**THE ORIGIN OF OUR NUMBER SYMBOLS**

Concepts for the numbers 1, 2, 3, 4, 5, 6, 7,...can be traced back to the origins of human history. Representations of these numbers must have arisen naturally as soon as humans started to count objects, animals, or members of a clan. While finger-counting might have been the first counting method in history, recording the result requires the use of a permanent representation of the corresponding number, such as putting down a mark for each object counted. Representing a certain number by a corresponding number of marks (for example, notches on a wooden stick or on a bone) will eventually lead to the invention of numerals. Tally marks are the most primitive and oldest numeral system (see image below). They are still used today for counting or tallying the score in a game.

Since the representation of any number is obtained from that of its predecessor by simply adding one mark, tally marks are very convenient for documenting ongoing results. Historically, they constitute the origin of all numeral systems, and their usage dates back to the Upper Paleolithic age (roughly 50,000 to 10,000 BCE). References to tally marks can also be found in much more sophisticated numeral systems of ancient cultures, and the Japanese symbols for 1, 2, and 3 bear this resemblance still today (see image below).

The introduction of numerals for the quantities represented by 1,2,3,4,5,6,7,...is an almost inevitable consequence of the act of counting. We then could say that the positive integers were not “developed” or “invented”; rather, they were “discovered.” The German mathematician Leopold Kronecker (1823–1891) is often quoted with the phrase, “God made the natural numbers; all else is the work of man.” Here, the term “natural number,”1 referring to an element of the set N={1, 2, 3,...}, was introduced in 1888 by the German mathematician Richard Dedekind (1831–1916).