The history of mathematics can be traced to the very origins of humanity and perhaps even earlier. While modern human ability to understand mathematics is a certainty, studies have shown that many animal species also have a degree of mathematics ability, chiefly the ability to count (or at least to differentiate between large groups from small ones). This very basic counting ability is important for nearly every aspect of animal survival, from developing effective hunting strategies to monitoring the whereabouts of offspring. It is most conceivable that many animals of the past, even back to the age of dinosaurs, had similar counting abilities.

Because human mathematics stretches well into prehistoric history, the knowledge of its origins and initial applications is mostly built on speculation. It is reasonable to assume that basic counting was facilitated by use of the hands, with each finger representing a numeral. In this way, humans could more accurately keep track of a count and perform simple addition and subtraction. When early humans began using notches or marks to represent numerals, they not only created the first mathematical records, but they also discovered a method for tracking larger numbers. By the time agriculture had been invented, it is a well-held idea that humans had already developed the skills to add, subtract, multiply and divide.

The Ishango bone is considered by many to be the earliest pure mathematic artifact ever recovered. It was discovered around 1960 on the border of Zaire and Uganda by the Belgian geologist Jean de Heinzelin. Carbon-dating has indicated that the origins of this artifact date to approximately 20,000 B.C.E., a full 10,000 years before the commonly accepted origin of agriculture. The significance of this small animal bone is a set of notches that are inscribed upon it which partly correlate with the prime number sequence.

The Ishango Bone, courtesy of the Royal Belgian Institute of Natural Sciences

The Ishango bone is approximately 10 cm long, and it has a piece of quartz crystal imbedded in one end, indicating that it was perhaps used for religous or ceremonial purposes. There are groups of notches of varying numbers that are organized into 3 columns. The following numbers series are in each column:

COLUMN 1: 11, 13, 17, 19
COLUMN 2: 3, 6, 4, 8, 10, 5, 5, 7
COLUMN 3: 11, 21, 19, 9

The first column contains part of the prime number sequence. The second column features two sets of numbers (3 & 6 and 4 & 8) that could represent multiplication by 2, and one set of numbers (10 & 5) that relates to division by 2. Lastly, the first and third columns both add to 60, while the second column adds to 48. Both 48 and 60 are divisible by 12. These trends in these notches have led some to believe that the Ishango bone was a primative counting or computational tool. Critics state that mathematical trends are not significant enough to be sure. Their argument is strengthened by the absense of any other archaelogical discoveries that indicate an understanding of the prime number sequence before the Classical Greek period.

Although considerable debate surrounds the actual implications Ishango bone, the notion that early humans understood complex mathematics is also supported by the Lascaux cave paintings in France that were created 10,000 years earlier. Depicted on the cave walls are several sets of markings that indicate a basic human understanding of the 29-day lunar cycle. In one instance there are 14 forteen dots followed by an empty square, which experts believe represent the 14 days that the moon is visible in the night sky and the day that it disappears. Other markings nearby seem to resemblance constellations, such as the Pleiadies.

Lascaux Cave Painting, 14 dots and one empty square


Lascaux Cave Painting, 29 dots representing the lunar cycle
images courtesy of the WebExhibits website

A later example of early mathematic knowledge is the famous Stonehenge in southern England. Archaeologists beleive the origins of Stonehenge date back to 8000 B.C.E. when a series of holes were dug to support timber posts aligned in an east-west orientation. Later additions to the site included a circular ditch, and 56 holes thought to have supported a circle of wooden posts. Stonehenge was continually developed over thousands of years, eventually featuring a circle of gigantic stones that aligned with both the solstice and equinox points. Humans had used mathematical analysis and tools to predict the changing seasons from the angle of sunlight.

Stonehenge at sunset

As humans began to grasp the concepts of mathematic order, they gained an incresing understanding of the world around them. Impulse and instinct gave way to logic and reasoning, and humanity began to differentiate itself from the animal world in a very distinct way.