From the dawn of civilization, humankind has needed to count and measure. Even the earliest civilizations developed effective and efficient number systems. Ancient mathematics is surprisingly sophisticated and, in many cases, quite similar to the mathematics used today.

Tally Bones

An early evidence of a "mathematical system" was found on a bone discovered in the Czech Republic. It dates from about 30,000 B.C.E. The bone contains fifty-five individual tally marks, divided into eleven groups of five marks each, just as tally marks might be grouped today. There is a dividing line, separating the first twenty-five marks from the remaining twenty, that makes totaling the tally marks even easier. No one knows just what the bone's owner was counting, but it may have been domestic animals such as sheep or some type of game animal.

Another ancient tally bone is the Ishango Bone, found...