 If Hobbes’ mathematical and natural-philosophical endeavors failed to be taken seriously by his contemporaries near the end of his life, what purpose is served by understanding these failed  attempts?[1]  Apart from interest in them on their own terms as episodes in the history of science and philosophy, there are several reasons why we may find these areas of Hobbes’ thought valuable for study. First, Hobbes himself understood his political philosophy, or as he called it “civil philosophy”, to be a science capable of demonstration. Thus, understanding his general views about the nature of scientific demonstration promises to shed light on the way in which he saw civil philosophy as scientific. Second, Hobbes understood natural-philosophical explanations in physics as needing to make use of mathematical principles to count, as he says, as “true physics”. This may seem like a banal claim to a twenty-first century reader, but it was not so to many in the sixteenth and seventeenth centuries. Hobbes’ natural philosophy thus situates him within the shift from qualitative to quantitative physics. Third, Hobbes’ conflicts with the Royal Society show us not only his views of the role of experimentation but also contextualize the rise of experimentalism. After discussing Hobbes’ criteria for scientific knowledge, this entry will address each of these three areas.