Last week I read about this in "Fermat's Last Theorem": While the fascinating thing about Penrose’s tiled surfaces is their restricted symmetry, the interestin

Last week I read about this in "Fermat's Last Theorem": While the fascinating thing about Penrose’s tiled surfaces is their restricted symmetry, the interesting property of modular forms is that they exhibit infinite symmetry. The modular forms studied by Taniyama and Shimura can be shifted, switched, swapped, reflected and rotated in an infinite number of ways and still they remain unchanged, making them the most symmetrical of mathematical objects. When the French polymath Henri Poincaré studied modular forms in the nineteenth century, he had great difficulty coming to terms with their immense symmetry. (Fermat's Last Theorem was ultimately proven by proving the Taniyama-Shimura Conjecture)