Science

Plimpton 322

the trigonometry fight
A pocket-size Babylonian tablet of fifteen Pythagorean triples, written around 1800 BC, kept at Columbia University, and the subject of an ongoing academic brawl over whether it is the world's oldest trigonometric table or a teacher's worksheet.
Documented

The documented tablet

Plimpton 322, about 1800 BC and probably from Larsa, was bought by New York publisher George Arthur Plimpton in the 1920s and donated to Columbia in 1936. Neugebauer and Sachs identified its structure in 1945: four columns, fifteen rows, generating Pythagorean triples, integer right triangles, in sexagesimal notation. In 2017 Daniel Mansfield and Norman Wildberger argued in Historia Mathematica that it is a working trigonometric table based on exact ratios rather than angles, potentially more precise for whole-number surveying than modern trig.

Assessment: Fully documented: the object, the math, the 1945 analysis, the 2017 claim. The tablet's purpose, as opposed to its content, is exactly what the fight is about.
Stories

The world's oldest homework

The Assyriological reading, developed by Eleanor Robson: the tablet is a scribal teaching aid for setting and solving reciprocal problems, the triples a byproduct of the exercise list, and its numbers chosen for classroom convenience rather than surveying grandeur. On this view Plimpton 322 is the world's oldest math worksheet, which is arguably more impressive: a civilization that drilled its teenagers on integer triangles.

Assessment: Stories: both readings are published and defended. The homework reading has the advantage of context, hundreds of school tablets; the trig reading has the advantage of the table, which works.
Interesting claims

The reception war

The 2017 announcement drew named return fire: Robson called the trigonometry reading tediously wrong and conceptually anachronistic; Joran Friberg and Christine Proust noted no supporting evidence in any other surviving text; Evelyn Lamb charged in Scientific American that the paper borrowed prestige for Wildberger's fringe rational trigonometry; Alexander Jones called it rather speculative. The authors answered: you do not make a trigonometric table by accident.

Assessment: Interesting: a rare archive file where the dispute itself is the exhibit, both sides named, both published, no verdict. The archive files the tablet under mathematics and the fight under how knowledge polices its borders.
Sources and further reading
  1. the tablet: Columbia University, Plimpton collection, donated 1936; c. 1800 BC, probably Larsa
  2. Neugebauer and Sachs, Mathematical Cuneiform Texts (1945), the triple structure
  3. Mansfield and Wildberger, Historia Mathematica (2017), the exact sexagesimal trigonometry claim
  4. Robson, Words and Pictures (2002) and her 2017 tediously wrong verdict
  5. Lamb, Scientific American (2017); the cautionary responses of Friberg, Proust, and Jones
Worth asking

What does it take to know what a table of numbers is for: the numbers, or everything around the numbers?

Open in the interactive archive
GR8YFILES · competing origin stories, labeled by the strength of their evidence · readers 14+