When Christian Agrillo runs number-related experiments in his lab, he wishes his undergraduate subjects good luck. For certain tests, that’s about all he says. Giving instructions to the people would be unfair to the fish.

Agrillo, of the University of Padua in Italy, is finishing up several years of pitting humans against fish in trials of their abilities to compare quantities. He can’t, of course, tell his angelfish or his guppies to choose, say, the larger array of dots. So in recent tests he made the bemused students use trial and error too.

“At the end, they start laughing when they find they are compared with fish,” he says. Yet the fish versus humans face-offs are eye-opening comparisons in his search for the deep evolutionary basis of what has blossomed into human mathematics. If it turns out that fish and people share some idiosyncrasies of their number sense (like spidey sense, except focused on quantities rather than danger), those elements might in theory date from a common ancestor more than 400 million years old. Comparisons of animals’ mental powers are “the paleontology of cognition,” Agrillo says.

No one seriously argues that animals other than people have some kind of symbolic numeral system, but nonhuman animals — a lot of them — can manage almost-math without numbers.

“There’s been an explosion of studies,” Agrillo says. Reports of a quantity-related ability come from chickens, horses, dogs, honeybees, spiders, salamanders, guppies, chimps, macaques, bears, lions, carrion crows and many more. And nonverbal number sensing, studies now suggest, allows much fancier operations than just pointing to the computer screen that shows more dots.

News stories on this diversity often nod to the idea that such a broad sweep of numberlike savvy across the animal tree of life could mean that animals all inherited rudiments of quantification smarts from a shared ancestor. Some scientists think that idea is too simple. Instead of inheriting the same mental machinery, animals could have just happened upon similar solutions when confronting the same challenge. (Birds and bats both fly, but their wings arose independently.)

Chasing down those deep origins means figuring out how animals, including humans too young or too rushed, manage quantitative feats without counting. It’s not easy. Putting together what should be a rich and remarkable story of the evolution of nonverbal number sense is just beginning.