Remarkably means to a surprising degree — more than you would expect, enough to make you look twice. She is remarkably calm. The two stories are remarkably similar. It does not have to be a miracle; it often just means unusually, and I notice. Teachers, news, and polite talk use it a lot. Though actually, in careful English the surprise can fade, and the word works almost like a soft very: remarkably good, with only a light lift left. The adjective remarkable is for the thing itself (a remarkable student). Remarkably is the how-much word that sits in front of an adjective or another adverb, not in front of a person.