In modern German, one can make tief into the comparative tiefer, regardless of whether the word is used as adjective or adverb. In English, I now have a sentence in which I want to do the same thing with the English deep, because more deeply does not suit the cadence of my sentence and, frankly, deeplier looks dippy. Can I do what I want? Can I use deeper as an adverb? Is this good usage? Is it good philology? Is it sanctioned by practice? If so, why, please? If not, why not?
My Webster's Ninth New Collegiate Dictionary surprisingly seems to offer no clue.
I realize that English occasionally allows the positive deep as an adverb, but such usage probably would be pretentious in my particular instance -- or, at best, would serve only to dodge the linguistic question. If such dodging makes bad English in principle, then one prefers not to dodge. It is not that I wish to convert the poetic adverb deep into deeper, but the more pedestrian adverb deeply into deeper.
(I do not know how interesting or relevant my specific sentence is to readers of this site, but if it interests you: "Ideally, the professional mathematician knows or precisely specifies in advance -- or, deeper, reveals the very wisdom of -- the set of fundamental axioms he means to use to derive a result.")