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from c. 3000 BCEReputable source · 2 sourcesWell documented

Mesopotamian Mathematics: Counting in Base 60

The reason a clock has 60 minutes and a circle has 360 degrees traces straight back to Sumer

On the timeline · around from c. 3000 BCE · Sumerian City-States and the Akkadian EmpireSettlement to the First CitiesSumerian City-States and the Akkadian EmpireMesopotamian Mathematics: Counting in Base 605,000 BCE4,500 BCE4,000 BCE3,500 BCE3,000 BCE

Quick facts

Number system
Sexagesimal (base 60)
In use from
c. 3000 BCE
Modern legacy
60 minutes/hour, 360-degree circle
Later development
Adopted and extended by the Babylonians

What happened

Alongside their writing system, walled cities, and irrigation networks, the Sumerians built a number system on base 60, sexagesimal counting, rather than the base 10 most of the modern world uses. Around 2300 BCE, when Akkadian speakers took over the region, they mixed their own methods, including the abacus, with Sumerian arithmetic, and the resulting mathematical tradition persisted for two thousand years. A sexagesimal fraction written as '5; 25, 30' represents a value built from sixtieths and thirty-six-hundredths rather than tenths and hundredths, and Babylonian scribes kept reciprocal tables running into the billions to make sexagesimal division practical for surveying, accounting, and astronomy.

Why it matters

This is not a historical curiosity confined to old tablets: the 60 minutes in an hour, 60 seconds in a minute, and 360 degrees in a circle are all direct inheritances from Mesopotamian base-60 counting, still governing how every clock and compass on Earth is divided today.

How we know

Thousands of surviving Old Babylonian mathematical tablets, including tables of reciprocals, squares, and multiplication tables, are held in museum collections worldwide and have been systematically translated and analyzed by historians of mathematics.

Sources

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Part of a timelineAncient Mesopotamia30 events · The land between the rivers where farming villages became cities, cuneiform became writing, and kings first wrote their laws downView all →