Arithmetic was the first and most basic branch of math to emerge in the earliest societies. The more primitive the society, the closer representation of its number system tended to sets of straight lines. The earliest writings of the Mesopotamians and Egyptians from 3400 bce showed vertical straight lines to signify quantities.
In the 3rd century BCE the Hindus made a most important advance in numeral designation. A straight line represented the number 1, but distinct symbols were used for greater quantities.
Meanwhile, the Etruscan civilization was still using tally sticks. These evolved into Roman numerals, with a notch for 5 (V) and a crosscut for 10 (X).
Roman numerals were similar to the Babylonian numeral system, which first appeared ~3100 BCE. The Babylonians had the first known positional numeral system, in which the value of a particular digit depended upon the digit itself and its position within a number.
The Babylonians understood the notion of nothingness, but it was seen as a lack of a number, not a number unto itself. The Babylonians used a space to mark the nonexistence of a digit at a certain place.
In calculating Jupiter’s orbit, Babylonian astronomers came close to discovering calculus. Their mathematical techniques ~350 BCE were long thought by historians to have developed only in the 14th century.
The Babylonians developed abstract mathematical, geometrical ideas about the connection between motion, position and time that are so common to any modern physicist or mathematician. ~ German astroarchaeologist Mathieu Ossendrijver
The Arabs learned of the Hindu numbering system a millennium after its invention, in the 8th century ce. It first appeared in European arithmetic in 976, using the 9 digits: 1, 2, 3, 4, 5, 6, 7, 8, 9.
Though a tremendous step forward, the lack of a digit for zero precluded important arithmetic operations. Subtraction was problematic if not impossible.