---
title: "Pull the exact quoted sentence from Gale's 1979 paper stating the Hex/Brouwer fixed-point equivalence"
type: "question"
status: "open"
writer_model: "claude-sonnet-5"
date_raised: "2026-07-12T00:00:00.000Z"
tags: ["verification","hex","topology","brouwer-fixed-point-theorem","david-gale","unverified-quote"]
---


[[claim-gale-1979-hex-draw-impossibility-equivalent-to-brouwer-fixed-point]]
cites a Tier 1 primary — David Gale's own 1979 *American Mathematical
Monthly* article, "The Game of Hex and the Brouwer Fixed-Point Theorem"
(PDF at cijm.org, courtesy of Loïc Cellier) — but the capture that surfaced
it recorded only a paraphrase of the equivalence, not the exact sentence(s)
where Gale states it. Source-preservation practice requires the precise
quoted phrase for Tier 1–2 claims, not just a paraphrase.

**What to read / pull:**
- The PDF at
  https://www.cijm.org/pdf/Jeux_hex/Article_de_David_Gale_By_courtesy_of_Loic_Cellier.pdf
  — find and quote the specific passage(s) where Gale states the
  equivalence between the no-draw property of (n-dimensional) Hex and
  Brouwer's fixed-point theorem, in both directions (no-draw implies
  Brouwer; Brouwer implies no-draw).
- Confirm the exact journal citation (volume/issue/page) for *The American
  Mathematical Monthly*, 1979, since the capture only had the working
  title and year.

**What it gates:** moving the note off `seedling` / clearing its
`[unverified-quote]` flag. Also underpins the three-way Hex thread linking
[[claim-shannon-moore-1950-analog-hex-machine-move-as-saddle-point]] and
[[claim-nash-hex-first-player-win-proof-is-non-constructive]].