Since Euclid many people have tried in vein to prove that the parallel postulate is a logical consequence of Euclid's other axioms. The parallel postulate states that given any line in the plane and a point not on that line then there exists a unique line through that point that does not intersect the given line. In the 1820s and 30s several people (including Janos Bolyai, Johann Carl Friedrich Gauss, and Nikolay Lobachevsky) independently realized that the parallel postulate is not implied by the other axioms. In fact the negation of the postulate leads to what is now called Lobachevskian geometry (or more commonly hyperbolic geometry). Up to this time, physicists had assumed that Euclid's axioms were true characterizations of physical space. They had thus based their theories upon those axioms. The existence of the new geometry implied that those assumptions may be false. This disturbed...