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I have recently been told of a proposal to produce an English translation of Landau's Handbuch der Lehre von der Verteilung der Primzahlen, and this prompts me to ask a more general question:

Which foreign-language books would you most like to see translated into English?

These could be classics of historical interest, books you would like your students to read, books you would like to teach from, or books of use in your own research.

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The Russian translation of Milnor's Morse Theory. That's a nice book. :) –  Ryan Budney Mar 11 '10 at 0:04
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I also have both of them! And I've just check (fast checking) that pictures are absolutely same. Russian version contains small attachments (by Anosov), but they are not... as good as the book and really short, few pages. You know, translation should be a translation (I am sure Arnol'd could add smth interesting to Milnor, I am a student of V.I., but it is not the case). –  Petya Mar 11 '10 at 0:36
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At least I understood a meaning of your smile! –  Petya Mar 11 '10 at 0:49
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48 Answers

Grothendieck's EGA and SGA.

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I can't help but think: if you can't manage to pick up very simple mathematical French, what hope do you have to learn Grothendieck-style algebraic geometry? These are not books for people with poor language acquisition skills. –  Pete L. Clark Mar 11 '10 at 2:55
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Pete: I somehow suspect Dmitri does have good language acquisition skills. Dmitri: Трудно читать математические книги по-французски? –  KConrad Mar 11 '10 at 3:32
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I doubt that EGA or SGA will ever get translated given how long they are and how much background knowledge a translator would need to do a good job. However, even though I can read mathematical French (and German, for that matter) just fine, it goes a lot slower than English. I have to devote a portion of my mental powers to translating, and thus I can't be thinking about the math as deeply as I would otherwise! If somehow a translation got produced, it would make this whole process a lot easier. –  Andy Putman Mar 11 '10 at 4:01
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@Pete and KConrad: I fully agree with Andy Putnam on this matter. I can read mathematical French without too much difficulty, but it goes slower than English and requires additional mental effort. @Shizhuo: Only the introduction to EGA I was translated into Russian. –  Dmitri Pavlov Mar 11 '10 at 5:06
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@ Pete: most people who read EGA/SGA aren't native speakers of French. Even if it's not too difficult for any individual to translate, we are collectively wasting a lot of effort on repeated translations. –  userN Mar 11 '10 at 16:31
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The other two volumes of Kazuya Kato's trilogy on Number Theory (the first vol. is "Fermat's Dream").

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I only regret that I have but one +1 to give to this entry. –  Cam McLeman Mar 12 '10 at 5:57
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That's +10 from me, too. –  Alon Amit Mar 12 '10 at 19:35
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The second one appeared recently in 2011- hopefully this means that work on the third one is in progress... –  sisn May 6 '12 at 8:58
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The third volume Number Theory 3: Iwasawa Theory and Modular Forms (Translations of Mathematical Monographs) was published in 2012 –  Dominik Kwietniak Feb 12 at 14:58
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Gabriel's dissertation,Serre's FAC and Beilinson-Bernstein-Deligne

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Also, Serre's dissertation. Wonderful source for spectral sequences. –  Ilya Grigoriev Mar 11 '10 at 17:30
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Hanspeter Kraft's invariant theory book.

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At least this one is available in Russian (see MR0917727). –  Igor Pak Mar 11 '10 at 3:44
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Oh my. Since English is already so overwhelming in international scientific literature, I think it will look a bit peculiar to the non-native English speakers who read this site to see a question like this asking for yet more work to be put in English. Perhaps those of us who already speak that language should expend some more effort in the other direction if we want to read something in those other languages.

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No, actually "non-native English speakers" would like more English translations as well. It's hard enough to learn one foreign language - learning few more just to be able to read mathematical literature feels like waste. Since just about everything is either written or already translated into English, it would be really nice to have the rest. Of course, I am not complaining - there are so many great translations into Russian I rarely see books not available in either language. In fact, there used to be even a journal with Russian translations of the best contemporary math papers... –  Igor Pak Mar 11 '10 at 3:59
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If there is a choice available, I'd think most people would prefer something in their own language that has grammatical errors over having to read a language they are not comfortable with, particularly if the ultimate point is to get out some kind of information (like math content) rather than being concerned over the writing style itself. –  KConrad Mar 11 '10 at 16:30
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I was interpreting the end of Poineau's question to mean (bad English) versus (good French, German) rather than versus (bad French, German). –  KConrad Mar 11 '10 at 16:33
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"Champs algébriques" by Laumon and Moret-Bailly.

