Traditionally highly-accurate numerical solutions to the quantum many-body problem have high computational cost and low interpretability, hindering their applicability and utility for (bio)chemical problems, where systems are large and extracting conceptual insight to guide experimentalists is of paramount importance. In this talk, I’ll explain how every quantum system can be exactly described using a (possibly symmetry-broken) product wavefunction with a finite number of factors. This gives an interpretable mean-field description and provides a systematic way to control the cost/accuracy trade-off in practical computations. This new twist on an old approach has special relevance in chemistry (because it reinforces the “electron pair picture”) and quantum computing (because boson-product wavefunctions are described by the permanents of coefficient matrices). If time permits, I’ll describe some related approaches, including "generalized DFT" methods, which fit into the same conceptual framework.