A major development of the period after the Agriculture Revolution was the inventions ways more complex than tallies to record numbers, leading eventually to numeration systems.

The Greeks place the origin of their mathematics in Egypt, but it seems that Egyptian mathematics was limited to practical mathematics.

The Egyptian has a decimal numeration system, but the place value was not clear; they used fraction, which they always decomposed into the sums of unit fractions with 1 as numerator.

In Mesopotamia the early ways of recording numbers seem to have led directly to writing. The earliest evidence of written texts at the end of the fourth millennium BC consists of records of names as well as commodities and their quantities.

It is not clear how writing arose in other parts of the world, but numerals probably preceded words in eastern Asia and in the America as well.

By 4000 years ago, positional notation was in use in Mesopotamia, with separate developments by the Chinese and the Maya some hundreds or thousands of years later.

In Mesopotamia, the base 60 system of numeration led to a mathematics capable of solving quadratic equations.

The Mesopotamian kept exact records of astronornical observation for long period of time.

Geometric designs are even older than the first recorded numbers, but it is a big step from craving a triangle to measuring it and computing its area.

Systems of measurement, like numeration systems, appear to have arisen from trade needs. Later, something closer to true geometry also progressed in both Egypt and Mesopotamia, with improvements in the ability to measure area and volume and the discovery of the Pythagorean theorem.

They used a sexagesimal system of numeration with place value and also used sexagesimal fractions; however they lacked a cipher to denote zero until the 4th century BC.

Toward the end of the period, symbols for zero as a placeholder were introduced.

The prehistoric period ended in Egypt and Mesopotamia in 3000 BC, and a little later in the valleys of the large rivers in India and China.

By the century, the Mayas in central America also possessed a numeration system,. with base 20.

*Brief History of Mathematics*