The Mathematical Writings of Evariste Galois (Heritage of European Mathematics) by Peter M. Neumann (PDF)

Description

Before he died at the age of twenty, shot in a mysterious early-morning duel at the end of May 1832, Évariste Galois created mathematics that changed the direction of algebra. This book contains English translations of almost all the Galois material. The translations are presented alongside a new transcription of the original French and are enhanced by three levels of commentary. An introduction explains the context of Galois’ work, the various publications in which it appears, and the vagaries of his manuscripts. Then there is a chapter in which the five mathematical articles published in his lifetime are reprinted. After that come the testamentary letter and the first memoir (in which Galois expounded on the ideas that led to Galois Theory), which are the most famous of the manuscripts. These are followed by the second memoir and other lesser known manuscripts. This book makes available to a wide mathematical and historical readership some of the most exciting mathematics of the first half of the nineteenth century, presented in its original form. The primary aim is to establish a text of what Galois wrote. The details of what he did, the proper evidence of his genius, deserve to be well understood and appreciated by mathematicians as well as historians of mathematics. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

User’s Reviews

Editorial Reviews: Review This book provides a version of Galois’ work in French that faithfully reflects the appearance of the manuscript along with the emendations made by the author accompanied by an English translation, hitherto unavailable in most cases. –Mathematical Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I had the copy of the original in French and a Translation in Spanish, however I understood The Works of Mr Galois until I read this Book

⭐I have a doubt about “mis-spellings and infelicities” in the section “A ‘warts and all’ transcription”. It is said that in France at early 19th century the accents such as ” ‘ ” and ” ` ” were omitted occasionally because the spelling or the orthography was not yet standardized. For example, you can find several omissions of accents in the letters of Sophie Germain.

⭐This book is superfluous. If one wants to read Galois’ original memoirs, see Harold M Edwards’ ‘Galois Theory’. Galois’ few additional results on primitive groups can be found in many books on group theory and under Galois’ name. Galois was just one of many contributers to modern Algebra. If one is interested in the history of Algebra, try Ian Stewart’s ‘Galois Theory’.

⭐本書は群論をはじめ現代数学に大きな影響を与えた数学者エヴァリスト・ガロアの数学論文集である。ガロア生誕200年を記念して刊行された全集で、見開きで仏語原語と編集者であるヌーマンによる英語翻訳が併記され、解説にガロアの数学史的業績に関する研究も収録されている。フランスで８０年代末に刊行されたガロアの草稿・メモまで網羅的に収集された、非常に分厚い決定版一巻本全集”Œuvres mathématiques ”とは異なり、習作論文、第一論文、第二論文、最後の書簡、自筆原稿写真、主要草稿が厳選され、コンパクトに編集された本書のほうが、個人的には数学論文集として読み易い。ガロアの専門家であれば本書収録の原論文や、厳密な日本語訳の高瀬正仁訳『アーベル/ガロア 楕円関数論』、守屋美賀雄訳『群と代数方程式』を参照するのだろうが、専門外でもガロアの数学に興味を持ったガロア・ファンやガロアを初めて知った人には、数学者彌永昌吉による優れた評伝・論文翻訳『ガロアの時代ガロアの数学』全2冊が最も参考になる。やがてガロアが気に入り、ガロアの原論文を傍に留めたく思ったのであれば（古書価が高騰しているのが大変に難点だが）、文字や数式がつぶれた校訂不十分な19世紀の全集版をもとにした粗悪な電子書籍よりも、ぜひ本書をこそお勧めしたい。ガロアの数学は非常に難解で、自分を含めて専門外である読者には理解が難しい部分も多いのだが、不思議なことに個人的な体験だが、ガロアを読んでいると以前の自分では考えもつかなかったことが思いつくことがある。そのような未知への発見に誘う数学者だからこそ、ドゥルーズ『差異と反復』や花田清輝『復興期の精神』でガロアが新たな思考の発見者として現代においても論じられるのだろう。レヴィ＝ストロース『親族の基本構造』における数学者ヴェイユによる部族の婚姻関係を群論的分析（正確にはアーベル群による分析）で解決した人類学的研究も、ガロアの数学の派生的な展開として面白い。近年の大きな収穫である、ガロアの数学の意義を初学者にも十二分に理解させてくれる注釈的解釈の決定版とさえいえる金重明『方程式のガロア群』や、現在のガロア・ブームの発端となった石井俊全『ガロア理論の頂を踏む』など、良質な解説が普及している現在こそ、これまでにないガロアの新たな読解が待ち望まれている。数学の専門内外を問わず熱心なガロア・ファンのための、本書のような行き届いた編集で作られた、日本で最初のガロア全集の刊行を心から希望したい。

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