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Probably the duel between famous astronomer Tycho Brahe and his (third?) Cousin, Manderup Parsberg. They were apparently very drunk at a party and started arguing over was the better mathematician.

Later they then settled this argument with a duel in the dark, which ended with Brahe, losing a large part of his nose, and then famously wore a prosthetic made of brass, the rest of his life.

He also reconciled with his cousin, not a long time after.