Bose-Einstein Condensation as a Mathematical Challenge

A mathematical analysis of the Bose-Einstein condensation (A. Einstein, 1925) by G. Uhlenbeck (1927) called this phenomenon in question until 1938, when it was solved by F. London. The aim of my lecture is to present a review of selected (solved and unsolved) mathematical problems motivated by attempts of rigorous description the condensation of bosons, which is in fact known experimentally.