If it's proven to be the case that P != NP, it would hardly change much on the grand scale of things as generally, that's what most people believe anyway. In particular, the world continues to function mostly in the same way (since, even if it was the case that P = NP, we haven't found any polynomial reductions yet, so we're effectively living in a P != NP world). Of course, for mathematics and CS, this would be huge, because the techniques used in a proof would likely be very interesting and novel.
If it's proven to be the case that P = NP, then it remains to be seen whether this knowledge can be turned into actually efficient algorithms (polynomial algorithms are not all efficient in practice). If that is the case, I think it might have more downsides than upsides, since all of cryptography would collapse.