In this introduction to this special issue of Studium devoted to Johannes Hudde, member of an Amsterdam family of patricians, it is argued that most of Hudde’s achievements in mathematics, optics, medicine and philosophy were related to a Cartesian research program that became fashionable in Dutch Republic the 1650s and 1660s. Hudde foremost owes his ‘claim to fame’ to his mathematical discoveries, as published in the Latin translation and elaboration by Leiden Professor Van Schooten Junior of Descartes’ new geometry. However, Hudde is also known as the inventor of the single lens microscope and was also active as an author in the controversy on the Copernic system, which played central role in Descartes’ Natural Philosophy. In 1666 Hudde was also one of Spinoza’s correspondents, asking Spinoza’s about the nature of the Creator, and sharing his knowledge about the construction of telescope lenses. After having become a regent in 1667, Hudde used his scientific skills in several advisory roles, for instance as an Amsterdam Mayor and a Director of the Dutch East India Company. In that capacity he also became a patron of the arts and the sciences.