  We discuss an application of the known in QCD large $N$ expansion to strings
and supermembranes in the strong coupling. In particular we use the recently
obtained master field describing $ SU(\infty)$ gauge theory to argue that
quantum extreme black holes obey quantum Boltzmann (infinite) statistics. This
supports a topological argument by Strominger that black holes obey infinite
statistics. We also speculate on a formulation of $X$-theory of strings and
p-branes as theory of Grothendieck's motives. The partition function is
expressed in terms of $L$-function of a motive. The Beilinson conjectures on
the values of $L$-functions are interpreted as dealing with the cosmological
constant problem.

High Energy Physics - Theory;Algebraic Geometry;Algebraic Geometry