The question
How did people write numbers with only two symbols?
The short answer
Babylonian scribes combined a sign for 1 and a sign for 10 to write every number from 1 to 59, then used place value in base 60. It was one of the first positional number systems.
What science knows
Historical FactBy the Old Babylonian period, around 1800 BCE, scribes wrote numbers positionally in base 60: 1,1 meant 60 + 1 = 61, just as our 11 means 10 + 1.
For centuries there was no zero, so an empty place had to be inferred from context. A placeholder sign appears in texts from the last centuries BCE, though never at the end of a number.
The pattern
Established MathematicsThe tablet YBC 7289 shows a square with its diagonal marked 1;24,51,10 in base 60. That is 1 + 24/60 + 51/3600 + 10/216000 ≈ 1.414213, within about a millionth of the true value of √2.
What is still uncertain
Mixed EvidenceWhy base 60 was chosen is uncertain: its many divisors, the merging of earlier counting systems, or finger-counting methods have all been proposed.
Why humans find it interesting
Historical FactGreek astronomers adopted base 60 for fractions and angles, which is why we still count 60 minutes, 60 seconds and 360 degrees.
CUE perspective
CUE PerspectiveBase 60 is an ancient idea that became everyday mathematics: every clock still runs on it.
For CUE it is a good example of how a number system shapes the way people experience time.