The use of sexagesimal place value notation (hereafter SPVN) is one of the most striking features of cuneiform mathematics. The earliest attestations of a systematic use of SPVN in cuneiform sources are found in a small set of mathematical texts dated to the Ur III period (ca. 2112to 2004. Besides this mathematical corpus, traces of numbers written in positional notations have been found in some Ur III administrative texts. Just a few dozen tablets, among tens of thousands of known Ur III administrative documents, exhibit such numbers noted in positional notation. Moreover, such numbers noted in positional notation appear almost only as a kind of graffiti in the margins. This chapter focuses on these scanty 'marginal numbers'. Marginal numbers in Ur III administrative texts testify to diverse practices with positional notations and sexagesimal factors in an administrative context, and, in this way, exemplify different 'cultures of computation and quantification' in the Ur III period. Through a close analysis of the positional notations found in Ur III administrative texts, we detect a diversity of graphical systems for what was considered until now as a uniform notion of SPVN. We show that these graphical systems vary according to the operations (multiplication, reciprocal, addition, subtraction), the contexts (administrative or mathematical), and the archaeological sites considered in this study (Umma, Girsu, Puzriš-Dagan, Nippur). Our goal is to show that this diversity of notations reflects different computational methods.

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Israel, a small, perfectly intact stamped bulla dating to the Persian period was found. The bulla originally sealed a papyrus document. Thanks to its excellent preservation, it is possible to identify a series of key aspects of the object: the motif and type of seal used to stamp it, the way the bulla was created, and even the way in which the original document was folded and tied. These details allow us to identify the probable origin and date of the seal and contextualize its associated bulla within the site of Qedesh. This evidence, in conjunction with information from the late 5th century b.c.e. Murašû archive in Nippur, allows us to suggest that the seal's user may have been a person with Tyrian ties-perhaps a member of the Tyrian diaspora-who acquired his seal in Nippur and traveled to Qedesh where he used it to seal a document.