It used to happen every day at the London Zoo: Out came the dainty table and chairs, the china cups and saucers — ­afternoon tea, set out for the inhabitants of the ape enclosure to throw and smash. It was supposed to be amusing — a ­comic, reckless collision of beasts and high ­culture. But, as Frans de Waal explains in “Are We Smart Enough to Know How Smart Animals Are?,” apes are actually innovative, agile tool-users. For example — one of many examples — wild chimps in ­Gabon have been observed employing five different tools, in a methodical sequence, to break open beehives, pry the chambers apart, scoop out the honey and convey it to their mouths. Not surprisingly — to de Waal, at least — the apes in London quickly mastered the teacups and teapot too. They sat there civilly, having tea.

“When the public tea parties began to threaten the human ego, something had to be done,” de Waal writes. “The apes were retrained to spill the tea, throw food around, drink from the teapot’s spout,” and so on. The animals had to be taught to be as stupid as we assumed they were. But, of course, the fact that they could be taught to be stupid is only more perverse evidence of their intelligence.

For centuries, our understanding of animal intelligence has been obscured in just this kind of cloud of false assumptions and human egotism. De Waal, a primatologist and ethologist who has been examining the fuzzy boundary between our species and others for 30 years, painstakingly untangles the confusion, then walks us through research revealing what a wide range of animal species are actually capable of. Tool use, cooperation, awareness of individual identity, theory of mind, planning, metacognition and perceptions of time — we now know that all these archetypically human, cognitive feats are performed by some animals as well. And not just primates: By the middle of ­Chapter 6, we’re reading about cooperation among leopard coral trout. (The book’s main weakness is that de Waal has too much evidence, from too many corners of the animal kingdom, to convince us with; eventually, it feels a little repetitive — we’re not at all surprised that the bonobo knows to look in the stupid tube for the piece of food.)

Frankly, it all deals a pretty fierce wallop to our sense of specialness. And it can provoke some desperate resistance. De Waal quotes one American psychologist, insistently holding the line of our humanness at our ability, even as children, to work together toward a shared goal: “It is inconceivable that you would ever see two chimpanzees carrying a log together,” the psychologist says. But then, 25 apes at a Dutch zoo prop a tree trunk against the wall of their enclosure, climb out and raid the restaurant. What is true, it becomes clear, is that you’ll never see animals doing such intelligent things if you smugly refuse to look for them, or — and this is de Waal’s real point — if you don’t know how to look.