Muslim tiles herald early mathematical breakthroughs

A new study of Islamic tile art indicates that the designers had made stunning breakthroughs in mathematics. The quasicrystalline designs, produced in the 15th century, were not created until 500 years later in the western world.

According to Paul Steinhardt in an article for Science, the patterns were first described by British mathematician and cosmologist Roger Penrose in the 1970s. Quasicrystalline patterns "comprise a set of interlocking units whose pattern never repeats, even when extended infinitely in all directions, and possess a special form of symmetry."

Quasicrystalline pattern have been identified at the Darb-i Imam shrine in Isfahan.