The ancient Greek sculptor Phidias (c. 480-430 BC), who designed the statue of Zeus at Olympia and of Athena in Parthenon, apparently used golden proportions in his sculptures and made them a part of Greek artistic canon. The notation $\varphi$ for golden ratio is said to come from the first letter of his name.
Islamic architects used aperiodic tilings of the plane in their decorative designs since c. 1200 using a set of Girih tiles. In modern times they were rediscovered and mathematically studied by Penrose and others.
Italian architect Brunelleschi (1377-1446), one of the founding fathers of Renaissence, developed the techniques of linear perspective, a practical application of geometric optics, in modern times (it was already used in some ancient Roman paintings) and employed it in designing the dome of the Florence Cathedral. Many other prominent Renaissence figures contributed to the development of the technique. Alberti's De Pictura ("On Painting", 1436) was first to treat perspective mathematically, but only for objects on the ground plane, della Francesca in 1470s extended it to solids anywhere in the picture plane, Luca Pacioli's 1509 De Divina Proportione (On Divine Proportion), illustrated by Leonardo da Vinci, summarized the use of perspective in painting, as well as promoted the use of golden ratio. Development of linear perspective eventually led to a new mathematical discipline, projective geometry, in the hands of French engineer and architect Desargues.
In the early 20th century new developments in physics inspired a number of poets and artists see Parkinson's Surrealism, Art and Modern Science. Valery visited physical laboratories and befriended Bohr, Perrin, Langevin and de Broglie. Breton and Soupault’s surrealist painting Magnetic Fields (1919) is meant to capture the spirit of relativity, Paalen’s 1940 Figure Pandynamique tries to picture the wave/particle duality artistically, it depicts a set of repeating rings culminating in spheres.
Perhaps the most famous mathematics inspired modern artist is Escher (1898–1972), who wrote "mathematicians have opened the gate leading to an extensive domain". His initial inspiration was Polya's paper on plane symmetry groups, and his discussions with Coxeter, a prominent Canadian geometer, led to Escher's famous tessellations of the hyperbolic plane. Aside from tessellations Escher is known for using impossible objects, conformal maps, and other mathematical constructions in his paintings.
There is plenty of poetry inspired by mathematics. English poet Coleridge (1772–1834) wrote a poem inspired by Euclid's construction of equilateral triangle. Lyrics to Coulton's song Mandelbrot Set go like this:
Pathological monsters! cried the terrified mathematician
Every one of them is a splinter in my eye
I hate the Peano Space and the Koch Curve
I fear the Cantor Ternary Set
And the Sierpinski Gasket makes me want to cry
And a million miles away a butterfly flapped its wings
On a cold November day a man named Benoît Mandelbrot was born
