---
title: "Towards a Mathematical Science of Computation"
authors:
  - "John McCarthy"
year: 1962
venue: "IFIP Congress"
arxiv: null
doi: null
source: "https://www-formal.stanford.edu/jmc/towards.html"
topics:
  - semantics
  - program-correctness
  - mccarthy
seed_rank: 578
seed_batch: "foundations-greats-2026-08-13"
reviewed: "2026-08-13"
pool: "languages"
relevance_score: 8
lineage: foundations-of-computing
cites:
  - title: "A Basis for a Mathematical Theory of Computation"
    url: "https://www-formal.stanford.edu/jmc/basis.html"
    year: 1963
    arxiv: null
    doi: null
  - title: "An Axiomatic Basis for Computer Programming"
    url: "https://doi.org/10.1145/363235.363259"
    year: 1969
    arxiv: null
    doi: "10.1145/363235.363259"
see:
  - "577-a-basis-for-a-mathematical-theory-of-computation"
  - "592-an-axiomatic-basis-for-computer-programming"
---

# Towards a Mathematical Science of Computation

## One-sentence takeaway

McCarthy's IFIP-62 address argues that programming needs a mathematical science of meaning and correctness, and introduces abstract syntax to that end.

## Why it matters here

Formal methods and language semantics in the Broadside stack start here as an agenda: prove properties of programs, don't just run them.

## Key ideas

- Extends the 1961/63 "Basis" paper from recursive functions to a science of computation presented at IFIP Congress 62.
- McCarthy later identified this paper as perhaps the first use of the term *abstract syntax*.
- Program properties are mathematical claims about recursively defined functions and syntactic structure.
- Abstract syntax separates the tree of a program from any particular concrete notation.
- Author-hosted HTML/PDF at Stanford is the stable source; the proceedings printing is the IFIP 62 volume.

## Caveats

## Links

- URL: https://www-formal.stanford.edu/jmc/towards.html
- PDF: https://www-formal.stanford.edu/jmc/towards.pdf