A new internal description of fundamental fermions (quarks and leptons), based on a matrix-generalization (F) of the scalar fermion-number f, predicts that only three families of quarks and leptons, and their associated neutrinos (nu_e, nu_mu and nu_tau), exist. Moreover, this description places important topological constraints on neutrino mixing. For example, with respect to F, the topology of the nu_e (nu_mu or nu_tau) is that of a cylinder (Mobius strip). Assuming that a change in topology dudring neutrino-neutrino transitions is suppressed (e.g., one cannot continuously deform a donut into a sphere), while neutrino-neutrino transitions without topology-change are (relatively) enhanced, one may have an explanation for recent short-distance experimental observations of (nearly) maximal nu_mu-nu_tau mixing at the Super Kamiokande. To test this idea, I was able to use simple topological arguments to deduce a matrix describing long-distance neutrino mixtures, which is identical to that proposed by Georgi and Glashow on different grounds. Experimental confirmation of this prediction would strongly support the new description of fundamental fermions, which requires, among other things, that the nu_e and (nu_mu or nu_tau) neutrinos start life as topoligically-distinct quantum objects.