Abstract

This essay continues the reconsideration of the thought of Jacob Klein now under way, largely by situating one key phase of it in the context of Edmund Husserl’s first writings on arithmetic. Klein’s most important work is Greek Mathematics and the Origin of Algebra. In its first part, Klein undertakes the retrieval of the ancient account of number, setting forth the understanding of ἀριθμόσ articulated by the Pythagoreans, Plato, and Aristotle. This retrieval is in part meant to pave the way for the work of the second half of the book, in which Klein sets out the seventeenth-century transformation of the ancient understanding of number in symbolic forms of reckoning, such as algebra and analytic geometry. Klein believes that this transformation lies at the basis of our modern forms of knowledge, and in particular modern mathematical physics.