The best way to avoid overly general openers is to write them.
Go ahead, write them all down. Get them out of your system. If you don't, they're gonna be on your brain distracting you.
Once you finish your opening paragraph, go back and cut it ruthlessly. That first line is out of there. Maybe the second and third line too. Start at the line that matches what you told us the paper is about. That is your intro. The P vs NP problem. I have no idea what that is but your readers will (if they don't all already know, then your intro needs to have a description of it).
Everyone knows math has hard problems. That's what makes it fun. You don't need to tell anyone that. Just tell them what problem you're working on and why.
For other academic work, you might find yourself quoting the dictionary or talking in vague terms about the topic. Write it. Get it completely out of your system. Then slash and burn.