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What Do You Need a Mathematician For? Martinus Hortensius ’s “Speech on the Dignity and Utility of the Mathematical Sciences ” (Amsterdam 1634)

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Send submissions to David E. Rowe, Fachbereich 17--Mathematik, Johannes Gutenberg University, D55099 Mainz, Germany. I n early modem Europe the term mathematical sciences was used to describe those fields of knowledge that depended on measure, number, and weight--reflecting the much-quoted passage from the Wisdom of Solomon 11, 20: "but thou hast ordered all things in measure and number and weight." This included astrology and architecture as well as arithmetic and astronomy. These scientiae or disciplinae mathematicae were generally subdivided into mathematicae purae, dealing with quantity, continuous and discrete as in geometry and arithmetic, and mathematicae mix tae or mediae, dealing not only with quantity but also with quality--for example astronomy, geography, optics, music, cosmography, and architecture. The mathematical sciences, then, consisted of various fields of knowledge, often with a strong bent toward practical applications. These fields became independent from one another only through the formation of scientific disciplines from the late 17th to the early 19th century, i.e., in the aftermath of the Scientific Revolution. One of the important preconditions for this transformation was the rapidly changing status of the mathematical sciences as a whole from the mid-16th through the 17th century. The basis for the social and epistemological legitimation of the mathematical sciences began to be laid by mathematicians and other scholars in the mid-16th century. Their strategy was essentially twofold: in the wake of the 16th-century debates about the certainty of mathematics and its status in the hierarchy of the scientific disciplines (quaestio de certitudine mathematicarum [Mancosu 1996; Remmert 1998, 83-90; 2004]), the mathematicae purae were taken to guarantee the absolute certainty and thereby dignity of knowledge produced in all the mathematical sciences, pure and mixed; the mathematicae mixtae, on the other hand, confirmed the utility of this unerring knowledge. Throughout the 17th century, the legitimation of the mathematical sciences was pursued in deliberate strategies to place the mathematical sciences in the public eye. These strategies often involved the use of print media in one way or another-through mathematical textbooks, practical manuals, books of mathematical entertainments, edi-