Kurt Gödel letter to Turing "Only" formulated the problem that, does a polynomial time algorithm exist to answer yes, no question in mathematical statements. Which is considered the source of P vs NP problem, with the "belief" that Verification is poly time ( easy ), and proof is NP ( Hard ). The belief or conjecture of verification being easy is held by almost everyone. I found the following article in Nature Journal : http://www.nature.com/news/the-biggest-mystery-in-mathematics-shinichi-mochizuki-and-the-impenetrable-proof-1.18509
Which stands as a counter example to the belief that proof verification is easy, there are other proofs in finite simple groups not verified for decades. I only shared the one example with authoritative source, to deduce, that while finding proof is hard, verification is also hard, which can be due to introduction of new mathematical objects as in abc conjecture, or due to reductions between different fields, which needs to be verified beyond doubt to be sound. Does this mean, Math is harder than NP, and is infact PSPACE Hard? since both finding and verifying the proof are hard.