Seems to me like the initial causing of the problem would have to be a one-time self-destructive event. Like maybe we blow up the moon or something and then don't survive the aftermath. We can't use tech to solve the problem if the problem is that we're extinct.

I think that's pretty far out from the sort of thing that people are thinking of when they talk about things you can and can't do with technology, so I think it's more sensible to just say that the category is empty.

> a concrete example of caused by technology, but not solvable

Consider any kind of unrest caused by the automation of tasks that formerly required a professional human, such as how the industrial revolution affected textile-manufacturing and the Luddite reaction. The new technology is a major and necessary cause of the situation, yet even with 200 years of hindsight it's hard to imagine any new followup invention that would promptly solve it.

Another category would be ecological or pollution issues, which in many cases involve social and legal solutions. For example, the new chemical technology of leaded gasoline. We didn't solve by inventing a De-Leadifier Device, or even the Cheaper New Formula, but because it became (mostly) banned.

It probably goes without saying, but for "solvable with technology" I am not including things like inventing a time-machine to go back and make it never-have-happened, or the idea that it'll be solved eventually when the Ascension Device elevates our descendants beyond such mortal concerns, etc.