How much would you like one million dollars?
I for one would.
I can imagine endless sleep-filled nights with that amount snoozing soundly in my bank account. To get it, I could rob a bank, be lucky and successful in business, poison my parents surreptitiously, or simply solve P vs NP.
If you do solve it, the Clay Mathematics Institute will send you that right away.
The problem is, of course, that even the greatest mathematicians on our planet can’t do it, and that has huge implications for our surge into artificial intelligence and its applications.
Now, not being a professor or reader in pure mathematics or computer science, you're going to have to read this knowing I had to ask where to write my name on my maths O level exam. However, that has never stopped us before, so let's proceed.
The key to this is algorithms.
Those are what are driving our ability to create artificial intelligence. An algorithm itself is even difficult to define, but generally it's a set of dynamic and interactive instructions used to solve problems by artificial intelligent ‘beings’, like computers or robots.
These beings can solve many challenges via algorithmic deduction and process, but they have to do it in a reasonable amount of time. I can certainly paint the Forth Bridge (which it is said needs repainting upon completion as it takes that long to decay), but the time it would take me would be far too long to be useful, viable, or ever repeated.
In a similar way, algorithms need to solve in polynomial time, P, which has an end and is useful, and not in nondeterministic polynomial time, NP, which basically goes on forever, and while we may know the algorithm is doing the right thing we will certainly die before we know the answer.
The concept was explored by Douglas Adams in The Hitchhiker's Guide to the Galaxy, in which the supercomputer Deep Thought spends seven-and-a-half million years working out the answer to the ultimate question. Unfortunately, we don't know what that question was, but we do know the process showed NP to not equal P.
Other examples of the challenge are quite mind-boggling. For example, let's consider the famous Traveling Salesperson conundrum.
An algorithm that can quickly determine the shortest route for the salesperson to visit