Introduction
 
Have you heard the story about the world's smartest animal? In the early 1900s, a horse named Hans answered questions. Not just your average questions--but challenging math problems! What if your pets were that smart? Your dog could help with math homework by barking correct answers. Woof! Or your cat by swishing her tail. Seems too good to be true, right? Yet every day, crowds in Germany gathered to see Hans, Wilhelm von Osten's brainy horse, answer math problems.
   Von Osten was a retired schoolteacher. He spent years treating Hans like one of his students. Except instead of giving grades, he would reward the horse with bread and carrots. Von Osten taught Hans colors, the alphabet, and how to tell time. And, of course, he taught him math.
   Von Osten wanted people to see what Hans could do. So, he and his horse put on shows for the public. Von Osten would ask the audience for questions. Then Hans would tap out the answer with his hoof. Sometimes the questions involved counting, like how many women in the crowd were wearing a hat. Other questions asked Hans to add or subtract two numbers. He was even asked questions with fractions. For example, 2∕5 + 1∕2. Hans would tap his answers, first the numerator, then the denominator, and was almost always correct. Wunderbar!
   Newspapers nicknamed the horse Clever Hans, and he and von Osten became worldwide sensations. Even the New York Times declared: "BERLIN'S WONDERFUL HORSE; He Can Do Almost Everything but Talk." Although many experts trusted the horse's abilities, not everybody believed in Clever Hans. A psychologist named Oskar Pfungst was certain there was more to the story. He decided to test Hans.
   Pfungst knew that if Hans were really solving problems, he would tap correctly even if nobody else knew the answer ahead of time. So, Pfungst designed an experiment where only the horse knew the entire question. Pfungst would whisper a number in Hans's ear so quietly that no one else could hear it. Next, von Osten, the horse's owner, would do the same with another number. Then, Hans was asked to add the two numbers together. Nobody knew the answer until Hans finished tapping. Finally, Pfungst and von Osten said their numbers out loud. They repeated this test thirty-one times. Hans was right only three times. Then they repeated the experiment. But this time the men told Hans their numbers out loud so everybody could hear them. Hans was right
twenty-nine out of thirty-one times. There was the catch. For Hans to tap correctly, the people around him needed to know the answer first.
   Was Hans reading people's minds? Of course not! He wasn't doing calculations, either. Pfungst realized von Osten was the one doing the math. Hans simply tapped his hoof until he saw von Osten signal him to stop. But it was not a trick. Von Osten didn't know he was signaling the horse. Without realizing, he would move his head slightly when Hans reached the correct number of taps. When Hans saw this tiny movement, he would put his hoof back on the ground.
   All those years of schooling had not taught the horse math. They had taught him how to read a person's body language. No matter who asked the question, Hans could read their movement. Hans was certainly clever--just not in the way his fans and the newspapers had thought.
   After learning about Clever Hans, you probably have doubts about any animal doing math. It's just too complicated, right? Surely only humans can understand numbers. Many people used to agree. Number skills were once believed to be uniquely human and beyond the brainpower of any other creature. Now we know that's simply not true.
   For years, scientists have studied what animals know about numbers. But after Clever Hans, scientists have been more careful about how they ask their questions. They don't want to be fooled again. Instead, they design controlled experiments to reveal how animals think. Scientists make sure not to give any clues about the correct answer. And guess what? They have discovered that even though Clever Hans couldn't do math, other animals can.
   Some animals have mind-boggling number skills. We know that fish can tell large numbers from small ones. Hyenas count. African grey parrots use symbols to represent numbers. Chimpanzees do addition. And honeybees understand zero. Amazing! How do they do it, and why have they developed these skills? Read on to discover all about the mathematical abilities of animals.

---

Excerpted from Calculating Chimpanzees, Brainy Bees, and Other Animals with Mind-Blowing Mathematical Abilities by Stephanie Gibeault
All rights reserved by the original copyright owners. Excerpts are provided for display purposes only and may not be reproduced, reprinted or distributed without the written permission of the publisher.