Electronic – How many hairy crazy ants does it take to short out an electrical system

Short to ground, just means to have a direct connection to Ground. A "short" is any direct connection between two nodes. In any circuit, technically, you have shorts everywhere, but the term "short to.." is generally used for ground or some power node.

So you have a direct connection between ADD and GND would be a short.

You can look at it this way (since you said you want an answer based on math):

The equation for the current through a capacitor is the following:

\$ I_C = C \dfrac{dV}{dt} \$

So at \$ t=0 \$, when the switch is closed, there's a voltage across the capacitor and \$ \frac{dV}{dt} \$ is really large (theoretically infinite) because there is a change in the voltage in technically 'no time,' therefore the slope \$ (\frac{dV}{dt}) \$ approaches infinity at \$ t=0 \$. Since \$ \frac{dV}{dt} \$ is in theory infinity so is the current through the capacitor (they are directly proportional). That explains why it looks as a short at time zero.

As you probably know differentiation does not exist at sharp edges and this is exactly what is happening from a mathematical point of view. Hope it helps!