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> AlphaGo Zero kind of explains how people can do something really difficult, even strategy based, without exactly knowing what they are doing.

Yet neither does Alpha go. Finding solutions really is an NP-class problem, while proving them is much easier.

> Machine learn that stuff. Give feedback to users, they will find it easier to use the system interactively.

This is interesting. I wonder how much could the computer learn about our natural (or mathematical) language if we were to express problems before coding them, and then feeding both to the ML system.

Going a step further, having the ML system generate the code, and the user correct it (as far as my understanding of deep learning goes, correcting a net's output and backfeeding it is currently strictly equivalent to just providing that data in the training set before performing stochastic gradient descent. We might be missing something here, as it is obviously much more effective with us, and that would make ML a lot eaier to work with, requiring less training data).






> Yet neither does Alpha go. Finding solutions really is an NP-class problem, while proving them is much easier.

That's not really true. Proving that an already found solution is correct might be easy for certain solutions (that's the whole idea of proof certificates). But finding a proof for an arbitrary theorem is certainly not easy. And that is what mathematicians do. Here, finding the proof IS finding the solution.


Of course, but when you have found a proof, verifying that it is correct is fairly trivial (if tedious by human standards, it's only verifying that each statement is correct).

I meant proving in the sense of "checking that the solution works". In a mathematical problem, the solution would be a tentative proof for a theorem. Proof which needs to be verified. I should probably have used "verify" instead of "prove" in this context.




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