NEW DIRECTIONS IN MESOPOTAMIAN MATHEMATICS DUNCAN J. MELVILLE Abstract. We survey recent developments and new directions in Mesopotamian mathematics over roughly the last decade. These are brief, informal, uncorrected notes to accompany my talk at the Joint Math Meetings in San Antonio, Sunday, January 11, 2015. A more de- veloped preprint will be forthcoming. Comments and corrections are welcome. Contents 1. Introduction 1 2. Access and Dissemination 2 3. New Sources 3 4. The Nippur Curriculum 3 5. Problems and Scholars 5 6. Distinctions in Space and Time 7 7. The Third Millennium 8 8. Connections and Comparisons 9 Appendix: Periodization 10 References 11 1. Introduction The basics of Mesopotamian mathematics: the use of the sexagesimal system; the use of tables; the interest in word problems and their algorithmic solutions, are now well-known. In the late 80s and 90s there were major developments in un- derstanding of mathematics from earlier than the Old Babylonian period (approx- imately 1900–1600 BC) (see [26]), and in Jens Høyrup’s geometrical interpretation of arithmetical procedures. Høyrup’s work culminated in his book, Length, Widths, Surfaces published in 2002 [14]. We shall assume these ideas have now been widely disseminated and consider developments since that point. For other surveys on the evolution of Mesopotamian mathematics and its historiography, see in particular Høyrup’s masterly Changing Trends paper from 1996 that covers the field from the 1930s up to the time of writing [13], and for a general survey of developments since the publication of Neugebauer and Sachs’ Mathematical Cuneiform Texts [25] in 1945 see my preprint After Neugebauer [23]. There is inevitably a certain amount of overlap between this current paper and [23], but the focus is somewhat different and I have tried to minimize repetition. Date : January 10, 2015. 1991 Mathematics Subject Classification. 01A17. Key words and phrases. Mesopotamian mathematics, Babylonian mathematics. 1