Galois's writings collected in a single volume ----------------------------------------
Galois's original manuscripts are held at the library of the Institut de France. They have been digitized and are freely available online at the following address:
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They form an exceptionally rich corpus for historians: because so many drafts have survived, they offer a window onto mathematical discovery in the making, showing the mathematician's ideas as they emerged.
The first to bring together all of Galois's writings in a major editorial undertaking were Robert Bourgne and Jean-Pierre Azra (Écrits et Mémoires mathématiques, Gauthier-Villars, 1962, with a preface by Jean Dieudonné). This colossal project began with deciphering Galois's handwriting, complete with deletions, cross-references, missing words… The texts were then typed up and set in clean type on the right-hand pages, while the left-hand pages reproduced the crossed-out lines, cross-reference notes, Liouville's corrections…
The most recent reprint of this monumental work was published by Éditions Jacques Gabay in 1997.
Published mathematical texts --------------------------------
• April 1829: *Démonstration d’un théorème sur les fractions continues périodiques (Annales de mathématiques pures et appliquées – known as the Annales de Gergonne* –, volume 19).
• April 1830: Analyse d’un mémoire sur la résolution algébrique des équations (Bulletin des sciences mathématiques, astronomiques, physiques et chimiques – known as the *Bulletin de Férussac* –, volume 13); this article summarizes the memoir submitted for the Grand Prize of the Académie des sciences.
• June 1830: Note sur la résolution des équations numériques (Bulletin de Férussac, volume 13).
• June 1830: Sur la théorie des nombres (Bulletin de Férussac, volume 13); this memoir forms part of Galois's research into the theory of permutations and algebraic equations.
• December 1830 : Note sur quelques points d’analyse (Annales de Gergonne, volume 21).
The four memoirs -------------------
People often speak of Galois's "lost" memoir, lost by the Académie des sciences. In fact, Galois submitted four memoirs to the institution.
The first two were presented by Cauchy in 1829, on May 25 (Recherches algébriques) and June 1st (Recherches sur les équations algébriques de degré premier). It is thought that these were two parts of the same work, with the second supplementing the first. The original manuscripts were "lost" by Cauchy, who had been asked to report on them. Nevertheless, Cauchy advised the young man to refine his work and enter it for the Académie des sciences' Grand Prize in mathematics in 1830.
Galois therefore submitted his Mémoire sur les conditions de résolubilité des équations par radicaux in February 1830. Fourier, who had been asked to assess it, died on May 16, and the memoir was not found among his papers. That year, the Grand Prize was awarded to Abel and Jacobi.
Galois rewrote his memoir and submitted it in January 1831. Six months later, however, Poisson issued an unfavorable report. Disappointed, the young mathematician reworked it from Sainte-Pélagie prison, where he was being held. He planned to publish it with his famous "preface" (see Briefly "Perspectives on teaching"). "The enclosed Memoir is taken from a work that I had the honor of presenting to the Académie a year ago," he wrote. "As that work was not understood and the propositions it contained were called into question, I had to content myself with presenting, in synthetic form, the general principles and a single application of my theory."