In the delightful and informative Veritasium video How One Line in the Oldest Math Text Hinted at Hidden Universes, physicists Alex Kontorovich and Derek Muller discuss how the mathematics of General Relativity emerged from careful examination of Euclid’s millennia-old Fifth Postulate about parallel lines never intersecting. The far-ranging discussion also addressed the twenty-three Definitions that preceded Euclid’s five Postulates:
17:26 AK: “[Euclid’s] Definition 1: ‘A point is that which has no part.’ What does it mean to have a part? What is a part? What does it mean not to have a part?”
18:58 DM: “You can think of geometry as a game. The first four postulates, [which in turn are based on 23 definitions,] are like the minimum rules required to play.”