Imagine if there was some kind of way to cryptographically 'prove' your GPU is doing some kind of 'work' here and contributing to the network.

You could even hand out some kind of digital 'currency' to the people proportional to the amount of work their doing!

I've occasionally written comments about the difficult of achieving proof-of-useful-work mechanisms and I should probably find or write a standard post about this question.

In order to be as decentralized as Bitcoin and related PoW mechanisms, a proof-of-work mechanism should have

* the ability to create an unbounded number of instances of the problem deterministically from numeric seeds

* the ability to scale difficulty up and down using a difficulty parameter

* in a way where anyone can easily confirm that a given problem instance corresponds to a given seed, and anyone can easily confirm that a given solution correctly solves a given problem instance

I'm not aware of a proof-of-useful-work mechanism that meets these criteria. (I'm also not aware of an argument that it's impossible to have one. Zero-knowledge proofs might actually go far toward making it possible in the future. but it's kind of complicated.)

As we've seen, that's a solution looking for a problem.