[nextaccountic]

What if there is no solution?

An expert trying to find a solution for a problem with no solution may sometimes spend decades with no results

Worse yet, proving there is no solution often requires totally different techniques

There's some problems that are currently in a limbo of sorts. We tried to tackle them, were not successful, and currently we don't know if we just need new math to solve them, or if they can't be solved at all

[pks016]

That would be something. Definitely more exciting. But, from I have seen so far, the models are not there yet.

It's a tricky situation for people who might want to work on hard problems like this. Is it worth spending time and money fiddling around the models?

In research, you can't show your progress by showing how many ways you have failed (which I don't like). The universities, grant agency etc. require you to work on solvable problems.