Clever Hans the Math Horse

In the late 1800s, a German high school mathematics instructor named Wilhelm Von Osten was pushing a few scientific envelopes from his home in Berlin. Among other things, he was a student of phrenology, the now discredited theory that one's intelligence, character, and personality traits can be derived based of the shape of one's head. But it was his keen interest in animal intelligence that would ultimately win him fame.
Von Osten firmly believed that humanity had greatly underestimated the reasoning skills and intelligence of animals. To test his hypothesis, he took it upon himself to tutor a cat, a horse, and a bear in the ways of mathematics. The cat was indifferent to his efforts, and the bear seemed outright hostile, but the arab stallion named Hans showed some real promise. With further tutelage, Hans the horse learned to use his hoof to tap out numbers written on a blackboard. Much to Von Osten's delight, jotting a "3" on the blackboard would prompt a tap-tap-tap from his pupil, a feat which Hans could repeat for any number under ten.
Encouraged by this success, Von Osten pressed his student further. The scientist drew out some basic arithmetic problems on his chalkboard, and attempted to train the horse in the symbols' meanings. Hans had no problem keeping up with the curriculum, and soon he was providing the correct responses to a variety of math problems including basic square roots and fractions. Hans was proving to be a clever horse indeed.