Hippasus

[14] Iamblichus says about the death of Hippasus: According to Iamblichus's The life of Pythagoras,[16] Aristotle speaks of Hippasus as holding the element of fire to be the cause of all things;[17] and Sextus Empiricus contrasts him with the Pythagoreans in this respect, that he believed the arche to be material, whereas they thought it was incorporeal, namely, number.

"[7] According to one statement, Hippasus left no writings,[7] according to another he was the author of the Mystic Discourse, written to bring Pythagoras into disrepute.

[20] Hippasus is sometimes credited with the discovery of the existence of irrational numbers, following which he was drowned at sea.

Pappus (4th century AD) merely says that the knowledge of irrational numbers originated in the Pythagorean school, and that the member who first divulged the secret perished by drowning.

[24] Iamblichus clearly states that the drowning at sea was a punishment from the gods for impious behaviour.

[25] In principle, the stories can be combined, since it is possible to discover irrational numbers when constructing dodecahedra.

Irrationality, by infinite reciprocal subtraction, can be easily seen in the golden ratio of the regular pentagon.

Plato in his Theaetetus,[27] describes how Theodorus of Cyrene (c. 400 BC) proved the irrationality of

[31] The method is a proof by contradiction, or reductio ad absurdum, which shows that if the diagonal of a square is assumed to be commensurable with the side, then the same number must be both odd and even.

Some writers have Hippasus making his discovery while on board a ship, as a result of which his Pythagorean shipmates toss him overboard;[32] while one writer even has Pythagoras himself "to his eternal shame" sentencing Hippasus to death by drowning, for showing "that