They both mean "to think" or "to consider". Is there a usage difference between the two?

up vote 10 down vote accepted

以为 carries with it the nuance of thinking or considering something mistakenly.

我以为你们已经分手了。 - I thought you had already broken up (but it seems you're still together.)

认为 doesn't have any such connotation and can be used generally to mean "to think," "to consider."

我认为他是我最重要的朋友。 - I consider him to be my most important friend.

Putting it simple:

认为 - think or consider

以为 - thought or considered (but I was wrong).

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