system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: People say that proving P=NP would change computing overnight, but how? Wouldn't you still have to figure out the programming/computing technology to solve the NP problems? How would it affect our current computing?
gpt
First you have to understand a little bit about the P and NP problem classes. For instance computer scientists already know a fast algorithm to multiply two numbers together, which happens to be a P problem.

However computer scientists don't know a fast algorithm to solve the Traveling Salesman Problem, which happens to be an NP problem. The Traveling Salesman Problem is defined as so: Given a list of cities what is the shortest possible route that a traveling salesman can visit each city exactly once and return to the origin city? Alternatively computer scientists also don't know a fast algorithm to solve the Knapsack Problem, which also happens to be an NP problem. The knapsack problem is defined as so: Given a set of different objects, each with a weight and a monetary value, determine the number of each item to put into the knapsack so that the total monetary value is as large as possible. 

What computer scientists learned is that some problems can actually be converted into other problems by using clever logic. For instance the Traveling Salesman Problem can actually be converted to the Boolean Satisfiability Problem, where the details to this problem are not really important here (just know that it is also an NP problem and does not have a fast algorithm to solve it as well). Computer Scientists also found out that the Knapsack problem can be converted to the Boolean Satisfiability Problem, along with many other problems (Decryption is another one of these problems, which also happens to be an NP problem). These problems, that can converted to the Boolean Satisfiability Problem, are actually called NP-Complete problems. 

Now IF a computer scientist figures out a fast algorithm to solve the Traveling Salesman Problem it would mean that we could convert that algorithm to solve the Boolean Satisfiability Problem as well. In turn we could use the fast algorithm to then solve the Knapsack problem and all the other NP-Complete problems. 

The important part of all this discussion is that, if in fact P does equal NP, that means there MUST exist a fast algorithm to solve the Traveling Salesman Problem and therefore a fast algorithm to solve all the NP-Complete problems (which there are a fair amount of). This would be a major discovery because then programmers would be able to use fast algorithms to solve problems that they previously thought could only be solved with slower algorithms. Which means that programmers would be able to make much faster software than they previously thought was possible just by modifying the algorithm alone and not relying on hardware advances.