THE EARLY USE OF NUMBERS

From 8000 B.C. to 3300 B.C. in lower Mesopotamia, hunter-gatherers, or mesolithic people, used clay tablets to assist in counting and distributing their numerical and bookkeeping information. This early math gave rise to the subsequent form of Sumerian writing.

Interestingly enough, accounting clearly predated other forms of writing, making accounting and the use of numbers the oldest documented profession.

In 6000 B.C., the early brewing of beer took very strict attention to measurements, according to early beer-brewing traditions and rituals.

From 3300 to 2050 B.C., the Sumerians of Mesopotamia used pictographs before they used cuneiform markings in their early math. Our contemporary expression of circular or angular measurement and time is based on the Sumerian legacy of sixty degrees, minutes, and seconds. The word “dozen” derives from the Sumerian word meaning “a fifth of sixty.”

In 3100 B.C., near what is now Salisbury, England, there was another significant mathematical expression, in the first phase of building Stonehenge. It was a large circular ditch, with fifty-six pits around it. It represented the number that is double the number of days in a sidereal month… so it might be that the pits were related to the days in the month.

From 2700 to 2200 B.C., the Egyptians of the Old Kingdom Era developed a 365-day calendar which, of course, we’re using to this day. Pyramids near Cairo, that are thought to have been built between 2600 and 2500 B.C., are an early indication of the understanding of geometrical and mathematical abilities.

About 2100 B.C., near Salisbury, England, the second phase of building Stonehenge happened. It was important because a thirty-five-ton stone was carefully placed so that it marked the rising of the sun on the summer solstice, June 21.

According to the American astronomer Gerald S. Hawkins, Stonehenge was used to predict the summer and winter solstices, the vernal and autumnal equinoxes, and eclipses of both the moon and sun. In addition, an assortment of other information pertaining to the sun and moon could be predicted with remarkable accuracy. Hawkins concluded that Stonehenge served as a means of predicting the positions of the sun and moon relative to the Earth, and thereby called the seasons and perhaps also acted as a simple daily calendar.

From 2000 to 1700 B.C., the Babylonians of Mesopotamia inherited the cuneiform number system from the Sumerians. It had been used to record interest payments, deposits and loans. These people understood the principle of the Pythagorean Theorem, and might even solve algebraic problems.

Around 2000 B.C., the Hittites invaded the Middle East, calling cuneiform their own, after learning it from the Hurrians.

Also around 2000 B.C., the Mayans of Central America used a numerical system that was very sophisticated, and comprised a symbol for zero.

About 1900 B.C., the Egyptians fleshed out their numerical system with an understanding of base ten, which used additive symbols.

The Greek mathematician Euclid, who lived around 300 B.C., led the classic work, Elements, which is a comprehensive treatise on mathematics. It is thirteen volumes on these subjects as plane geometry, proportion in general, the properties of numbers, incommensurable magnitudes, and solid geometry. Euclid made several original discoveries in the theory of numbers. Even today we use a modified version of Euclid’s Elements. It forms the basis of high school instruction in plane geometry.