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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.
The Egyptian system for doing this, hieroglyphs, is an additive system, meaning that each symbol represents a set value and a number is represented by a collection of symbols whose sum has the desired value. By introducing new symbols for powers of 10 as the need arose, they could abstractly express any natural number.
What is a Number?
A Quick Survey of the Last Two Millennia
Number Theory in Z Beginning
Number Theory in the Mod-n Era
Gaussian Number Theory: Z½i of the Storm
Number Theory, from Where We R to Across the C
Cyclotomic Number Theory: Roots and Reciprocity
Number Theory Unleashed: Release Zp!
The Adventure Continues
Appendix I. Number Systems