The local scaled spacing distribution between the eigenvalues of a random large symmetric matrix whose entries are chosen to be I.I.D. Gaussian is a well known celebrated result from random matrix theory. It is believed (and is a central open problem) that the same universal laws hold for the eigenvalue spacings if one chooses the matrix entries as I.I.D., but not necessarily Gaussian. There is not that much evidence for such a universality conjecture and numerical experiments would be illuminating (there are some done for matrices of size 20x20 going back to the 50's and 60's, but one can go a lot further with today's eigenvalue algorithms and computers).