Earlier quoted context omitted.
It is impossible to create a "useful" PoW. The issue comes down to incentives. As bitcoin is a decentralized, trust-less system, there needs to be constant and powerful incentives to prevent miners from cheating (by creating forks, or executing any number of other attacks). The current main incentive against cheating is that miners will lose their invested PoW (compute time + electricity) if they cheat and get their…
In that case, you'd want everybody running profitless basic research scientific computations for other people's research teams. Eventually we may be able to buy cloud compute by inventing a new coin with a proof of work useful only to us, buying some Etherium to back it with (so that there's some initial value to mining it), and then letting speculators put it in there currency baskets to give it long-term value.
May not scale in 20 years. Useless research can become very valuable in a decade or two.