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This book argues that we can only understand the transformations of nature studies in the early modern period, often called the Scientific Revolution, if we take seriously the interaction between those who know by doing (practitioners or craftsmen) and those who know by thinking (scholars or philosophers). Mathematical practitioners played an essential role in this transformation; this book examines the role of mathematics and mathematical practice on the changing ideology and methodology of science. We first set out the problematic, examining the argument from both sides: articulating Zilsel, Cormack identifies those dimensions of practical mathematics that showed up as important aspects of ‘the new science’; Schuster focuses on the new scientists as selective appropriators of ideas, values and practices originally embedded in practical mathematics. This book furthers the debate about the role of mathematical practice in the scientific revolution in four ways. First, it demonstrates the variability of practical mathematicians and of their practices. Second, it argues that in spite of this variability, participants were able to recognize the family resemblance between the different types. Third, differences and nuances in practical mathematics typically depended on the different contexts in which it was practiced. Fourth, this book shows that diverse and new historiographical approaches to the study of practical mathematics should be considered.