---
title: "Review of Turing: On Computable Numbers (Church–Turing thesis framing)"
authors:
  - "Alonzo Church"
year: 1937
venue: "Journal of Symbolic Logic"
arxiv: null
doi: "10.2307/2268810"
source: "https://doi.org/10.2307/2268810"
topics:
  - church-turing-thesis
  - church
  - turing
seed_rank: 514
seed_batch: "foundations-greats-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 9
lineage: foundations-of-computing
cites:
  - title: "On Computable Numbers, with an Application to the Entscheidungsproblem"
    url: "https://doi.org/10.1112/plms/s2-42.1.230"
    year: 1936
    arxiv: null
    doi: "10.1112/plms/s2-42.1.230"
  - title: "An Unsolvable Problem of Elementary Number Theory"
    url: "https://doi.org/10.2307/2371045"
    year: 1936
    arxiv: null
    doi: "10.2307/2371045"
  - title: "Computability and λ-Definability"
    url: "https://doi.org/10.2307/2268280"
    year: 1937
    arxiv: null
    doi: "10.2307/2268280"
  - title: "General recursive functions of natural numbers"
    url: "https://doi.org/10.1007/BF01565439"
    year: 1936
    arxiv: null
    doi: "10.1007/BF01565439"
see:
  - "515-on-computable-numbers-with-an-application-to-the-entscheidun"
  - "507-an-unsolvable-problem-of-elementary-number-theory"
  - "517-computability-and-lambda-definability"
  - "525-general-recursive-functions-of-natural-numbers"
---

# Review of Turing: On Computable Numbers (Church–Turing thesis framing)

## One-sentence takeaway

Church's 1937 JSL review of Turing is the printed speech-act that equates λ-definability with Turing computability.

## Why it matters here

Best short primary cite for the Church–Turing thesis as a historical identification, not a later textbook slogan. When Anoptic says "Turing = Church," this review plus Turing's own 1937 equivalence paper (card 517) are the two sentences that did it.

## Key ideas

- Accepts Turing's a-machines as capturing the same informal idea of effective calculability that Church had defined via λ.
- Explicitly identifies the two notions, which is what later writers call the thesis.
- Connects the AJM 1936 paper to the PLMS 1936/37 pair in one paragraph.
- A review, not a theorem paper: pair it with the two 1936 primaries.

## Caveats

## Links

- DOI: [10.2307/2268810](https://doi.org/10.2307/2268810)
- JSTOR: https://www.jstor.org/stable/2268810