Sumerian·Book

Reading track · 3,557 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.

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. In the month of Ab (month V), Adad raised his voice: the sky was darkened, the heaven rained down, lightning flashed, / waters were withheld in the spring(s). / 1. When Adad cried out on a cloudless day, / it is the 'daummattu'-omen: ditto. Famine will be in the land. / Regarding the unfavorable body[-omen]: / the king, my lord, should not speak from his heart [about this], / illness — that year is it. / As many of the people as are sick — / all [will have] well-being. / It will turn around, and the king, my lord — / he who fears the gods, / day and night the gods will pray for him / …

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

SAA 04 002. Will Mugallu ...? (PRT 089) [military and political]

(Beginning destroyed) (1) From [this] day, [the ...th day of this month ..., to the ...th day of the coming month, the month ... of this year], (2) for [these ... days and nights, the term stipulated for the performance of (this) extispicy — within this stipulated term, will ...] (3) [will] either [......] (4) or Mu[gallu ......] (Break) (r 1) that city, [......]. (r 2) in [......] (Break) (e. 1) [...... Third exti]spicy. (e. 2) [...... Marduk-šu]mu-uṣur.

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

SAA 04 003. Will the Chief Eunuch Drive Mugallu away from a Fortress of Melid? (AGS 055) [military and political]

(1) Šamaš, great lord, [give me a firm positive answer] to what I am [asking you]! (2) Mugallu and the troops [of ..., (allied) with him], who have now [set up ca]mp aga[inst ..., a fortress] of the city Melid — (4) [will the chief eunuch of Esarhaddon, ki]ng of Assyria, and [his] troop[s and army who] have gone against him, [drive Mugallu and his troops away] from the w[all of ..., and will he] aban[don the w]all? (9) Does your great divinity kn[ow it? Will he who can see, see it? Will he who can hear, hear it]? (10) Disregard the (formulation) of [to]day's case, [be it good, be it faulty].…

Religion & MythAstronomy & Mathematics

Browse all 2,410 astronomy & mathematics tablets of this period in the catalogue →