The article describes the social and cultural roles of Mesopotamian mathematics and the interplay of these roles with such patterns of mathematical thought as can be traced through the sources; it covers the period from the first formation of a genuine state, shortly after the mid-fourth millennium b.c.e., until the end of the Old Babylonian epoch, c. 1600 b.c.e. The picture presented is a historical reconstruction; little of what it asserts can be found directly in a single source. Full documentation would ask for a bibliography longer than the article. This being both impossible and without purpose, some publications of importance are listed in the concluding "Bibliographic Remarks" (Section 4); in these, further bibliography can be found. The description of the many interconnected aspects of Mesopotamian mathematics evidently has no implications for how mathematics should be taught. It is meant as inspiration for how mathematics educators and didacticians think "about" mathematics, and to give input to the teaching "about" mathematics.