TMH 05, 065

~2400 BCE·Early Dynastic·P020479

About this tablet

This is one of the oldest mathematical problem texts known, written at Nippur in southern Iraq around 2500 BCE. A scribe sets a geometry exercise: a rectangular field is 67½ rods long and must have an area of exactly 1 iku (100 sar); how wide must it be? The answer given—1 rod, 5 cubits, 2 spans, 3⅓ fingers—is arithmetically exact, showing that Early Dynastic scribes could already divide area by length using a multi-level system of length units. The final word may be the name of the student or teacher, Il-il.

Plain-language summary by the engine — meant as a doorway into the literal translation below.

Written in modern English

A field is 67½ rods long. Its width is to be such that the field covers exactly one iku. The width works out to 1 rod, 5 cubits, 2 spans and 3⅓ fingers. Signed (or attributed to): Il-il. A worked school problem in field measurement.

A modern paraphrase of the literal translation — same content, contemporary voice.

Translation — our engine

Our engine

High confidence

67½ nindan, the long side (length), the short side (width): (so that the area is) 1 iku of field. (Result:) 1 nindan, 5 cubits, 2 šu-du-a (spans), 3 fingers and ⅓ finger. Il-il (?).

Our translation engine — Fable 5. Reads the photo, translates the cuneiform, and writes a plain-language interpretation. See methodology for limits.

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Transliteration

1(gesz2@c)# 7(asz@c) 1/2(asz@c) us2 nindax(DU)
sag 1(iku@c) GAN2
1(asz@c) nindax(DU) 5(disz@t) kusz3 2(disz@t) szu-du3-a# 3(disz@t) szu-si 1/3(asz@c) szu-si
il il

Scholarly note

Catalogue entry from CDLI (ED IIIb (ca. 2500-2340 BC)) — TMH 05, 065. No scholarly translation has been published; the transliteration is from the ATF (CDLI's Atf-Friendly format).

Attribution

Image: Hilprecht Collection, University of Jena, Germany (P020479) — Photo via Cuneiform Digital Library Initiative. source
Translation excerpted from engine:claude-fable-5 (2026-07-12/v7-evolved).

Related tablets

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~1800 BCE

Plimpton 322

Whatever its purpose, this single tablet shows that Babylonian mathematicians, working in base-60, had an arithmetic understanding of right triangles a millennium before Pythagoras was born.