The expression is "Pontifex Maximus". Pontifex literally means "bridge-builder" (pons + facere) and "maximus" means "greatest". This refers to one of the vocations of the pope i.e. to build bridges between people.
There are two ways that max can be used as a noun. Max, in itself, is not a real word. It's slang for Maximum. To use it in a sentence as a noun could be: Timothy pushed his brother's patience to its...