Non-constructive algorithm existence proofs

The vast majority of positive results about computational problems are constructive proofs, i.e., a computational problem is proved to be solvable by showing an algorithm that solves it; a computational problem is shown to be in P by showing an algorithm that solves it in time that is polynomial in the size of the input; etc. However, there are several non-constructive results, where an algorithm is proved to exist without showing the algorithm itself.

Source: Wikipedia — Non-constructive algorithm existence proofs (CC BY-SA 4.0)