I will review the mathematical research on the Bose gas going back to the influential 1957 paper of Dyson. This was probably the first mathematically rigorous paper on many-body quantum mechanics and pioneered the mathematical physics of many-body quantum systems that has been an active research area ever since. This paper was published in the same issue of Physical Review as the famous paper by Lee-Huang-Yang that gave a two-term expansion for the ground state energy of a thermodynamically homogeneous Bose gas in the dilute limit. The Lee-Huang-Yang asymptotics can be seen as a natural continuation of Bogolubov’s 1947 theory of super-fluidity. Dyson attempted to rigorously derive the leading term in the Lee-Huang-Yang expansion and succeeded in doing so as an upper bound but his corresponding lower bound did not match the lower bound. It took nearly 40 years before Elliott Lieb and Jacob Yngvason realized how to use a key ingredient in Dyson’s lower bound argument to derive the leading term in the dilute asymptotics of the ground state energy. The Lieb-Yngvason paper was the beginning of an extremely active period of mathematical physics work on the Bose gas. It will not be possible to review all this very beautiful work, but we will give some highlights. There were many contributions of Jacob Yngvason and his students and postdocs. Eventually the Lee-Huang-Yang two term formula was proved (except for one remaining case) and there are by now even several proofs.