Day 40 · Feb 9

Birthday of Farkas Bolyai (1775) — 'Do Not Attempt the Parallels'

Farkas Bolyai was born in Bolya, Transylvania on February 9, 1775. He spent decades trying to prove Euclid's parallel postulate from the other four axioms — and failed, as had every mathematician before him. His son János Bolyai became interested in the same problem. In 1820, Farkas wrote him the most poignant letter in mathematical history: 'You must not attempt this approach to parallels. I know this way to its very end. I have traversed this bottomless night, which extinguished all light and joy of my life. Do not attempt the parallels.' János ignored him and by 1823 had constructed a consistent non-Euclidean geometry. His father's despair had guarded a door that his son was the first to open.

If you assume the parallel postulate is false and there can be many lines through a point parallel to a given line, what kind of surface naturally satisfies this geometry?

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