What is a Number?

Abstract

Roughly 37,000 years ago, for reasons not completely understood, one of the first humans scratched 55 tally marks into a wolf bone (now called the Lebombo bone after the mountain range in which it was found). Perhaps they were tallying kills, marking time as a primitive calendar, or merely expressing an early interest in number theory as a hobby. Regardless of the intent, other bone artifacts from the Paleolithic era show a clear progression of this system, moving from individual marks to groups of marks organized in a way similar to the modern system of tallying in groups of five. This progression from tally marks to groups is the first of countless small steps in the evolution of human understanding of numbers. Further milestones tie inexorably with the needs of culture, and interlace with other developmental breakthroughs in society and technology. For example, agricultural advancements allowed the cultivation of much larger quantities of crops and the congregation of much larger populations, which necessitated the ability to describe and record significantly larger numbers than is feasible using tally marks.