Two wedges, one big idea
Cuneiform means “wedge-shaped”, and the name comes from the marks pressed into damp clay with a cut reed stylus. Babylonian scribes, working in a tradition inherited from the Sumerians, wrote numbers using only two basic marks: a vertical wedge for one and a corner-shaped (chevron) wedge for ten. Combining them gave every number from 1 to 59. For example, 23 was two chevrons and three vertical wedges, grouped neatly together.
The striking part is what happened next. Rather than inventing a new sign for 60, scribes started a new position. The same vertical wedge that meant 1 in the first place meant 60 in the second. This is a place-value system, and its base is 60. Texts from the Old Babylonian period, roughly the early second millennium BCE, already show it in full use, though its roots lie earlier in Sumerian practice.
Reading a number
Each position held a value from 0 to 59, and each step to the left multiplied the value by 60. The number we write as 75 is one 60 and fifteen ones. A scribe wrote one vertical wedge, left a small gap, then a chevron and five vertical wedges. The number 3,661 breaks into 1 times 3,600, 1 times 60 and 1 times 1, so it would be three single wedges with gaps between them.
Because the system uses the same signs at every place, the neat grouping of wedges within a place and the spacing between places did a lot of work. Careful scribes kept the spacing clear. Tablets with cramped writing can be hard for modern readers to interpret.
The missing empty-place marker
This is where the problem of the empty place appears. In a system like ours, 3,601 needs a zero to show that the middle position is empty. For a long time Babylonian scribes had no such sign. A scribe might leave a slightly wider gap, but a gap is not always visible, and it could not be used at the end of a number. As a result, the same pattern of wedges could stand for 1, 60 or 3,600, and a reader had to infer the size from context, such as what was being counted.
In later centuries, in the last part of the first millennium BCE, a separate sign appears in some texts, usually drawn as two slanted wedges. It marked an empty position inside a number. Scholars generally agree that it was an empty-place marker rather than a number in the modern sense of zero: it did not stand alone as a quantity, and it was apparently not used at the end of a number. The full story of how zero developed is told in the history of zero, which involves later developments elsewhere.
Fractions in the same system
The positional idea carried over to fractions. Positions to the right of a marked point stood for 1/60, 1/3,600 and so on, much as decimal fractions extend to tenths and hundredths. Modern scholars write these numbers with a semicolon between the whole part and the fraction, for example 1;30 for one and a half. Scribes themselves did not write a mark for the point, so context decided again.
A well-known clay tablet in the Yale collection, catalogued as YBC 7289, gives an approximation of the square root of 2 as 1;24,51,10. Converting it, 1 plus 24/60 plus 51/3,600 plus 10/216,000 comes to about 1.41421296, which is very close to the true value of roughly 1.41421356. The tablet shows how comfortable trained scribes were with long positional fractions.
Why 60?
No one knows for certain why base 60 was chosen. A common point made by historians is that 60 divides evenly by many numbers: 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. That makes halves, thirds, quarters and fifths easy to handle, which is helpful in a world of shares, rations and measures. Some scholars suggest the system grew from blending two earlier counting habits, though the evidence is limited and the story is debated. The broader pattern of the Mesopotamian sexagesimal system and its links with measuring, trade and astronomy is a topic in itself. Comparing it with duodecimal counting, which also favours easy division, shows a similar logic at a smaller scale.
What survived
Babylonian astronomers’ base-60 fractions were taken up by Greek astronomers and passed on to later scholars. The result is still with us in the division of the hour into 60 minutes and the minute into 60 seconds, as well as in the 60 minutes of arc in a degree. The 360 degrees of a circle are often connected with this tradition too, although the reasons for choosing 360 are not fully settled and other explanations connected to calendar systems have been proposed.
A comparison with other place-value systems
Babylon was not the only civilization to arrive at position-based numbers. Chinese rod calculation was decimal and used blank spaces, the Maya used a base-20 variant with a dedicated zero shell, and Indian mathematicians combined decimal place value with a true zero. Maya numerals show an independent solution to the same empty-place problem. The Babylonian case stands out for its age and for how long it worked without the sign that now seems indispensable.