I'm really trying to get a grip on trans-cranial electric stimulation. The specificity of effects claimed from from such a general manipulation (enhanced learning, better mathematical skills) is a little unbelievable.

Statements like "warns me that if I remove an electrode and break the connection, the voltage passing through my brain will blind me for a good few seconds." which may be a misreporting, don't help to bolster credibility. It may indeed blind you due to some neurophysiological effect, but breaking the connection of a direct current circuit will simply stop the current (unless there is a huge inductor in the circuit somewhere, in which case there will be a spark to your scalp as the SAME current tries to keep flowing).