MUCH · How Much Is It? The Pre-Modern Philosophical Outset of the Algebraic Variable

MUCH delves into the crucial and still vastly understudied interplay between mathematics and philosophy in the 14th c., shedding light on pre-modern questions that resonate with ongoing concerns on mathematical knowledge, abstraction, and reality. What is the link between calculation and the conception of a quantified item? How do we think of a quantifiable unknown in equations? The case of 14th-c. Italy is key to grasp the emergence of such problems, their development and cascade-effect on European mathematics of the following centuries. MUCH unravels the feedback loop between philosophical notions and processes involved in mathematical practices, prominently algebra: quantum, inquantum, and variable in equations. Rooted in pre-modern notions of extension, quantum represents an existing quantified substance, while the variable (i.e., unknown value) stands as a neither continuous nor discrete thing that can be quantified. Inquantum is the specific epistemic process connecting quantum and the variable: a layered abstraction that allows mathematical properties to be distilled from non-mathematical ones. For the first time, MUCH implements a careful study, connecting pre-modern texts and actors from different institutional and professional settings (universities, religious and merchant schools). By intertwining historical contexts, MUCH disentangles how quantum’s and inquantum’s philosophical underpinnings paved the way for Ch’s mathematical application, contributing to a more comprehensive understanding of the pre-modern scientific thought. MUCH’s leading-edge hypothesis has the broader academic goal of bridging the research fields of history of mathematics and philosophy, deepening our comprehension of historical mathematical development but also emphasizing the inseparable relationship between philosophical inquiry and scientific progress.