Piero della Francesca

In the middle of the 15th century, painters across Italy were racing to work out how to make a flat panel look like a real, measurable space, building on rules the architect Filippo Brunelleschi had worked out in Florence a generation earlier. Piero della Francesca, working out of the small Tuscan town of Borgo Sansepolcro, pushed the problem further than almost anyone. He was also a working mathematician, and in the 1470s he set his method down in a treatise called De Prospectiva Pingendi, walking through geometric proofs in his own hand for how to construct perspective correctly.

That double training shows in paintings like The Flagellation of Christ and the frescoes he made for the court of Federico da Montefeltro, the one-eyed duke of Urbino, where architecture, light and figures sit inside one precisely calculated space.

Piero's late years are thin on record. Giorgio Vasari, the 16th-century biographer of Italian artists, claimed he went blind before his death in 1492, and for a long time afterward Piero was remembered mainly as a mathematician whose ideas other painters borrowed without much credit. His paintings were only properly re-attributed and celebrated starting in the 19th and 20th centuries, once historians untangled which frescoes and panels were really his.