Until the 19th century, mathematicians knew about only two kinds of geometry: the Euclidean plane and the sphere. It was therefore a deep shock to their community to find that there existed in principle a completely other spatial structure whose existence was discerned only by overturning a 2000-year-old prejudice about 'parallel' lines. The discovery of hyperbolic space in the 1820s and 1830s by the Hungarian mathematician Janos Bolyai and the Russian mathematician Nicholay Lobatchevsky marked a turning point in mathematics and initiated the formal field of non-Euclidean geometry. For more than a century, mathematicians searched in vain for a physical surface with hyperbolic geometry. Starting in the 1950s, they began to suggest possibilities for constructing such surfaces. Eventually, in 1997, Daina Taimina, a mathematician at Cornell University, made the first useable physical model of the hyperbolic "