Together with Maxwell electromagnetism and Newtonian, relativistic and quantum mechanics, Boltzmann-Gibbs statistical mechanics constitutes one of the pillars of contemporary theoretical physics. A generalization of this magnificent theory, which is based on the additive entropic functional S BG = −k W i=1 p i ln p i , was proposed in 1988, based on the generically nonadditive entropic functional S q = k 1− W i=1 p q i q−1 (q ∈ R; S 1 = S BG ), and is currently referred to as nonextensive statistical mechanics. The analytical, experimental and computational validity of this generalization has been profusely verified in natural, artificial and social complex systems. Still, various interesting mathematical issues have been elusive and remain up to now as open questions in areas such as the theories of probabilities and nonlinear dynamics. Here, we briefly review several among them: their mathematical focus would be most welcome.