In a course on the Early Italian Renaissance, this unit investigates the reappearance, in Europe around 1500, of original mathematics. Main questions include what was the state of mathematics at this time? Who was thinking about it, and why? Materials by Leonardo da Vinci, Piero della Francesca, Luca Pacioli, and the anonymous authors of abacus school texts are examined.
Summary of Project
Target course: The Dawn of the Italian Renaissance, Italian D212f
This course is an exploration of the Italian renaissance organized around personalities. The most "mathematical" figures in the course as it has existed are Leonardo da Vinci and Leon Battista Alberti, although neither of them did any significant mathematics. We are adding two new people, Piero della Francesca and Luca Pacioli. They contribute a significant new direction to the course.
It is precisely in late 15th century Italy that original mathematics begins once again to be done in the West. This is something that took us awhile to realize, as standard histories of mathematics put this development about 50 years later. We will translate original materialshaving to do with this development and add them to the course. There are multiple connections to the course as it already exists: Luca Pacioli was a close associate of Leonardo, Piero knew and learned from Alberti (it is widely assumed), Piero and Pacioli were from the same small town (Borgo San Sepolcro) , and their relationship has been a subject of heated controversy for 500 years. The stories which interconnect these people are fascinating and raise other issues.
There are several ways this material could be used. The most obviously mathematical exercises would be to work through some of the mathematics of the period, to see how the demands of commerce and the arts encouraged certain kinds of mathematical proficiencies. On the algebraic side one sees how school children from mercantile families learned the arithmetic of trade. Doing one of these problems is a role-playing introduction to the kind of economic activity which produced the wealth of the Italian cities, surely more memorable than just reading about it. on the geometric side, one might work through a construction of Piero in perspective painting, to see how the requirements of art stimulated geometry.
Less obviously, and less overtly mathematical there are issues of what might be called "intellectual property" which seem to arise here as if for the first time. There seems to be genuine confusion over the notion of NEW mathematics, how to classify it, recognize it, attribute it, or deal with it. There seems almost not to be a word for it, as if it did not exist as a concept. This confusion is apparent when one compares various early books of mathematics. In their preambles, dedications, and self-descriptions of what they are doing, they exhibit many peculiarities, and are, in their assumptions, quite inconsistent with each other. This is an opportunity to see how a revolution in the realm of the intellect -- which the reawakening of mathematics unquestionably was -- appeared to those who were making it.