This chapter looks at the mathematization of the study of nature by focusing on how practical mathematicians from the sixteenth century onward understood mathematics as primarily devoted to solving problems through mathematical construction. This constructive understanding of the nature of mathematics is then related to the double movement of physicalizing mathematics (giving physical interpretations to mathematical constructions) and mathematizing physics (understanding physics as basically involving the solution of problems). The work of seventeenth-century thinkers like Galileo, Descartes, and Mersenne is used to further illustrate these ideas, which led to the establishment of mathematical physics as characterized by its problem-solving nature.

This contribution will consider early modern and analytic descriptions of sundials as ‘cosmographic instruments’, and consider the advantages and disadvantages of classing dials, globes, and certain paper volvelles as ‘cosmographic’ rather than simply ‘mathematical’ instruments. It will thus contribute to historiographical debates about how historians of scientific instruments and mathematical practice can best acknowledge and make use of period descriptions of instruments and disciplines without either overwriting them with our own categories, on the one hand, or appropriating them in such a way as to disguise genuine variations in terminology across different languages, cultures, and settings. The discussion will connect to broad classes of objects in the Whipple collections, but also to specific objects such as the ‘Regiomontantus-type’ dial and the ‘Castlemaine’ or ‘English’ globe, as well as drawing on some examples from the Whipple Library’s rare book collections.