Albrecht Dürer, born in 1471, believed ‘the new art must be based upon science’
, a close associate of Leonardo da Vinci, and became familiar with his mathematical work. Pacioli had a deep appreciation of mathematics in art.Dürer returned to Nuremberg feeling he must delve yet more deeply into the study of mathematics. He began to collect material for a major work on mathematics and its applications to the arts.
Dürer’s final masterpiece, his treatise on proportion, which was in proof stage at the time of his death, was published shortly afterwards. In applying mathematics to art, Dürer developed new and important ideas within mathematics itself. He studied several curves, such as epicycles, spirals and conchoids, although he did not possess the mathematical tools necessary for their analysis.
While engaged in his mathematical studies, Dürer continued to produce art of outstanding quality. His understanding of the principles of perspective is clear from his engraving, Saint Jerome in his Study, made in 1514. In the same year he made Melencolia, one of the most brilliant engravings of all time, and among the most intensively debated works of art. There is much of mathematical interest in this work: a magic square, several mathematical instruments, a sphere and a large polyhedron.
The use of perspective in the hands of Dürer and other Renaissance masters has changed the way that we look at the world.