There’s an artificial intelligence technique that models the functions of nature (specifically related to reproduction) to make use of the concept of P=NP to solve problems. The technique is generally referred to as the formation of a “genetic algorithm” whereby the computer starts with a random collection of “DNA” (just a collection of bits, 1s and 0s) called a gene. The information encoded in a gene can be anything, a video stream, a series of characters, a series of numbers, whatever. The algorithm checks each gene to see if it contains a correct solution to the problem being solved and assigns it a score. A certain percentage of bits are then randomly selected from two of the highest scoring parent genes and joined to create a new child gene. This process is repeated a predetermined number of times. Random changes like frame shifts or mutations are also introduced to inject a little change into the process so the algorithm doesn’t get stuck. The resulting child genes are then given scores of their own. If one of the children is scored highly enough, then it can be considered to contain a solution to the problem. With enough repetition, genetic algorithms can find solutions to problems that we never thought of. Consider this: a genetic algorithm (a program) that writes programs!
Genetic algorithms are kind of an answer to the P=NP problem because the scores are usually easy to calculate. The solutions themselves, however, can’t necessarily always be found quickly, so it’s not really a correct P=NP solution. If some mathematician proves P=NP, AI will move forward in leaps and bounds because it will prove that things like genetic algorithms can work to solve literally any computer-related problem given enough computing time and memory. It’s not so much that we haven’t invented the math for it yet – we just don’t know if it’s even possible because all the math that we do know hasn’t shed any light on an answer.