There is a fairly extensive list of problems in various fields that have been shown to be undecidable. For example, see
https://en.wikipedia.org/wiki/List_of_undecidable_problems
And certainly, an open question that is resolved by either a proof or a counter-example is decidable.
But my question is—is there any known unsolved problem in mathematics that is known for sure to be decidable?
Lastly, is a proof of the decidability of say, Goldbach's Conjecture, a possibility, or simply out of the question?
Thank you.
Best Answer
There are open questions which could in principle be resolved by some finite (but extremely long) calculation, such as the value of the Ramsey number $R(5,5)$. Any problem which can be so resolved must be decidable.