Original sources for the multiply transitive permutation groups discovered by Émile Mathieu.
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1860 — Émile Mathieu, Mémoire sur le nombre de valeurs que peut acquérir une fonction quand on y permute ses variables de toutes les manières possibles, Journal de Mathématiques Pures et Appliquées, 2e série, 5, 9–42.
- Original paper, PDF preserved in this repository
- Numdam source scan
- Bibliographic record
- Introduces cyclic substitutions and multiple transitivity, the starting point for Mathieu's later constructions.
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1861 — Émile Mathieu, Mémoire sur l'étude des fonctions de plusieurs quantités, sur la manière de les former et sur les substitutions qui les laissent invariables, Journal de Mathématiques Pures et Appliquées, 2e série, 6, 241–323.
- Original paper, PDF preserved in this repository
- Numdam source scan
- Bibliographic record
- Develops the multiply transitive construction, including the fivefold transitive action on 12 points; announces the 24-point case.
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1873 — Émile Mathieu, Sur la fonction cinq fois transitive de 24 quantités, Journal de Mathématiques Pures et Appliquées, 2e série, 18, 25–46.
- Original paper, PDF preserved in this repository
- Numdam source scan
- Bibliographic record
- Supplies the explicit 24-point construction, now associated with M₂₄.
These are Mathieu's writings, not modern retellings. Both are in French. The digitizations are provided by Numdam / Mathdoc and the Bibliothèque nationale de France's Gallica program; preserve that provenance.
The papers/ directory holds copies of all three complete scans, imported directly from the sources above. papers/SHA256SUMS records their SHA-256 hashes. Do not replace the originals with generated transcriptions or paraphrases.
A related existing interaction is coefficient-root-dance: coefficients on one side, roots on the other, and continuous dragging with root tracking. It is a useful visual and interaction precedent for showing permutations as choreography.
The distinction matters: generic polynomial coefficient loops produce root braids and permutations; this does not by itself implement a Mathieu group. For Mathieu, animate exact generators acting on 11, 12, 22, 23, or 24 points, and independently check the subgroup and transitivity invariants.
For subsequent context, Robert L. Griess Jr., Twelve Sporadic Groups (1998), discusses the Mathieu groups, Golay codes, and their relationship to later sporadic groups. That copyrighted book is a secondary reference, not an original Mathieu paper.
The annotated paper index follows Griess's bibliography through Witt, Todd, Curtis, Golay, Leech, Conway, Fischer, and later constructions, with original full-text or publisher links and explicit local-versus-external status. No copyrighted book or paper is silently rehosted.
The cartographic source notes follow the Malle, Zvonkin and NeverEndingBooks references in the 2019 M₁₂ post, with author/conference full-text links, exact source-labeled permutations and later Belyi-function references.