Sumerian·Book

Reading track · 3,470 tablets

The Sky & the Number

From base-60 arithmetic to the first mathematical astronomy — the corpus's longest intellectual project.

Every time you read a clock or a compass rose you are using Mesopotamian mathematics. The sexagesimal system — counting in sixties — grew out of Sumerian metrology, and its convenience (sixty divides evenly by 2, 3, 4, 5, 6, 10, 12, 15, 20, 30) kept it alive in astronomy long after every other trace of cuneiform culture had died. Sixty minutes, 360 degrees: the tablets' fingerprint on the modern world.

Old Babylonian schools taught a mathematics of real sophistication: tables of reciprocals and squares, quadratic problems, and computations that presuppose the rule we call the Pythagorean theorem — the tablet Plimpton 322, on most readings, organizes what are effectively Pythagorean triples a millennium before Pythagoras. Whether it is trigonometry, number theory, or teacher's problem-sets remains honestly disputed; what is not disputed is the competence.

Astronomy began not as science but as statecraft. The sky was a text the gods wrote, and the omen series Enuma Anu Enlil — thousands of entries interpreting eclipses, planetary stations, and halos — made its reading a profession. Assyrian kings kept staffs of celestial scholars whose reports survive in the hundreds; our corpus is unusually rich in them. Out of that anxious watching grew something without precedent: centuries-long observational archives (the astronomical diaries kept at Babylon from the eighth century BCE), and eventually mathematical models predicting lunar and planetary phenomena with striking accuracy. When Greek astronomy rose, it rose on Babylonian data and Babylonian parameters — a debt Greek astronomers themselves acknowledged.

Anchor tablets below are selected automatically from the corpus — the richest readable witnesses of this subject in each era — and new ones surface as the translation engine works through the backlog. Every translation is labeled with its source; engine translations carry their confidence level on the tablet page.

2900 – 2334 BCE

Early Dynastic

~2400 BCE · HS 0815 — Hilprecht Collection, University of Jena, Germany

TMH 05, 065
“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 (?).”

Source: engine:claude-fable-5 (2026-07-12/v7-evolved)

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Browse all 4 astronomy & mathematics tablets of this period in the catalogue →

2334 – 2154 BCE

Akkadian Empire

~2270 BCE · SM 1998.04.011 — Harvard Museum of the Ancient Near East, Harvard University, Cambridge, Massachusetts, USA

HSS 10, 024
“1. 30 (nindan) — the width(s) being equal; 2. 120 (nindan) — the length(s) being [equal]; 3. its area: 2 bur3 of field — 4. Itur-EN[...]. 5. 20 (nindan) — the width(s) being [equal]; 6. [...] 60 (nindan) — the length(s) being [equal]; 7. Da-[...]. 8. 20 (nindan) — the width(s) being equal; 9. 120 (nindan) — the length(s) being equal; 10. its area: 2 bur3 of field — 11. Išbu. 12. 1 bur3 of field, (at) the levee of Dada.”

Source: engine:claude-fable-5 (2026-09-20/v8-evolved)

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Browse all 3 astronomy & mathematics tablets of this period in the catalogue →

2000 – 1600 BCE

Old Babylonian

The mathematical golden age: school tablets with reciprocal tables, geometric problems, and calculations that command respect from modern mathematicians.

~1800 BCE · Plimpton Collection, Columbia University

Plimpton 322
“A table of fifteen rows, each giving three numbers in sexagesimal (base-60) corresponding to Pythagorean triples — right triangles whose sides are whole numbers.”

Source: Robson (2002); Mansfield & Wildberger (2017)

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.

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Browse all 954 astronomy & mathematics tablets of this period in the catalogue →

911 – 609 BCE

Neo-Assyrian

The observatory as an organ of state: celestial omen reports and letters from scholars stream to Nineveh, interpreting every eclipse and planetary approach for the king's safety.

~655 BCE · Reconstructed composite — see ORACC entry for manuscript witnesses

Ashurbanipal 084
“(i' 1') [it (an eclipse) lasted like this the entire day, (thus signifying) the end of the reign of the king of the land] Elam [(and) the destruction of his land]. (i' 2') [“The Fruit” (the god Sîn) revealed to me his decision], which cannot be chang[e]d. [At that time, a mishap befell him]: His lip became paralyzed and his eye became small. (i´ 5´) [He was not ashamed by thes]e [measures] that the deities Aššur and Sîn, [Šamaš, Bêl (Marduk)], Nabû, Ištar of Nineveh, [Ištar of Arbela, Ninurta], Nusku (and) Nergal had taken against him, [(and) he mu]stered his troops. (i' 8') [During the month…”

Source: Novotny, J. & Jeffers, J. 2018–. The Royal Inscriptions of Ashurbanipal (668–631 BC), Aššur-etel-ilāni (630–627 BC) and Sîn-šarra-iškun (626–612 BC), Kings of Assyria. RINAP 5. University Park, PA: Eisenbrauns. https://oracc.museum.upenn.edu/rinap/rinap5/Q003783/

Links a lunar eclipse, divine omens, and the Elamite king's physical affliction — paralyzed lip, diminished eye — to justify Ashurbanipal's campaign: a rare royal text weaving extispicy logic directly into annalistic narrative.

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~670 BCE·Neo-AssyrianOur engine

SAA 08 001. Thunder in Ab, King Ill (RMA 257) [weather]

(1) If in Ab (month V) Adad thunders, the day becomes cloudy, it rains, (and) lightning flashes: the waters will decrease at the source. (4) If Adad shouts on a cloudless day: there will be darkness — variant: famine — in the land. (6) Concerning this ill health, the king, my lord, should not worry (lit. 'should not speak from his heart'). (8) It is a disease of the season; all the people who are sick will get well. (11) Moreover, the king, my lord, who is one who reveres the gods — day and night he prays to the gods … (The text continues but the remainder is not preserved in the given transli…

Religion & MythAstronomy & Mathematics
~675 BCE·Neo-AssyrianSAA 4

SAA 04 017. Cimmerian and Cilician Invasion of ... (PRT 043) [military and political]

(Beginning destroyed) (r 0) [Let them be taken out] and put aside! (r 1) [I ask you, Šamaš, great lord, whether the troops of the C]immerians, [or the troops of the ...ians, or the troops of the] Cilicians [......] (r 4) [...... will go] to the district of [......] (r 5) [......] who inhabit the land of U[...] (r 6) [......] will wage [war ...].[Be present] in [this ram, place (in it) a firm positive answer], favorable designs, [favorable, propitious] omens [by the oracular command] of your great divinity, [and may I see (them)]. (Rest destroyed)

Religion & MythAstronomy & Mathematics
~675 BCE·Neo-AssyrianSAA 4

SAA 04 022. Fragment Similar to Nos. 20-21 (AGS 087) [military and political]

(Beginning destroyed) (1) honestly [...... speak friendly words of] reconciliation [with Esarhaddon, king of Assyria, keep the treaty, and do] what[ever is pleasing] to [Esarhaddon, king of Assyria]? (4) [Be present in] this ram, [place (in it) a firm positive answer, favorable designs], favorable, [propitious] omens [by the oracular command of your great divinity, and may I see (them)]. (6) [May (this query) go to] your great [divini]ty, [O Šamaš, great lord, and may an oracle be given as an answer]. (7) [......] It has a 'station.' The 'pa[th' ......]. (8) [...... The right of the 'finger']…

Religion & MythAstronomy & Mathematics

Browse all 2,323 astronomy & mathematics tablets of this period in the catalogue →