Since the early days of cuneiform studies it was known — and hardly considered amazing, given among other things the importance of measure and number in the Old Testament — that the Babylonians were in possession of numbers and metrology; since the later nineteenth century the existence of a place value system with base 60 (the “sexagesimal” system) and its use in Late Babylonian mathematical astronomy were also well-known facts. During the following few decades, finally, a number of Babylonian and Sumerian mensuration texts were deciphered. By the end of the 1920s it was thus accepted that Babylonian mathematics could be spoken of on an equal footing with Egyptian mathematics, as indirectly acknowledged by Raymond C. Archibald when he added a section on Babylonian mathematics to his exhaustive bibliography on ancient Egyptian mathematics.
KeywordsStandard Interpretation Mathematical Text Problem Text Technical Terminology Procedure Text
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- 1.The main part of the bibliography is in [Chace et al. 1927: 121–206]; an unpaginated supplement with the section on Babylonian mathematics is in [Chace et al. 1929]. The state of the art of the early twentieth century is illustrated by the treatment of the Babylonians in [Cantor 1907: 19–51]; a thorough coverage of publications from the period 1854–1929 that somehow deal with the topic (even when as a secondary theme only) can be found in [Friberg 1982: 1–36] — a recommendable annotated bibliography also for later decades, from which the (much less extensive but still annotated) chapter on the subject in [Dauben 1984: 37–51] is drawn.Google Scholar
- 2.In 1985 I was told by Kurt Vogel about the intense amazement with which theGoogle Scholar
- 6.Many recent publications introduce a further distinction and write sign names in large capitals when used in isolation or within genuine Sumerian texts, and use small capitals for all logograms used within Akkadian texts, irrespective of whether the corresponding Sumerian value is identified or not. The reason for this convention is that this Sumerian value will only in exceptional cases have corresponded to the intended pronunciation of the words; in the context of the present argument, however, I have found it more adequate to facilitate the identification of terms that possess a Sumerian interpretation — not because the use of Sumerian terms implies general continuity with third millennium mathematics, but in order to provide a basis for distinguishing cases where the evidence suggests continuity from those where the use of Sumerian appears to be an Old Babylonian construction.Google Scholar
- 8.It is generally not possible to determine the length of vowels from the syllabic writing; whether one or the other spelling is correct thus depends on the root from which the word is derived.Google Scholar
- 12.Actually, this was not the “algebra” Neugebauer had put into them; but most readers understood as interpretations the symbolic computations by means of which Neugebauer had established the correctness of the Babylonian solutions. His conjecture about the possible function of logograms notwithstanding, Neugebauer remained an agnostic as to the interpretation of the mathematical thinking of the Babylonians, and argued explicitly for agnosticism. That he shared the numerical understanding wholeheartedly and without hesitation illustrates how natural it wasGoogle Scholar
- 13.For several of these categories and names I am indebted to Jöran Friberg — after two decades of discussion I am not sure exactly which, but most will be his. The notion of “series texts” goes back to Neugebauer.Google Scholar