Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are also in P. This is generally considered one of the most important open questions in mathematics and theoretical computer science as it has far-reaching consequences to other problems in mathematics, and to biology, philosophy and cryptography (see P versus NP problem proof consequences).
Siden førstnævnte beskriver en klasse af problemer der kaldes NP, mens sidstnævnte beskrives P er spørgsmålet det samme som at spørge om alle problemer i NP også er i P. Dette betragtes et af de vigtigste åbne spørgsmål inden for matematik og datalogi, da det har vidtrækkende konsekvenser for andre problemer i matematik, biologi, filosofi og kryptografi.