【Discover】 , 【ascertain】 , 【determine】 , 【unearth】 , 【learn】 mean to find out something not previously known to one.

【Discover】 may presuppose investigation or exploration, or it may presuppose accident, but it always implies that the thing existed, either actually or potentially, in fact or in principle but had not been hitherto seen or known or brought into view, action, use, or actual existence.

【Ascertain】 seldom if ever implies accidental discovery; it usually presupposes an awareness of one’s ignorance or uncertainty and conscious efforts (as by study, investigation, observation, and experiment) to find the truth or 【discover】 the facts.

【Determine】 (see also DECIDE) differs from 【ascertain】 only in its greater emphasis upon the intent to establish the facts or the truth or to decide a dispute or controversy. Its use is largely legal and scientific.

【Unearth】 is freely used in the sense of to bring to light or out into the open something that has been hidden, forgotten, or lost or that is exceedingly difficult to trace.

Frequently it also suggests intensive or prolonged investigation preceding discovery.

【Learn】  implies acquirement of knowledge; it commonly suggests little or no effort on the part of the one who discovers.