The adam of mad scientists is unquestionably one Herr Doktor Victor Frankenstein. On a technicality, Frankenstein is Swiss by way of Italy. This isn't a mystery; Mary Shelley wrote Frankenstein on varying amounts of wine and laudanum for a group literary challenge in Cologny, on Lake Geneva. Switzerland is a multilingual land and Cologny is in the predominantly French portion. But the book of ghost stories that spurred the gathered poets into competition was a French anthology translation from German sources, and the atmosphere and settings of the tales is consistently German. Shelley followed suit and set the monster's creation at the conveniently-in-limbo University of Ingolstadt (in the process of reestablishing itself in Landshut and ultimately in Munich).
Dr. Frankenstein isn't the only fictional mad scientist to emerge from 19th century literature, and this select group was joined by more than a couple eccentric actual scientists. But Shelley's doctor and monster retained (and retains) a grip on the western cultural imagination unlike the others.
But when we look at the earliest film adaptations of Frankenstein, from the 1910s, there is still a missing piece of the mad scientist archetype. You'll notice that Frankenstein is neatly coiffed and hairstyled. The monster, on the other hand, is the unkempt, wild, uncivilized mess. That's not our stereotypical mad scientist portrayal, is it?
Enter one Albert Einstein, celebrity scientist with a very, very distinctive look.
You could say the Metropolis (1927) choice of a German mad scientist is a coincidence; director Fritz Lang was German, after all. You could say it was a silent movie, who cares if the doctor's name was German. (It's also a book, but again, in German.) But you can't deny the influence of Metropolis in solidying the course of the Streamline Moderne sci-fi aesthetic (r/Retrofuturism shoutout)--and just check out our [mad robotics engineer.] (http://s3.amazonaws.com/auteurs_production/images/film/metropolis/w1280/metropolis.jpg)
The archetype of a fictional mad scientist is German (well, German enough); the visual archetype of a mad scientist is also German (well, German enough) with a very conveniently overlapping name. Dr. Strangelove probably solidified the trope, but it existed before him.