ABSTRACT
In the summer of 2013 Marcus, Spielman, and Srivastava gave a surprising and beautiful solution to the Kadison-Singer problem. The current presentation is slightly more didactical than other versions that have appeared since; it hopes to contribute to a thorough understanding of this amazing proof. The KadisonSinger problem posed in the 1950s, probably in relation to a statement of Dirac concerning the foundations of quantum mechanics. It has since acquired a life of its own. On one hand, there have been several notable attempts to prove it. On the other hand, it has been shown that it is equivalent to various problems in Hilbert space theory, frame theory, geometry of Banach spaces, etc. However, for five decades the problem has remained unsolved. It is therefore very remarkable that in 2013 a proof was given by Marcus, Spielman, and Srivastava. The methods used were rather unexpected; moreover, they had shown their strength in some totally unrelated areas (Ramanujan graphs).
