There are some cases where math alone is not enough to reproduce the results though. It's easy for a paper to say something like "pick the set of N points that

There are some cases where math alone is not enough to reproduce the results though. It's easy for a paper to say something like "pick the set of N points that minimizes `median(f(x))`" without saying how the points were chosen (gradient descent? simulated annealing? brute force? some analytical method?). What happens if you pick one optimization method and your results are different than the ones in the paper? There's no way for you to know if the paper is wrong or if you just picked the wrong method.