. Both concrete and abstract, depending. Both the Chimp Chocolate Stakes and Chaitin’s Unknowable Number. (Denyse O’Leary)
The mystery of numeracy: How DID we learn to count? Some animals can do rough figuring but only humans count. It goes beyond counting. Numbers lead to a world of wonders, only apprehended by abstraction.