well cryptography builds on "p != np" so basically cryptography would have to rethink their approaches.

besides that better optimizations I guess.

• AI would have a benefit because we reduce energy waste in the calculations
• the box problem could be solved

• our energy consumption for complex/heuristic computations could go down

  I'm not a mathematician so these are my crude laymen ideas about it.

You could always find the best route from A to B with any kind of traffic on the way. Today no algorithms knows the fastest or shortest way from New York to Washington.

Honestly it's always struck me as one of those bits of theoretical nonsense with little practical application, that is more philosophy than fact and the type of thing career educators and professional lecturers use to make themselves SOUND smarter than they are.

To imagine the consequences, you have to understand what is the meaning of 'P =NP' : If P = NP, we are able to solve every 'hard problem' in a polynomial time. Thus, there is no 'hard problem' anymore. Every problem can be rewritten to a polynomial problem (easy problem) and thus, be solved in polynomial time with a polynomial algorithm.

The whole cryptography must be rethinking. And this is not a tiny think. Every protocol, every communication, every auth will be rewritten.

Do not underestimate the consequences about this.

Cheers !