For an exact proof of correctness no, because that would only show the algorithm is correct for a selected set of input-output pairs. However, it is true that

For an exact proof of correctness no, because that would only show the algorithm is correct for a selected set of input-output pairs. However, it is true that validating it for a very large number of inputs and outputs has value. This is not uncommon even in mathematics. For example, Goldbach's Conjecture (https://www.wikiwand.com/en/Goldbach%27s_conjecture https://www.wikiwand.com/en/Goldbach%27s_conjecture) has not been proven but has been shown to hold for all integers less than 4 × 10^18