This is what I was trying to get to with "inherently." The information ITSELF that is yielded by the process is 100% arbitrary and not valuable, i.e. relays no additional useful information about the world (e.g. the boiling point of some new liquid or something), like many would think of when we think of people doing math to solve things.
I totally understood that you tried to define valuable in such a way to exclude cryptocurrency mining, as you can see below however it's not easy to create a definition like that. It also begs the question why that arbitrary definition of valuable is more correct than another arbitrary definition that excludes something else instead...
> valuable, i.e. relays no additional useful information about the world (e.g. the boiling point of some new liquid or something)
Theoretical mathematicians don't provide anything useful according to your definition.
Again, we're looking for a good definition for explaining it to laypeople, and I don't find it that difficult. "Pulling a slot machine" or the one from the "solving Sudokus" both work pretty well.
The theoretical mathematician definition isn't very good either because I think enough people get that the novelty has some kind of inherent value that doing something repetitive like the above does not?