---
title: "On Undecidable Propositions of Formal Mathematical Systems"
authors:
  - "Kurt Gödel"
year: 1934
venue: "Mimeographed lecture notes, Institute for Advanced Study"
arxiv: null
doi: null
source: "https://albert.ias.edu/20.500.12111/7996"
topics:
  - incompleteness
  - godel
  - recursive-functions
seed_rank: 506
seed_batch: "foundations-greats-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 9
lineage: foundations-of-computing
cites:
  - title: "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I"
    url: "https://doi.org/10.1007/BF01700692"
    year: 1931
    arxiv: null
    doi: "10.1007/BF01700692"
  - title: "General recursive functions of natural numbers"
    url: "https://doi.org/10.1007/BF01565439"
    year: 1936
    arxiv: null
    doi: "10.1007/BF01565439"
  - title: "An Unsolvable Problem of Elementary Number Theory"
    url: "https://doi.org/10.2307/2371045"
    year: 1936
    arxiv: null
    doi: "10.2307/2371045"
  - 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"
see:
  - "500-uber-formal-unentscheidbare-satze-der-principia-mathematica-"
  - "525-general-recursive-functions-of-natural-numbers"
  - "507-an-unsolvable-problem-of-elementary-number-theory"
  - "515-on-computable-numbers-with-an-application-to-the-entscheidun"
---

# On Undecidable Propositions of Formal Mathematical Systems

## One-sentence takeaway

Gödel's 1934 Princeton lectures recast incompleteness in a form that isolates general recursive functions and hands Church and Kleene the vocabulary of the 1936 computability cluster.

## Why it matters here

This is the hinge between the 1931 incompleteness paper and every later "what can a machine decide" argument Anoptic inherits. The Kleene–Rosser notes are the first readable statement of arithmetization plus recursion that Broadside should cite when it talks about self-describing systems.

## Key ideas

- Mimeographed notes of the February–May 1934 IAS lectures, taken by S. C. Kleene and J. Barkley Rosser.
- Cleaner exposition of Gödel numbering, representability, and the first incompleteness theorem than the 1931 paper.
- Introduces (via Herbrand) the equational schema that Kleene will call general recursive functions.
- Widely reprinted in Davis, *The Undecidable* (1965); the IAS scan is the original mimeograph.

## Caveats

## Links

- IAS handle: https://albert.ias.edu/20.500.12111/7996
- IAS record: https://albert.ias.edu/entities/publication/9587ae8c-4cc2-424f-ac21-8681a9c19d8a
- Davis anthology: https://archive.org/details/undecidablebasic0000mart