The central limit theorem states that if you add independent copies of a random variable and normalize correctly then you end up with a Gaussian (aka normal) random variable in the limit.  In what seems like an unrelated result, if you take a really large random Hermitian matrix with independent entries above and on the diagonal, then the distribution of the eigenvalues approaches a limit known as the semicircle law (when scaled properly).  I’ll review classical probability including the central limit theorem and then discuss random matrices, and hopefully explain how they’re connected.  No knowledge of probability is required.