What is a decision problem?
A decision problem is simply a problem where the required output is either a yes or a no.
What does it mean for a decision problem to be decidable?
A decision problem is considered decidable
if there is at least one algorithm that can output a yes or no answer in a set amount of time,
meaning that at some point the algorithm will stop running and produce an answer.
What is the class P? What is the class NP?
Class P refers to the problems that can be solved by an algorithm in a polynomial amount of time.
The time has to be reasonable as the input size increases.
Class NP refers to the class where a problem can have a proposed solution and can be proven or verified in polynomial time.
What is the intuitive meaning of the "P versus NP" question?
The "P versus NP" question asks if the solutions to a problem can be found and verified as efficiently as possible (P = NP).
This question hasn't been answered as of now,
and solving it would aid a lot of fields including cryptography, optimization, etc...
If you resolve the P versus NP question, how much richer will you be?
This question is considered one of the "Millenium Prize Problems",
and would win you a total of $1 million from the Clay Mathematics Institution.
References:
Stanford Encyclopedia of Philosophy. Computability and Complexity
https://plato.stanford.edu/entries/computability/
Complexity Zoo. Complexity Zoo:P
https://complexityzoo.net/Complexity_Zoo:P#p
Complexity Zoo. Complexity Zoo:N
https://complexityzoo.net/Complexity_Zoo:N#np
Clay Mathematics Institute. P versus NP
https://www.claymath.org/lectures/p-versus-np/