“Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I” was published by John McCarthy in April 1960 in Communications of the ACM, volume 3, number 4, pages 184 to 195. The source cited here is the copy McCarthy himself hosted on his Stanford web pages. The paper introduced Lisp, short for List Processor, which became the dominant programming language of artificial intelligence research for decades.
McCarthy designed Lisp around a single idea: that programs and the data they operate on can both be written as the same kind of object, a symbolic expression made of nested lists. Where earlier languages such as Fortran were built to crunch numbers, Lisp was built to manipulate symbols and structures, which is what reasoning about logic, language, and knowledge requires. The paper draws openly on the lambda calculus of Alonzo Church for its treatment of functions, and it makes recursion, a function defined in terms of itself, the natural way to express computation.
The paper’s most celebrated stroke is that McCarthy wrote a function, traditionally called eval, that could take any Lisp expression as data and compute its value. In doing so he gave a definition of Lisp in Lisp itself, a compact self-describing core from which the rest of the language could be built. This was both a piece of mathematics, showing how little machinery a universal computing language really needs, and a practical design that made Lisp unusually flexible and extensible.
The limit worth naming is that the paper is a theoretical and definitional document; the working Lisp system grew up around it through the efforts of McCarthy’s group at MIT, and many features now thought of as essential to Lisp arrived later. But the core that this paper set down, symbolic expressions, recursion, and a language that can describe and run itself, shaped programming language design far beyond AI and remains influential today.