"The beauty of FORTRAN--and the reason it was an improvement over assembly language--is that it relieves the programmer of the obligation to make up names for intermediate results."
--Andrew Appel, Compiling with Continuations
My knowledge of the early history of programming languages is limited, but I believe Backus is considered to have invented the compiler. Slashdot unfairly describes Backus's Turing Award lecture "Can Programming be Liberated from the von Neumann Style?" as "apologizing" for the creation of FORTRAN, but I think the idea of functional programming was already there in FORTRAN. Once the idea of a FORmula TRANslator had been invented--i.e., the notion of a programming language with expressions--it was a natural step to consider languages without any statements at all.
This is to say nothing of the enormous debt of gratitude we owe him for BNF.
Update: Oh dear, I spoke too soon. Grace Hopper wrote the first compiler (thanks to the anonymous commenter for setting me straight). Apparently the FORTRAN compiler is considered one of the first successful optimizing compilers for a high-level language.