I guess we can give her a pass, even if we don’t have much evidence of madness.
Click for larger: found at this forum at Megatokyo, which contains other images of interest. I think the original source might be a series called Oh My Goddess!, although I am not directly familiar with that particular source material.
This is indeed Urd, from Oh My Goddess! (Ah! Megumi-sama!)
Urd is the elder of the three goddess sisters. She is constantly making potions and pills of various sorts – that usually have unwanted effects. And her powers tend to focus upon calling down lightning on the ‘bad guys’. Whomever the bad guys happen to be, which is frequently annoying or undeserving people.
I would say that she does fit the mad scientist mold, as she is very frequently so focused on the end, that she doesn’t stop to think about the means that she’s using to get there. The example from the series is: When her younger sister fell ill, and the doctor pronounced that only a very rare flower could cure her, Urd jumped up and borrowed Sleipnir, Odin’s horse, to go get the flower. It took her days just to get Sleipnir reined in enough to go there and back, and she returned only to find that they’d teleported someone to the mountain and back with the flowers on the first day.