>>12700019Practical Applications:
- A lot of cryptography depends on P ? NP. i.e. decrypting with a key should be polynomial time (your computer should be able to do it), decrypting without a key should be exponential time (the computers at the NSA shouldn't be able to do it)
- If P = NP, then a lot of problems we though weren't in P would be in P. If we have a constructive proof of P = NP then we could solve some problems that are currently just too computationally intensive. Protein folding comes to mind but there are also many more optimization problems that we would now be able to solve with a standard desktop computer.
Philosophical Implications (note, this is my personal take):
- If P ? NP, then creativity is a thing. If P = NP, then there's an algorithm you could follow to be creative.
- If P ? NP, then individual contributions (in art/science/math) matter. You can help humanity make progress in a way I feel is significant. If P = NP then we just wait until a genius comes along or computers are fast enough and they'll figure out all that worth figuring out about science, math, and art from scratch, without having to look at what any other human did. If P ? NP, many different people will have to attempt many different things to make progress and it has to be a cumulative effort.
Also, the fact that P ? NP seems so obviously true but that we haven't figured out how to prove it makes this question interesting in itself.
