Birthday of John Playfair (1748) — The Parallel That Changed Everything

John Playfair was born in Benvie, Scotland on February 4, 1748. He is remembered for Playfair's Axiom — a restatement of Euclid's notorious Fifth Postulate: 'Through a given point not on a given line, there passes exactly one line parallel to the given line.' Euclid's own statement was clumsier; Playfair's version made it obvious why this postulate was different from the other four. For 2,000 years, mathematicians suspected the Fifth Postulate could be derived from the others. When Bolyai and Lobachevsky finally dared to deny it in the 1820s, entire new geometries opened up — curved surfaces where through a point infinitely many 'parallels' pass, or none at all.