I will discuss the many-body quantum problem of a gas of interacting bosons. This models the experimental situation of cold gases of bosonic atoms. I will, in particular, discuss the ground state energy per volume of such a gas in the thermodynamic limit, i.e., in the limit of a large volume. In 1957 Lee, Huang, and Yang gave heuristic arguments that in the dilute limit of low particle density there should be a universal two term asymptotic formula for the ground state energy per volume. Universality here means that both terms in the expansion depend on the interaction through only one length scale parameter called the scattering length. The Lee-Huang-Yang asymptotic formula has been verified in a few experiments. Recently together with S. Fournais we proved the Lee-Huang-Yang asymptotic formula. I will try to give an idea of the proof and, in particular, relate it to the celebrated Bogolubov approximation used to explain superfluidity.
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