Savants--the preferred term for mad scientists because it doesn't make them sound universally insane--are those who can see through the gaps and holes in our reality to the subjective truths that lie underneath, and are able to make inventions that rely on these subjective truths. That means superconductors that function at room temperature, super-efficient fuels that allow jet packs to actually work, or genetic engineering allowing the manipulation of genetic code like it was simple computer code. Telekinesis, nanotechnology, virtual reality, suspended animation, cryonics, cybernetics, dark energy--fringe science isn't fringe, it's just a bit beyond the conventional.
Mad science can do the improbable in ways that can only be described through maddening scientific explanations, from collecting phlogiston from the air to creating mech suits to unleashing zombie plagues to inventing countless variations on the "_____" ray, from death rays to shrink rays to lightning guns to transformation rays. Seriously, if a savant asks if you could try something for them, get the fuck out, because your humanity is probably at risk.
Now, unfortunately, most inventions and breakthroughs created by mad scientists are not replicable, because, well, they rely on the savant's own particular world view to function. Even if you replicated the death ray piece-for-piece exactly, your machine is going to be relying on conventional physics and not the raw, untapped potential of creation. Also, because most mad scientists are playing with forces they barely understand, they have the unfortunately tendency to cause catastrophic--and fatal--failures. Not just for them--entire towns have been wiped off the map because of a mad scientist. Have you ever heard of the town of Redfork, Virginia? Of course you haven't, the Veil Treaty erased all trace of it after a savant accidentally zombified the entire town. Plus, if a savant tried to explain their theories and findings to you, it would sound like the rambling of a mad man--of course the gravitational constant of Earth isn't mutable by human tech, and you can't force a pencil to hover by tossing it just right.
Unless of course you do happen to understand it, in which case, welcome to enlightenment. Here's your lab coat, mandatory evil laughter classes are at 5:00.