Discrete numbers and points, Hippasus proved, could never fully capture a world comprising continuous entities such as lines and surfaces. For another, it showed that lines could not be described as a sequence of tiny points strung together, or else these points would serve as a common measure for all magnitudes. For one thing, it showed that the proportion of a square’s side and diagonal could not be described as a simple ratio, dooming the Pythagorean enterprise. Hippasus’ discovery changed the course of Western mathematics. This means that no matter how many times the side is divided and how many times the diagonal is divided the resulting magnitudes would never be equal.
But Hippasus had proved that the diagonal of a square is incommensurable with the square’s side, or, as we would say today, that the square root of 2 (the length of the diagonal relative to the side) is irrational. Following the teachings of their founder, Pythagoras, they fervently believed that everything in the world could be described through whole numbers and their ratios. The Pythagoreans had good reason to turn on their brother. According to the legend, once the ship was far from shore the poor philosopher was set upon by his fellow Pythagoreans and tossed into the sea. We do not know why Hippasus was traveling or where he was journeying, but we do know he didn’t make it. the Greek philosopher Hippasus of Metapontum, a member of the secretive Pythagorean brotherhood, left his home in southern Italy and boarded a seagoing ship.
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