Why does Gauss' law hold for any closed surface?

[Physgeek64]

Main Question or Discussion Point

Why does Gauss' law hold for any closed surface? and can you show this mathematically.

Many thanks :)

 

[blue_leaf77]

Chapter 1 in Classical Electrodynamics by J. D. Jackson provides this derivation.

 

[jtbell]

can you show this mathematically.

Starting from what assumptions?

Also, a Google search for "proof of Gauss law" turns up a number of pages which may contain what you're looking for, including a number of previous threads here on PF.