Garbage collection (to my knowledge) was invented by McCarthy back in the late 1950s[1] in the following three paragraphs of his paper "Recursive Functions of Symbolic Expressions and Their Computation by Machine":
Nothing happens until the program runs out of free storage. When a free register is wanted, and there is none left on the free-storage list, a reclamation cycle starts.
First, the program finds all registers accessible from the base registers and makes their signs negative. This is accomplished by starting from each of the base registers and changing the sign of every register that can be reached from it by a car − cdr chain. If the program encounters a register in this process which already has a negative sign, it assumes that this register has already been reached.
After all of the accessible registers have had their signs changed, the program goes through the area of memory reserved for the storage of list structures and puts all the registers whose signs were not changed in the previous step back on the free-storage list, and makes the signs of the accessible registers positive again.
That's mark/sweep!
He adds as a footnote "We already called this process ``garbage collection'', but I guess I chickened out of using it in the paper--or else the Research Laboratory of Electronics grammar ladies wouldn't let me." but doesn't explain where the term came from. I suppose it's possible he didn't invent it, but I've never seen anything on that and I think most of the existing strategies used for memory allocation at the time were very explicit -- FORTRAN didn't even have ALLOCATE yet!