How did ancient numeral systems evolve?

Numeral systems have progressed from early fingers and tally marks over 40,000 years ago into sophisticated glyphs and notations capable of efficiently representing any number. The earliest known clear notations for numbers emerged in Mesopotamia roughly 5,000 to 6,000 years ago. Ancient systems varied widely in structure, with some systems like Roman, Greek, and Egyptian numerals lacking an official representation for zero.

What we know

• Numeral systems have progressed from fingers and tally marks used more than 40,000 years ago to sets of glyphs representing numbers efficiently. [2]
• The earliest known clear notations for numbers emerged in Mesopotamia about 5,000 or 6,000 years ago. [2]
• Roman, Greek, and Egyptian numerals all lack an official representation of the number zero. [3]
• Attic numerals used by ancient Greeks were a decimal system based on multiples of powers of ten. [5]

Where to go next

• a case in pointWhat are Attic numerals?
• how it workedHow do numeral systems work?
• whenWhen did tally marks start?
• the bigger pictureWhat is the history of mathematics?
• whereHow did ancient Mesopotamia record numbers?
• an unexpected connectionWhy do different numeral systems use the same symbol sequences for different values?The exact same sequence of symbols can represent entirely different numbers depending on the underlying system, such as '11' meaning eleven in decimal but three in binary.

Sources

• [1]history of writing ancient numbers (Wikidata Q12702745) · CC0 1.0
• [2]History of ancient numeral systems · CC BY-SA 4.0
• [3]Numeral system · CC BY-SA 4.0
• [4]List of numeral systems · CC BY-SA 4.0
• [5]Attic numerals · CC BY-SA 4.0