As the title says, I'm just curious if there are any problems with polynomial-time algorithms, but where no polynomial-time algorithm for it is currently known? Of course, this question would be trivial if the only method of showing a problem is in class P is by providing an algorithm. However, there can also be non-constructive proofs, which is why I ask.
A quick Google search turned up nothing. Also, this is my first question on this site, so my apologies if I'm breaking any rules.
