Summary: The title is a paraphrase of E. P. Wigner’s widely cited paper [Commun. Pure Appl. Math. 13, No. 1, 1–14 (1960; Zbl 0102.00703)]. In this paper, we try to reduce our scope from all fields of mathematics to symmetry, while we extend the study of the application of symmetry not only to natural sciences, rather “to wide branches of learning”. We justify the narrowing of our approach by the works of Wigner themselves and his own words. First, we follow a path paved by mathematicians (to solve analytical problems with tools of discrete mathematics). Similar to – among many others – E. Galois, F. Klein, S. Lie, E. Noether, and H. Weyl, E. P. Wigner made a great contribution to the application of methods of symmetry – and, in particular, handling them by group theory – to contemporary physics. This contribution was acknowledged by the Nobel Prize committee in 1963 “for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles”. Starting from Wigner’s symmetry concept in physics, we look beyond. This sequence of argumentation led to the application of the same symmetry principles in the non-physical sciences, including genetic biology and the humanities. Then, secondly, we present a short analysis, what did effectiveness of mathematics mean for Wigner more than a half century ago.