How Babylonian numbers work
The Babylonians wrote with two wedge shapes pressed into clay: a vertical wedge for 1 and a corner wedge for 10. Up to nine ones and five tens combine into a digit from 1 to 59. Digits are then placed side by side, each worth 60 times the one to its right: ones, sixties, 3,600s (60 × 60), 216,000s and so on.
Each group uses 1-59 expressed with these two symbols. Groups are positional (×1, ×60, ×3600…). For example, 𒐜 𒐐𒐚 is two groups: 8 and 56, so the value is 8 × 60 + 56 = 536. 𒌋𒌋𒁹𒁹𒁹 is a single group of two tens and three ones, 23.
| Number | Base 60 | Cuneiform |
|---|---|---|
| 1 | 1 | 𒐕 |
| 10 | 10 | 𒌋 |
| 23 | 23 | 𒎙𒐗 |
| 59 | 59 | 𒐐𒐝 |
| 60 | 1,0 | 𒐕 ␣ |
| 61 | 1,1 | 𒐕 𒐕 |
| 100 | 1,40 | 𒐕 𒐏 |
| 536 | 8,56 | 𒐜 𒐐𒐚 |
| 1,000 | 16,40 | 𒌋𒐚 𒐏 |
| 1,823 | 30,23 | 𒌍 𒎙𒐗 |
| 3,600 | 1,0,0 | 𒐕 ␣ ␣ |
| 2,026 | 33,46 | 𒌍𒐗 𒐏𒐚 |
| 86,400 | 24,0,0 | 𒎙𒐘 ␣ ␣ |
No zero, at first
Babylonian numerals had no symbol for zero until very late (c.300 BC), which could cause ambiguity in some numbers. A scribe left a small gap for an empty place, and readers used context to tell 1 from 60 or 3,600. Later texts used a separator sign of two slanted wedges inside a number, but never at the end, so the system never fully fixed the ambiguity.
Why 60?
The Babylonians likely chose 60 because it has many divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60), making fractions much easier than base 10. This system was so practical that we still use it today: 60 seconds per minute, 60 minutes per hour and 360 degrees in a circle.
Babylonian Mathematical Achievement
Babylonian scribes were highly sophisticated mathematicians. The Plimpton 322 tablet (c. 1800 BC) lists Pythagorean triples, showing knowledge of the theorem over 1,000 years before Pythagoras. They could calculate square roots, solve quadratic equations and model astronomical cycles, all using base 60. The tablet YBC 7289 gives the square root of 2 as 1;24,51,10 in base 60, correct to about six decimal places.