p vs np paradox is a paradox as stated only in the past, it was once a computer science proof, but has now grown beyond.

in easy words, we can say  this: 

P is what we call know problems we can solve (find answer) and if we have answer(s) we can verify (check they are true)

and 

NP are not problems we can't easily solve (find answers), but ironically we know ways to easily verify (we check if the answer are correct) 

So the challenge here is that for problems that we know how to check the answer but not yet easy to find answer, could we someday prove that it is also easy to solve these answer? 

That by definition IS acceptable as current paradox. 


Extra info:

Being a paradox does not mean something is infinitely unsolvable, it's just a paradox "for now".

SAT ( Boolean satisfiability problem) is the hardest know NP-complete scenario in. SAT has became the  NP goto test (in the constrain of time) to show that almost all (so far) know NP-complete problems can be expresses mechanically into SAT.

So solving SAT=P will prove that P=NP=SAT, there are in fact been a number of new theories now that have propose solutions to proven SAT=P, but it's outside the pure Computer Science Math, and has moved to Quantum Physics, or even new fields like Logical Physics, aka into the realm of Quantum computers, the future killer of many cryptographic keys, and possibly the demise of Cryto-Currency. 

Some emerging solutions:
1. https://medium.com/the-physics-arxiv-blog/the-astounding-link-between-the-p-np-problem-and-the-quantum-nature-of-universe-7ef5eea6fd7a
2. http://recursed.blogspot.com/2012/05/yet-another-p-vs-np-proof.html


Answering Wrong Paradox Assumptions:

Now I saw another answer that I like to elaborate on, the Twin Paradox and the 
Theseus Paradox. Both are or shall we say were paradoxes, but are no longer (or no longer complete paradoxes) 

Twin Paradox (a math paradox -  observation of fast moving object slowing down in time as observed by a twin moving away at very high speeds per Albert Einstein's formulas) - This one is actually solved by further proof of Special Relativity (in easy words - going very-very fast will slow time down for a person being observer relative to another at rest observing that person), so you could say time-dilation physics has solved this naive twin paradox. 

Thesueus Paradox (a philosophical paradox of identically replacing all parts of a body/item would still defines that as the same person/item) - This one has actually partially be solved by Biology, believe it or not, every existing soft cell in a body of a person >10 years has been replaced, most if not all the soft cells have been duplicated a new even though the position or the mass of that person stayed the same. By the very nature of long life organism changing cells, the biological definition is that if you change everything exactly the same in the cellular level at least (even thought the molecular level might have recycled some of the same atoms at different location), it is accepted as the being the same - hence paradox partially solved. 

In simple terms - think of paradox like magic, or until it becomes knowledge or science that we still do not know till the future arrives with new answer, once we know them, it's no longer a paradox