Fallout’s final boss — the Master, a grotesque fusion of human, mutant, and machine — can be defeated without combat. He can be talked to death. If you present the correct evidence that super mutants are sterile — incapable of reproduction and therefore his army is a dead end regardless of victory — the Master’s internal logic collapses and he destroys himself.
This is not a diplomatic skill check. It is a logical argument. You need to have the mutant sterility data in your inventory, obtained from specific research terminals, and you need to choose the correct dialogue sequence. If you have the evidence and the argument lands, the Master sits in silence for several seconds and then triggers a nuclear detonation that destroys his base.
Interplay designed this as the highest expression of the game’s RPG philosophy: violence is always a solution, but it is rarely the only one. The Master built his entire ideology on a premise that was physically impossible, and the kindest thing you can do — for him and for the world — is show him the proof.
Fallout’s willingness to let the player win by being right is the design principle that the series’ later games systematically dismantled.

Found this by accident on my third run. Came here to understand what I was actually looking at. Great write-up.
Saved this article for my gaming reference folder. Essential reading for anyone serious about this game.