In case the title is confusing, this is the older meaning of "Apology." Not, "I'm sorry," but "defense." This is a defense and justification for the field of mathematics.
As in Newman's Apologia Pro Vita Sua (L: A defence of one's own life)
so that's where Christian "Apologetics" comes from
Yeah, interesting that the meanings shifted over time. EG, look at Google Translate (E>L) where apology (E) becomes excusatione (L) with a back translation (L>E) of 'excuse'. Today an apology may or may not come with an excuse but back then an apology must have been a rationalization for some action.