Zero forced philosophers to treat nothing as a value
Numbers let us count, measure, order, and label—from natural 1, 2, 3 onward to zero, negatives, rationals, reals like √2 and π, and complexes built with a square root of −1. Accepting zero meant equating nothingness with a usable quantity, a philosophical jolt as much as a notational one.
Spoken number words and written numerals name the same objects, eleven versus 11, and since nobody can memorize endless symbols, numeral systems organize them; the decimal Hindu–Arabic system writes any non-negative integer with ten digits. Numerals do many jobs, counting a collection, labelling like a phone number, ordering like a serial number, or coding like an ISBN, and everyday speech rarely separates a numeral from the number it stands for.
Nineteenth-century algebra added structures that share some properties of numbers. Some carry the name, such as p-adic and hypercomplex numbers, and some do not, a matter of convention rather than of mathematics. Arithmetic, the study of calculating with numbers, can also mean number theory, the study of their properties.
Far earlier, bones such as the Lebombo specimen, about 43,000 years old, and the Ishango bone, somewhere between 22,000 and 30,000 years old, bear cuts some historians read as tallies of days, lunar cycles or animals, though that interpretation is disputed. A basic sense of quantity is shared with other species and probably predates language. Tallies lack place value, which makes large numbers clumsy, yet they count as the first abstract numeral system.
The earliest unambiguous numbers are Mesopotamian, a base-60 system from around 3400 BC, and place value appeared in the third millennium BCE. The oldest known base-10 system comes from Egypt around 3100 BC. A Babylonian tablet from 1900–1600 BC puts the ratio of a circle's circumference to its diameter at 3.125, possibly the oldest approximation of π.
Source: Number
