  We establish a quantum measure of classicality in the form of the occupation
number, $N$, of gravitons in a gravitational field. This allows us to view
classical background geometries as quantum Bose-condensates with large
occupation numbers of soft gravitons. We show that among all possible sources
of a given physical length, $N$ is maximized by the black hole and coincides
with its entropy. The emerging quantum mechanical picture of a black hole is
surprisingly simple and fully parameterized by $N$. The black hole is a leaky
bound-state in form of a cold Bose-condensate of $N$ weakly-interacting soft
gravitons of wave-length $ \sqrt{N}$ times the Planck length and of quantum
interaction strength 1/N. Such a bound-state exists for an arbitrary $N$. This
picture provides a simple quantum description of the phenomena of Hawking
radiation, Bekenstein entropy as well as of non-Wilsonian UV-self-completion of
Einstein gravity. We show that Hawking radiation is nothing but a quantum
depletion of the graviton Bose-condensate, which despite the zero temperature
of the condensate produces a thermal spectrum of temperature $T \, = \,
1/\sqrt{N}$. The Bekenstein entropy originates from the exponentially growing
with $N$ number of quantum states. Finally, our quantum picture allows to
understand classicalization of deep-UV gravitational scattering as $2
\rightarrow N$ transition. We point out some fundamental similarities between
the black holes and solitons, such as a t'Hooft-Polyakov monopole. Both objects
represent Bose-condensates of $N$ soft bosons of wavelength $\sqrt{N}$ and
interaction strength 1/N. In short, the semi-classical black hole physics is
1/N-coupled large-$N$ quantum physics.
