Old Babylonian mathematics: base-60 and Plimpton 322

Date

c. 1800–1600 BCE

Category

Science, technology & invention

Region

Mesopotamia (Iraq)

Era

Ancient Civilizations

Significance

Scribes of the Old Babylonian period developed a sophisticated place-value mathematics built on a sexagesimal (base-60) system, a choice whose highly divisible base (with factors 2, 3, 4, 5, 6, etc.) simplified work with fractions and survives today in our 60 seconds, 60 minutes, and 360 degrees of a circle.

School and reference tablets preserve multiplication and reciprocal tables, methods for solving quadratic and linear problems, area and volume calculations, and approximations of the square root of two accurate to several sexagesimal places. The famous tablet Plimpton 322 lists fifteen rows of numbers forming Pythagorean triples, demonstrating knowledge of the relationship between the sides of right triangles more than a millennium before Pythagoras and reflecting an advanced grasp of number theory or proto-trigonometry. This computational tradition underpinned later Babylonian astronomy and influenced Greek and ultimately modern mathematics.

Empires active in c. 1800–1600 BCE

• Old Babylonian Empire
  1894 BCE – 1595 BCE
• Bactria-Margiana Archaeological Complex (Oxus Civilization)
  2250 BCE – 1700 BCE
• Elamite Kingdom
  2700 BCE – 539 BCE
• Xia Dynasty
  2070 BCE – 1600 BCE

Related science, technology & invention events

• Proto-Sinaitic inscriptions: the first alphabetic writing
  c. 1850 BCE
• Development of the Linear A Script in Minoan Crete
  c. 1800 BCE
• The Taung Child and the naming of Australopithecus africanus
  1924–1925 CE (fossil c. 2.8 million years old)
• Edwin Smith Surgical Papyrus, earliest known treatise on trauma
  c. 1600 BCE
• Rhind Mathematical Papyrus copied by the scribe Ahmes
  c. 1650 BCE
• Sintashta culture and the first spoke-wheeled war chariots
  c. 2100–2000 BCE

Further reading

A Little History of Science

The wider story

A Little History of Science

William Bynum

Warm, jargon-free tour of discovery from Babylonian stargazers to the genome.

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