Our new ab initio methods for many-electron systems can be applied to other many-fermion species. In particular, we demonstrated that quantum-chemistry-inspired coupled-cluster methods can be applied to atomic nuclei. We performed several highly successful ab initio coupled-cluster calculations for 4He, 16O, and valence systems around 16O using modern nucleon-nucleon interactions. We developed several quantum-chemistry inspired coupled-cluster and equation-of-motion coupled-cluster approximations for routine use in nuclear structure theory, including pairwise and three-body interactions in the Hamiltonian. We also carried out unprecedented and widely publicized coupled-cluster calculations for 56Ni and its isotopes. We are looking for the alternative approaches to accurate calculations for many-fermion systems with pair-wise interactions, including the use of cluster expansions involving two-body correlation operators to represent nearly exact many-fermion states.