Was a Pythagorean really drowned for discovering irrational numbers?

Probably not, or at least nobody can show it. The story is famous: a follower of Pythagoras found a number that could not be written as a fraction, and his shocked fellow Pythagoreans threw him off a ship. The truth is murkier, and the murkiness is the interesting part.

What is solid is the mathematics. Pythagoreans preached that all numbers could be expressed as the ratio of integers, and the discovery of irrational numbers is said to have shocked them. The classic argument supposes the diagonal of an isosceles right triangle is commensurable with a leg, that is, that they share a common unit of measure. Then one of the lengths, measured in that unit, would have to be both odd and even, which is impossible. Greek mathematicians called such a ratio alogos, or inexpressible, and it posed a very serious problem for Pythagorean mathematics, since it shattered the assumption that numbers and geometry were inseparable.

Now the legend. Hippasus of Metapontum, an early follower of Pythagoras, is sometimes credited with the discovery. He is supposed to have drowned at sea, apparently as punishment from the gods for divulging it and crediting it to himself instead of Pythagoras. But the few ancient sources that tell the story either do not name Hippasus or say he drowned because he revealed how to construct a dodecahedron inside a sphere, and the discovery of irrationality is not specifically ascribed to him by any ancient writer. Other accounts have a Pythagorean merely expelled, or Hippasus merely exiled.

The ship scene, with shipmates tossing him overboard, is a later embellishment by modern writers. The murder is a legend that has little if any substantial evidence.