I mean are there examples of problems that have been proven to be undecidable, in the sense that it would not be possible to devise a deterministic computer program that outputs a solution for an instance of the problem. And yet human mathematicians have come up with such a solution.
2026-03-26 09:38:58.1774517938
On
Are there undecidable problems for which a solution has been found?
113 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
2
There are 2 best solutions below
2
On
In a certain sense made rigorous elsewhere in a mathematical logic conjecture whose origin I can't remember, every mathematician's proof is expressible in terms of basic semantics that a computer can understand given basic axioms and deduction rules. If you accept that, then no, there is no computer undecidable problem that a mathematician can figure out a deterministic decision procedure for.
It is common to find that undecidable problems often have a solution in certain special cases even though there is no general solution. The halting problem is an excellent example; certainly it is possible to prove that (most) programs written by humans intended for a practical purpose do eventually halt.