sourced story
c. 1900-1600 BCE (Old Babylonian period)Reputable source · 2 sourcesWell documented

The Babylonians Use the Pythagorean Relationship a Millennium Before Pythagoras

A clay tablet in the British Museum solves a right triangle problem a thousand years before the Greek who gets the credit

On the timeline · around c. 1900-1600 BCE (Old Babylonian period) · Ancient MathematicsAncient MathematicsThe Babylonians Use the Pythagorean Relationship a Millennium Before Pythagoras2,000 BCE1,750 BCE1,500 BCE1,250 BCE1,000 BCE

Quick facts

Key tablets
British Museum tablet, YBC 7289, Plimpton 322
Period
Old Babylonian Empire, 1900-1600 BCE
YBC 7289 value
Sexagesimal approximation of root 2 (1,24,51,10)
Gap before Pythagoras
Roughly 1,000 years

What happened

Four surviving Babylonian tablets from the Old Babylonian period, which flourished between 1900 and 1600 BCE, demonstrate a working knowledge of the relationship between the sides of a right triangle that would later be named Pythagoras's theorem. One tablet preserved in the British Museum poses and solves the problem directly: 4 is the length and 5 the diagonal, what is the breadth. Its worked solution runs, 4 times 4 is 16, 5 times 5 is 25, you take 16 from 25 and there remains 9, 3 times 3 is 9, 3 is the breadth. A second tablet, the Yale Babylonian Collection's YBC 7289, carries a diagram of a square with a diagonal drawn in and the value 1,24,51,10 written beside it, a sexagesimal approximation of the square root of 2 accurate to several decimal places. A third, known as Plimpton 322, lists number triples in which, in every row, the square of one number minus the square of a second is itself a perfect square, the defining property of Pythagorean triples.

Why it matters

The theorem carries Pythagoras's name because Greek tradition credited him with a general proof, not because he was first to notice the relationship. The Babylonian tablets show the numerical pattern was already in practical use for construction and land problems a thousand years before Pythagoras was born, which is why historians treat the theorem's naming as a case of proof, not discovery, being what the Greeks contributed.

How we know

The tablets are physical cuneiform artifacts held in museum collections, including the British Museum and the Yale Babylonian Collection, and their mathematical content was deciphered and analyzed by Otto Neugebauer and Abraham Sachs, whose reading of Plimpton 322's number columns is the basis for the modern understanding of the tablet.

Sources

See something wrong? . Corrections with a source get fixed fastest.

Part of a timelineHistory of Mathematics26 events · A number system built for taxes, a theorem older than the man it's named for, a proof too long for a margin, and an infinity too big to countView all →