Are there examples of similar things where we have failed? i.e. nature gives us an example, we expend massive resources on it over a long period of time and can

Are there examples of similar things where we have failed? i.e. nature gives us an example, we expend massive resources on it over a long period of time and cannot even make substantial progress? Probably I'd just say "tech in that area is only 10 years old" ;) Is the argument that we're still just hitting the low-hanging fruit of the technological age, so have false confidence in all the things we've equalled or beaten? I guess what I'm trying to get at is that most of the hardest things may not be logically possible (c.f. incompleteness theorem) or may not be physically possible (c.f. time travel). Having such clear physical possibility (and at multiple levels of complexity/advancement that only arose through selection and mutation) seems like strong evidence we will be able to do it eventually. A claim of impossibility is not illogical, but requires a stronger argument than "there's always a small chance".