  We prove that if a linear group $\Gamma \subset \mathrm{GL}_n(K)$ over a
field $K$ of characteristic zero is boundedly generated by semi-simple
(diagonalizable) elements then it is virtually solvable. As a consequence, one
obtains that infinite $S$-arithmetic subgroups of absolutely almost simple
anisotropic algebraic groups over number fields are never boundedly generated.
Our proof relies on Laurent's theorem from Diophantine geometry and properties
of generic elements.
