Francisco Sánchez and the Quaestio de certitudine mathematicarum: A sceptical approach

•Scepticism philosophical thought also questioned the status of mathematical certitude.•Christopher Clavius stressed the anti-sceptical function of mathematics, and Francisco Sánchez offered a refutation in a letter of 1589.•Artifacts and senses support the certainty of mathematics, according to Sánchez.•Conjectural empiricism could be applied to mathematical knowledge.•Clavius’sProlegomenaare crucial to analyzing Sánchez's position on the certainty of mathematics. In this paper I analyse Francisco Sánchez’s role in the Quaestio de certitudine mathematicarum debate. Despite some studies on the philosophical and medical scepticism of Sánchez and, his extant letter with Christopher Clavius, a participant in the debate, we have few analyses about Sánchez’s position regarding the certainty of mathematics. Sánchez discussed some problems that Clavius analysed in his Prolegomena to propose an empirical basis for mathematics through a questioning of its certainty. I will trace the conceptual connections between Sánchez’s 1589 letter to Clavius and the Quaestio debate, to introduce Sánchez’s sceptical approach to analysing the certainty of mathematics.