I say it's no accident that the first society to advance in ASTRONOMY was the first to advance in ALGEBRA: BABYLONIA. We learn this in Mathematical Thought From Ancient to Modern Times, v. I, pp. 8-10, Morris Kline.Babylon was situated in the area known as Mesopotamia (Greek for "between the rivers"). Mesopotamia was in the Near East in roughly the same geographical position as modern Iraq. Two great rivers flow through this land: the Tigris and the Euphrates. Along these two rivers lay many great trading cities such as Ur and Babylon on the Euphrates. Most of central Mesopotamia would have been desert except in the vicinity of the two rivers: the Tigris and the Euphrates which carry water to the area. These rivers formed the huge alluvial plain on which the agricultural prosperity of the region was built.
It was this area where Babylon was built. To the west of Mesopotamia stretches the Arabian desert. It is inhabited by nomads: the forerunners of the modern Bedouin. These nomads played a significant part in the history of Mesopotamia and of Babylon. Northern Mesopotamia encompasses the foothills of mountains of eastern Anatolia.
This is the area of Assyria. It has a wetter environment. This means crops could be grown partially without irrigation. Most of central Mesopotamia would have been desert except in the vicinity of the two rivers: the Tigris and the Euphrates which carry water to the area. These rivers formed the huge alluvial plain on which the agricultural prosperity of the region was built. It was this area where Babylon was built.
To the west of Mesopotamia stretches the Arabian desert. It is inhabited by nomads: the forerunners of the modern Bedouin. These nomads played a significant part in the history of Mesopotamia and of Babylon. To the east of Mesopotamia lay the land of Elam. Elam lay in present west Iran on the Zagros mountains. Central and southern Mesopotamia: the area south of modern Baghdad forms the area called Babylonia though it incorporates many other cities as well as Babylon. It was here where the conditions were correct because it had one commodity in huge amounts: clay.
Babylonian priests made ASTRONOMY in effect THE FIRST OF THE SCIENCES by devoting a period of 10,000 years to its development. This Near-Eastern record is unequaled in "Western" Science. Some historians of science date it back to Galileo, Tycho Brahe, Kepler and Newton. which would be less than 500 years. Even if we "date Rationality" back to the days of Thales and Pythagoras, this is only 2500 years -- one fourth the Babylonian record. And this record was made possible by advances in ALGEBRA.
Says Kline, "The Babylonians were able to solve special problems involving five unknowns in five equations. One problem, which arose in connection with the adjustment of astronomical observations, involed ten equations and ten unknowns, mostly linear.... Problems leading to a cube root also occurred. The modern formulation of such a problem would be: 12x = z, y = x, xyz = V, where V is some unknown volume. To find x here we must extract a cube root. The Babylonians calculated this root from [cube root tables they compiled]. They also did compound interest problems that called for finding the value of an unknown exponent." (LOGARITHMS! which we also take up elsewhere.)Today, we use SYMBOLIC ALGEBRA to avoid confusion with the (English) language discussion of the mathematics. The ancient Babylonians sometimes achieved this effect by using Sumerian-Akkadian words.
Some of this "Babylonian algebra" was needed to treat inheritance.
A good article on Babylonian mathematics is found online at www.math.tamu.edu/~don allen/history/babylon/babylon.html.
Repeating my initial statement: It's no accident that the first society to advance in ASTRONOMY was the first to advance in ALGEBRA: BABYLONIA (as implied in Mathematical Thought From Ancient to Modern Times, v. I, pp. 8-10, Morris Kline).The Babylonian priests studied the successive subevents of criticlal astronomical events. Then they studied these subevents back to their "beginning", to learn how to predict them. They did this with movements of the planets, with phases of the moon and sun, with eclipses of the moon and sun. Their predictions wre good except for those of the sun.
The "exercise" of solving algebraic equations (tracing back in arithmetic) prepared them for the "work" of predicting astronomical events, and the "exercise" of astronmy prepared them for the "work" of algebra. And they did all this thousands of years before the beginnings of "western science".