Similar to this topic, what are the easiest foundational French texts for someone learning the language? My intuition would be Cauchy and Lebesgue, but I have no idea where to start or which of their works are readily available.
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8$\begingroup$ As for the texts themselves, here is a useful link (complete works) : math-doc.ujf-grenoble.fr/OEUVRES .( $\endgroup$– js21Commented May 25, 2012 at 19:38
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$\begingroup$ @js Cool, I had no idea! $\endgroup$– Igor RivinCommented May 25, 2012 at 20:04
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$\begingroup$ In what fields of mathematics are you interested ? $\endgroup$– LierreCommented May 31, 2012 at 17:01
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$\begingroup$ @Lierre , My current work is in math bio, but I also have an interest in operator theory. $\endgroup$– Greg ZitelliCommented Jun 11, 2012 at 21:44
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11 Answers
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Since you mention Lebesgue, I would recommend the following two classics, which build on his lectures at the Collège de France :
Leçons sur les séries trigonométriques
Another suggestions : Topologie générale by Bourbaki, and Théorie des distrbutions by Laurent Schwartz.
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$\begingroup$ It's strange to mention Laurent Schwartz's Théorie des distributions and Bourbaki in the same sentence. I found Schwartz very readable with lots of useful and interesting material, but never managed to read much of Bourbaki before becoming bored. Have a look at Schwartz's first article on distributions to get a feeling for how readable he writes: archive.numdam.org/ARCHIVE/AUG/AUG_1945__21_/AUG_1945__21__57_0/… $\endgroup$ Commented May 27, 2012 at 21:22
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3$\begingroup$ @Thomas : It may depend on which Bourbaki book you chose to read. Personnally I think that Topologie générale is a masterpiece, but some people may have different taste. $\endgroup$ Commented May 28, 2012 at 8:52
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The canonical excellent French author is Serre (his books are also quite easy to find) -- Cours d'Arithmetique has some analytic content, if you like that sort of thing, as you say you do...
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50$\begingroup$ Just for the purpose of uniqueness: this Serre is Jean-Pierre Serre $\endgroup$ Commented May 25, 2012 at 19:40
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13$\begingroup$ Yes. Of course @Denis Serre has some pretty nice books himself (available in both languages, for ease of learning!) $\endgroup$ Commented May 25, 2012 at 20:04
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$\begingroup$ I have never really learnt to appreciate Serre's writing style. Too condensed and impersonal for my taste. $\endgroup$– R.P.Commented Jun 5, 2023 at 12:45
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If you're looking for French classics, I would recommend Darboux's Théorie générale des surfaces There is a lot of analysis there. In fact the text is mostly about the interplay between differential equations and differential geometry. Goursat's Leçons d'analyse are also quite nice. I read somewhere that Bourbaki started as a rejection to this text, but that only makes it more interesting. I also like Appell and Goursat's Théorie des fonctions algébriques et leurs intégrales. Appell's books on mechanics are really nice as well.
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Roger Godement. His courses (in analysis, differential geometry, algebra, etc.) are magnificient.
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I suggest that you have a look at Bourbaki's talks here as they range quite a few topics, are generally short enough, are often in french, and are regularly from masters. Of course, you'll find other interesting collections on the same website.
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$\begingroup$ Julien Puydt, thank you. To many, these Séminaire Bourbaki volumes were highly important, e.g. about Lie Algebras. $\endgroup$– Wlod AACommented Jun 6, 2023 at 8:22
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Actually Borel wrote a series of very nice little books, around 1900's. One of them is called "Sur les series de Taylor a coefficient positive". It has some very nice theorem, many of which are forgotten at this day; it reads like a beautifully written paper that just came out.
Also, Paul Levy. He has an exceedingly beautiful writting style. His 7 volume collected works should be available in a math library.
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Cauchy's Cours d'Analyse is beautifully written, and good for the "analytically inclined". His treatment of infinitesimals is very interesting, and it contains the famous "mistaken proof" that a limit of continuous functions is continuous. There's a CUP reprint, and it is online here
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Fourier's Théorie analytique de la chaleur is available online here. As an advantage, the English version The Analytical Theory of Heat is available here.
Do not forget François-Marie Arouet de Voltaire, Jules Gabriel Verne, Victor-Marie Hugo, Antoine de Saint-Exupéry, Jean-Paul Charles Aymard Sartre, ... :-)
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$\begingroup$ Et Balzac ? Et Stendhal ? $\endgroup$ Commented May 31, 2012 at 15:43
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$\begingroup$ ... Émile François Zola, Gustave Flaubert... !!! $\endgroup$– PapiroCommented Jun 4, 2012 at 10:53
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$\begingroup$ I think on the contrary that it is urgent to forget the morally repugnant Sartre and his verbal diarrhoea... $\endgroup$ Commented May 12, 2021 at 12:09
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For the really analytically inclined :), while I have not finished reading it myself, I have been told by multiple of my French colleagues that Leray's original paper on Navier-Stokes has interesting mathematics and quite penetrable language.
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$\begingroup$ If you don't want to pay Springer 35 Euros, Leray's paper is available here homepages.warwick.ac.uk/~masdh/Leray.pdf (retypeset) and here cmi.univ-mrs.fr/~gallouet/artbase.d/leray-ns.pdf (badly scanned) $\endgroup$– M TCommented Jun 1, 2012 at 12:58
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$\begingroup$ Indeed, my first PDE course involved translating and presenting sections of this paper. As I recall, none of the students nor the professor had French as a first, second, or even third language. It was a challenging but doable endeavour. (Hint: Chaleur is not the name of a professor.) Gerhard "Ne Parle Vouz Francais Still" Paseman, 2012.06.11 $\endgroup$ Commented Jun 11, 2012 at 21:48
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I'm not fit to properly judge the quality of the language, but I've always found Dixmier's papers very lucid (although mathematically demanding for this Bear Of Little Brain). Plus, one gets to see some of the theory of Von Neumann algebras at an interesting time. Looking on NUMDAM ought to yield several papers, including IIRC the paper on $C^k$ functional calculus for self-adjoins elements in $L^1$ of a nilpotent group.
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For operator theory, Dixmier seems to be a good option.
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1$\begingroup$ See mathoverflow.net/questions/97976/approachable-french-masters/… $\endgroup$ Commented Jun 12, 2012 at 0:25