Historically, the concept of number was first associated with integers, before expanding to encompass many other categories, from rational numbers to real numbers and then to complex numbers. Each of these "inventions" marked a decisive step forward for mathematics and its applications. It is a sweeping epic that continues to this day! Here, we shall consider only the earliest appearances of numbers and their spread around the Mediterranean basin: Mesopotamia, Egypt, Greece and Rome.
Early attempts --------------------
"Numbers," the German mathematician Richard Dedekind wrote in his 1893 work Was sind und was sollen die Zahlen?, "are free creations of the human mind. They serve as a means of apprehending the diversity of things more easily and more precisely." It was precisely to represent the reality of the world that early peoples engaged in numerical activity, albeit in rudimentary forms. As early as the Paleolithic period, some thirty thousand years ago, we find the first collections of objects that can be described as "tally sticks," as well as the earliest marks on pieces of wood or bone that may have represented quantities. Objects to be counted were also represented not by sticks but by "bullae." These hollow clay balls could contain tokens, also made of clay, symbolizing the quantities to be assessed. Checking them meant breaking open the bullae, so toward the end of the 4th millennium BC, people began inscribing symbols on them. Why not, then, flatten the bullae into tablets and engrave the same information on them? The idea of writing numbers was born.
Saying and writing numbers ------------------------------
The oldest documents attesting to genuine numeral systems, originating in the valleys of the Nile, Tigris and Euphrates, are hieroglyphs representing numbers as high as 1,000,000. They were found in the tomb of King Narmer, of Egypt's First Dynasty, dating from around 3000 BC: strokes for units, a basket handle for 10, a coil of rope for 100, a lotus flower for 1,000, a raised finger for 10,000, a stylized bird for 100,000 and a god for 1,000,000. Ancient Egyptian numerals formed a juxtaposition system that gave pride of place to 10 and its multiples, making addition and subtraction straightforward.