Especially in the mid-twentieth century, popular science fiction would often talk about "creatures from another dimension" and use similar language that suggested that a "dimension" refers to some kind of parallel or alternate universe. This usage is extremely different from the way that the term is used in actual mathematics, where "dimension" simply refers to the number of independent coordinates required to specify a location within an object. Loosely speaking, in the technical mathematical usage a "dimension" is more like a direction than a location. (It also doesn't really make any sense to talk about a being living "in" a particular dimension in the mathematical sense.)
How and when did "dimension" come to take on this connotation that seems completely unrelated to its actual technical meaning?