(I’m sure this is already a trope somewhere, and if so feel free to correct me so I can get rid of it, but until then…)
They say one failure doesn’t make or break you…but these guys never got the memo.
A “Gilligan’s Professor” is a brilliant genius who is able to do things no one else can with apparent ease and calmness, giving the idea that this individual is supposed to be incredibly smart and talented. However, one concrete fact remains that there is one single problem that they are unable to overcome and is relatively minor by comparison to other problems they routinely overcome, yet they are never able to do it. This is usually due to being a plot device to keep things moving, but the end result is to make a character who is supposed to be brilliant look like a moron.
One might consider this to be a sort of extreme example of “Blessed with Suck”, although the “suck” in this case comes from the writers.
The best example is, of course, the Professor from “Gilligan’s Island”, which is the source of the name for this trope. He’s smart enough to build a fully operational car out of bamboo and coconuts, and yet he can’t patch a hole in a boat.
Conan Edegawa in “Detective Conan/Case Closed”. He’s supposedly this brilliant detective who solves murders regularly…and yet it’s been over a decade and he still can’t find the guys who turned him into a child.
The aliens in “Signs”. They can travel millions and millions of light years to reach Earth, and yet can’t get through a thin, wooden pantry door. (They were also dumb enough to invade a world that’s 70% stuff-that-kills-them, but now I’m getting sidetracked…)
The crew of Voyager in “Star Trek: Voyager”. They can use the resources on Voyager to do pretty much anything and get out of any situation, even transmutation of crew members and making weapons that kill guys that destroy Borg Cubes with one shot…but they can’t get the warp drive working again.