Why is one of the seven most important open questions in mathematics relevant to you? Here’s what happens if someone finds that P=NP:
Since all the NP-complete optimization problems become easy, everything will be much more efficient. Transportation of all forms will be scheduled optimally to move people and goods around quicker and cheaper. Manufacturers can improve their production to increase speed and create less waste. And I’m just scratching the surface.
Learning becomes easy by using the principle of Occam’s razor—we simply find the smallest program consistent with the data. Near perfect vision recognition, language comprehension and translation and all other learning tasks become trivial. We will also have much better predictions of weather and earthquakes and other natural phenomenon.
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Don’t get your hopes up. Complexity theorists generally believe P ≠ NP and such a beautiful world cannot exist.
