My thesis examines Thomas Hobbes's attempt to develop a mathematical account of nature. I argue that Hobbes's conception of how we should think quantitatively about the world was deeply indebted to the ideas of his ancient and medieval predecessors. These ideas were often amenable to Hobbes's vision of a demonstrative, geometrically-based science. However, he was forced to adapt the ancient and medieval models to the demands of his own thoroughgoing materialism. This hybrid resulted in a distinctive, if only partially successful, approach to the problems of the new mechanical philosophy.

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published_or_final_version / Mathematics / Master / Master of Philosophy

Problem solving is a central activity of mathematics and has been throughout its history. Recognizing the problem of problem solving, however, seems to be less explicit in the historical record. In studying three principal contributors to the study of problem solving-Rene Descartes, John Dewey, and George Polya-I have found that problems arise in two broad categories. Mathematics itself generates more mathematical problems, and problems embedded in a wider context can generate mathematics. Recognizing a mathematical problem in a rich context-problem finding-has received much less attention. John Dewey recognized the importance of problem finding and emphasized its role in problem solving. Descartes and Polya spent less time on problem finding, Polya the least of all. / Department of Mathematical Sciences