  We give self-contained presentation of results related to the Kadison-Singer
problem, which was recently solved by Marcus, Spielman, and Srivastava. This
problem connects with unusually large number of areas including: operator
algebras (pure states), set theory (ultrafilters), operator theory (paving),
random matrix theory, linear and multilinear algebra, algebraic combinatorics
(real stable polynomials), algebraic curves, frame theory, harmonic analysis
(Fourier frames), and functional analysis.
