There are many terms from classic and modern SF that remain unresearched, and the Historical Dictionary of Science Fiction will be continually updated, especially as additional resources are put online. Boing Boing is syndicating new entries from the HDSF on a regular basis. (Read the series introduction.)
In the 1960s, around the time that soft science fiction was taking off—SF that was not focused primarily on science and gadgets—there was some concern about what to call the "real" stuff. Indeed, "real science fiction" was one suggestion, along with "straight science fiction", "Campbellian science fiction," "engineers' stories," and others. Eventually, hard science fiction became generally accepted as the name for this variety.
One common feature of such stories was the need to solve some difficult engineering problem by ingenious thinking. An almost impossibly clichéd version of this famously appears in the 1995 movie Apollo 13, when the astronauts have to fit a square peg in a round hole; the great power of the scene is that it is not fictional. But the idea that space travel involved brilliant technical feats is a core tenet of hard SF. Ross Rocklynne specialized in such stories, starting in 1938 with "The Men and the Mirror," in which two antagonists are trapped on the surface of a frictionless mirror, and must figure out how to escape it.
These puzzles were appealing to readers, who delighted in coming up with their own answers, or pointing out that the provided solutions didn't work. (In 2008, the writer Geoffrey A. Landis published "The Man in the Mirror," an updated version of Rocklynne's story, with improved physics. When Larry Niven published his popular Ringworld in 1970, about an artificial world in the form of a flat ring revolving around a star, he was quickly deluged with complaints that the world would be unstable, and needed to write a sequel to explain away the engineering issues.)
The very first examples of the term problem story, from the early 1940s, refer specifically to actual puzzles that readers could solve to win a prize, but our sense, 'a story concerned primarily with the resolution of a (technical) problem', turns up very quickly. Despite stylistic shifts within science fiction, these stories remain popular: Cory Doctorow argues that they are fundamentally "about technological self-determination", and thus aren't about the tech as such, but demonstrate "remaking the social relations for technology." Reintepreting classical hard-SF writers like Robert Heinlein as promoting "seiz[ing] the means of production"? Sounds like excellent problem-solving.