Reading Wikipedia, it looks like a naive definition of a set turns out to be internally inconsistent. Does that mean the concept of set was abandoned by mathematicians the way epicyles have been abandoned by physicists? That's not my sense, so I hesitate to say redefining set in a more coherent way is a paradigm shift. But I'm no mathematician.
Its a matter of degree rather than an absolute line. However, I would say a time when even the very highest experts in a field believed something of great importance to their field with quite high confidence, and then turned out to wrong, probably counts.
Here's the new thread for posting quotes, with the usual rules: