But simple, beautiful mathematical explanations can make us greedy. While we wish for all explanations of the world around us to be elegant, science often involves “the slaying of a beautiful hypothesis by an ugly fact,” in the words of biologist Thomas Henry Huxley. Before positing elliptical orbits, Kepler himself succumbed to the desire for beauty when he suggested that the planets’ orbits could be modeled as the Platonic solids nested inside each other. His theory was beautiful, but it was soundly disproved by later observations of the outer planets. In a way, it was almost too beautiful to be right. But beauty cannot be our only metric; beauty must be hampered by reality, if it is to have anything to say about the world around us. Gustav Fechner, a 19th-century psychologist, tried to experimentally prove that people naturally preferred golden rectangles in all kinds of settings, an effort that has not been borne out by subsequent research. It seems he was misled by his “vision of a unified world of thought, spirit and matter, linked together by the mystery of numbers.” This tendency can lead us astray. We see the golden ratio where it doesn’t really exist, and concoct beautiful theories that don’t describe reality.

via Math as Myth – Preview Issue: The Story of Nautilus – Nautilus.