We demonstrate quantitatively that, as predicted by evolutionary theory, sequences of homologous proteins from different species converge as we go further and further back in time. The converse, a non-evolutionary model can be expressed as probabilities, and the test works for chloroplast, nuclear and mitochondrial sequences, as well as for sequences that diverged at different time depths. Even on our conservative test, the probability that chance could produce the observed levels of ancestral convergence for just one of the eight datasets of 51 proteins is ≈1×10⁻¹⁹ and combined over 8 datasets is ≈1×10⁻¹³². By comparison, there are about 10⁸⁰ protons in the universe, hence the probability that the sequences could have been produced by a process involving unrelated ancestral sequences is about 10⁵⁰ lower than picking, among all protons, the same proton at random twice in a row. A non-evolutionary control model shows no convergence, and only a small number of parameters are required to account for the observations. It is time that that researchers insisted that doubters put up testable alternatives to evolution.