In Medieval Architecture, Signs of Advanced Math - New York Times
The New York Times reports that an article published in the journal science describes how certain medieval Islamic mosaic patterns made use of an advanced branch of mathematics known as quasi-crystals:
In the beauty and geometric complexity of tile mosaics on walls of medieval Islamic buildings, scientists have recognized patterns suggesting that the designers had made a conceptual breakthrough in mathematics beginning as early as the 13th century.
The tiles in the pattern can be rotated to form a pattern that is "infinitely big and yet the pattern never repeats itself, unlike the tiles on the typical floor." This branch of mathematics has only been understood by modern science within the past 30 years.