Yes, Ramanujan just floated around dealing with whatever number theories inspired him, sometimes in a nearly mystical way so he's not a good example.
Andrew Wiles is a better example, since he hit in plain sight working on Fermat's Last Theorem.
"He dedicated all of his research time to this problem for over six years in near-total secrecy, covering up his efforts by releasing prior work in small segments as separate papers and confiding only in his wife."