The good news is that there is solid reasoning behind when you use the prefix of “in-” versus when you use “un-”; the bad news is that this logic will only help you if you have a solid understanding of language history.
In all cases discussed here, these prefixes mean “not” or the opposite of something. We see them in action all of the time:
The answer to their usage relies on their roots. If the base word stems from a Germanic language, the proper prefix is “un-.” If it stems from a Latin word, the proper prefix is “in-.” Yes, it’s a nice simple answer, but not the easy answer that English spellers were hoping for.
If you’re still confused, don’t worry. Because this scholarly answer hasn’t been well understood over time, many words have fluctuated between prefixes. My favorite example is from the Declaration of Independence itself. There, as we all well know, is a discussion of “unalienable rights.” Are you doing a double-take? Yes, it’s written as “unalienable,” not “inalienable,” as is the more common form today—and technically, “inalienable” is the correct form, since we’re talking about a word with a Latin root.
If you’re arguing that this is unacceptable or inconclusive, I hear you. But at least you’ll have your answer now, whether it’s one that you’ll put to use or not.
*Answer – The correct word is “insurmountable,” since the root word comes from Latin.