The crux is the decisive point of a matter. The crux of the argument, that is the crux, the crux of the problem.
It nearly always takes of and always the definite article. In climbing it is the hardest move of a route, and the Latin behind it means a cross, from the old phrase for a puzzle that torments you.
1nouncruxThe decisive point of a matter.
“The crux of the problem is that we don't have enough money.”
crux is a point.
Latin crux means a cross; the sense of a difficulty comes from a puzzle that torments.
Proto-Indo-European
*(s)ker- (turn)
Proto-Indo-European
*(s)ker- — to turn, to bend
Latin
crux — cross, wooden frame for execution
English, today
crux
Latin crux (“cross, wooden frame for execution”), possibly from the Proto-Indo-European (s)ker- (“to turn, to bend”). a doublet of cross and crouch.
Etymology from Wiktionary, CC BY-SA