---
title: "Mathematical Problems (Hilbert's Problems)"
authors:
  - "David Hilbert"
year: 1900
venue: "International Congress of Mathematicians, Paris"
arxiv: null
doi: "10.1090/S0002-9904-1902-00923-3"
source: "https://www.ams.org/bull/1902-08-10/S0002-9904-1902-00923-3/S0002-9904-1902-00923-3.pdf"
topics:
  - metamathematics
  - entscheidungsproblem
  - hilbert-program
seed_rank: 487
seed_batch: "foundations-greats-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 10
lineage: foundations-of-computing
---

# Mathematical Problems (Hilbert's Problems)

## One-sentence takeaway

Hilbert's 1900 Paris lecture sets twenty-three problems, including the continuum hypothesis and a finite decision procedure for mathematical statements, that become the charter Gödel, Church, and Turing later settle.

## Why it matters here

Anoptic/Broadside treat computation as epistemology: this list is the public problem-setting that incompleteness and the Entscheidungsproblem answer, not a paper about machines.

## Key ideas

- Problem 2 asks for a finitistic consistency proof of the arithmetic axioms; problem 10 asks for a decision procedure for Diophantine equations.
- The Entscheidungsproblem — decide validity of a first-order formula by a finite procedure — is the logical form later named in Hilbert–Ackermann.
- Hilbert program: secure infinitary mathematics by finitistic reasoning about proofs themselves.
- English working text is Mary Winston Newson's 1902 *Bulletin of the AMS* translation (8:437–479) of the 1901 *Archiv* version.

## Caveats

## Links

- AMS translation PDF: https://www.ams.org/bull/1902-08-10/S0002-9904-1902-00923-3/S0002-9904-1902-00923-3.pdf
- HTML transcription: https://mathcs.clarku.edu/~djoyce/hilbert/problems.html