---
title: "Die Grundlagen der Mathematik"
authors:
  - "David Hilbert"
year: 1928
venue: "Abhandlungen aus dem mathematischen Seminar der Hamburgischen Universität"
arxiv: null
doi: "10.1007/BF01661237"
source: "https://doi.org/10.1007/BF01661237"
topics:
  - hilbert-program
  - consistency
  - proof-theory
seed_rank: 494
seed_batch: "foundations-greats-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 9
lineage: foundations-of-computing
cites:
  - title: "On the Infinite"
    url: "https://doi.org/10.1007/BF01206605"
    year: 1926
    doi: "10.1007/BF01206605"
  - title: "Grundzüge der theoretischen Logik"
    url: "https://link.springer.com/book/10.1007/978-3-642-86848-1"
    year: 1928
    doi: "10.1007/978-3-642-86848-1"
see:
  - "493-on-the-infinite"
  - "491-grundzuge-der-theoretischen-logik"
---

# Die Grundlagen der Mathematik

## One-sentence takeaway

Hilbert's 1927 Hamburg address restates the consistency program — arithmetic must be proved consistent by finitary inspection of proofs — at the public peak immediately before Gödel's incompleteness results.

## Why it matters here

Timestamp for the crisis Broadside's foundations spine narrates: the program's last confident statement, then incompleteness.

## Key ideas

- Proof theory as mathematics of proofs: treat formal derivations as concrete objects and show no derivation ends in \(0=1\).
- Consistency of arithmetic (and then analysis) is the central outstanding problem of the program.
- Same year as Hilbert–Ackermann's *Grundzüge*; together they are the 1928 package Gödel responds to in 1930–31.
- Published 1928 in the Hamburg *Abhandlungen* (DOI 10.1007/BF01661237).

## Caveats

## Links

- DOI: [10.1007/BF01661237](https://doi.org/10.1007/BF01661237)