  Borwein and Broadhurst, using experimental-mathematics techniques, in 1998
identified numerous hyperbolic 3-manifolds whose volumes are rationally related
to values of various Dirichlet L series $\textup{L}_{d}(s)$. In particular, in
the simplest case of an ideal tetrahedron in hyperbolic space, they conjectured
that a dilogarithmic integral representing the volume equals to
$\textup{L}_{-7}(2)$. Here we have provided a formal proof of this conjecture
which has been recently numerically verified (to at least 19,995 digits, using
45 minutes on 1024 processors) in cutting-edge computing experiments. The proof
essentially relies on the results of Zagier on the formula for the value of
Dedekind zeta function $\zeta_{\mathbb{K}}(2)$ for an arbitrary field
$\mathbb{K}$.
