Piero della Francesca
ca. 1412–1492
Italian painter and mathematician

Askilled painter who made advances in the use of perspective*, Piero della Francesca was also an important figure in the history of mathematics. He left a rich legacy, both through his works of art and his writing on various mathematical subjects. Born into a prosperous merchant family in a small town in Tuscany, Piero probably attended an "abacus school," which taught mathematics to boys destined for careers in commerce or banking. In addition, he served as an apprentice* under Antonio da Anghiari, a local painter.

Painting. Unlike many Renaissance artists, Piero della Francesca never ran a workshop. Furthermore, he probably relied more on income from his family's merchant business than on painting for his livelihood. Nevertheless, he did accept commissions to produce works of art. His first major project was the Madonna della Misericordia (1445), a set of painted panels. Around 1455 he began work on a series of frescoes*, The Legend of the True Cross, for the Church of San Francesco in Arezzo. His last painting, the Nativity of Christ (1480s), was left unfinished.

Scholars have difficulty dating Piero della Francesca's pieces because he worked slowly, sometimes taking years to complete a picture. It is thought that he used damp cloths to keep the plaster of his frescoes wet so he could continue working on them. Piero's paintings show the influence of earlier artists, especially Donatello, Masaccio, and Domenico Veneziano. They also reveal evidence of elaborate drawings beneath the paint, suggesting that he worked hard to perfect the design before adding layers of color. He was especially skillful at balancing the background and foreground of scenes and depicting delicate details.

Piero may have trained various other artists, including Luca Signorelli (ca. 1450–1523) and Melozzo da Forlì (1438–1495). In the 1500s, changing artistic tastes led to a decline in Piero's reputation as a painter. However, in the early 1900s art historians rediscovered his work, noting his many contributions.

Mathematics. Giorgio Vasari, the Renaissance artist and historian, wrote that Piero della Francesca produced many mathematical treatises*, but only three have survived. The Abacus Treatise, probably written before 1460, is a textbook for teaching arithmetic, algebra, and geometry. The Short Book on the Five Regular Solids, probably written after the Abacus Treatise, is devoted to geometry. Piero's On Perspective for Painting (late 1460s) is the earliest known work on the mathematics of perspective. It explains basic principles and describes the construction of both regular shapes and complex figures, such as the human head.

Although Piero della Francesca never taught mathematics, his books on the subject had a significant impact on other scholars. In the late 1400s, the mathematician Luca Pacioli used the Abacus Treatise extensively in writing his own Treatise on Arithmetic. Moreover, many Renaissance works on perspective echo Piero's ideas.

(See alsoArt; Art in Italy. )

* perspective

artistic technique for creating the illusion of three-dimensional space on a flat surface

* apprentice

person bound by legal agreement to work for another for a specified period of time in return for instruction in a trade or craft

* fresco

mural painted on a plaster wall

* treatise

long, detailed essay