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"La Clef des Songes", "Récoltes et Semailles" and the Long March through Galois Theory.

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I am afraid these are (mathematically) of anecdotical interest and that Grothendieck has again recently vetoed translations and publications in any form of his magnus opus. –  ogerard May 21 '10 at 7:37
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I'd second Allen Knutson's suggestion that the book Geometrische Methoden in der Invariantentheorie by Hanspeter Kraft (Vieweg, 1984) is a good candidate for translation into English. Since AMS distributes several Vieweg series in English versions, I'd suggest asking Sergei Gelfand at AMS whether such a translation could be commissioned by them.

Like most native users of English, I find mathematical French far easier than mathematical German. In any event, French books and papers are less likely to get translated than German ones. As far as books go, I regret that J.C. Jantzen's useful Springer Ergebnisse volume on primitive ideals in enveloping algebras is not available in English. His later books in English have become standard references for representations of algebraic groups and for quantized enveloping algebras.

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It's fun to make a wish list, but in real life it's hard to justify the cost of translating an advanced book for a limited market. It's always tricky to find a translator with the right mathematical as well as linguistic background, lacking which a reader may be better off struggling with the original book. –  Jim Humphreys Mar 12 '10 at 17:34
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Don Zagier's German book about quadratic forms.

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For what it's worth, I am working on a book on quadratic forms that will at least present Zagier's reduction theory in English. –  Franz Lemmermeyer Mar 11 '10 at 17:06
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G.M. Fichtenholz - Analysis (3 Tomes) - The course of real analysis for budding mathematicians beyond the Iron Curtain. Everyone knows it. It's the first book you read, and the last one you refer to before finishing your master's degree. It takes you from the definition of a set to advanced multivariate calculus; it gives you a lot of tools for classical mechanics in the meantime. It is so trustworthy that the single wrong theorem that it contained caused a telltale student to fail his dissertation, because neither he nor his professor checked the proof and they based the whole thesis on the false premise - that was a decade or two ago and the book is, right now, free of errors. Originally in Russian. Another book that kept the Russians strong during the cold war. Wikipedia entry about the author

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If I recall correctly Fichtenholz has defected to the West. There is shorten two volume English version of his Analysis. However, I would cold-heartedly agree that Russian version is far better. I would also agree that his books are somewhat outdated. My favorite work for the first/second year Analysis undergraduate course (Eastern European version of Calc 1-3) is Vladimir Zorich's two volume book. From the pedagogical point of view Fichtenholz books are far more appropriate for gifted high-school students. –  Predrag Punosevac Jul 19 '10 at 7:29
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Analysis Situs by Poincare.

This is the foundation of algebraic topology and illustrates its historical connection with dynamics.

According to Wikipedia it has been translated, but I can't find a copy in English.

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I don't know which translation the Wikipedia is referring to, but I have a translation of Analysis situs (together with the five Complements) which is going to be published by the AMS soon. You can access a preliminary version of it on Andrew Ranicki's page: maths.ed.ac.uk/~aar/surgery/notes.htm (near the bottom of the page). –  John Stillwell Mar 11 '10 at 22:08
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Endliche Gruppen by Huppert, though the German is like the French in EGA: "easy" going.

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As far as I know, none of Wilhelm Blaschke's books have ever been published in English, and he is the the author of possibly the most exciting and elegant serious mathematics books that I've ever encountered (comparable to the best of Felix Klein, but on a much higher mathematical level). I especially regret that his

Einführung in die Differentialgeometrie (1950; 2nd ed with Reichardt, 1960)

and

Elementare Differentialgeometrie (5th edition with Leichweiss, 1973)

have not been available, but really, all his books, from the elementary "Kreis und Kugel" to the state-of-the-art research "Geometrie der Gewebe" are incredible. Fortunately, most of them have been translated into Russian.

Does anyone know a credible explanation of why he was completely ignored in the English-speaking world? Anything to do with WWII? Although even Hasse got translated.

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G. Banaszak, W. Gajda - Elementy Algebry Liniowej (Elements of Linear Algebra), Poland, WNT - 2 tomes - Don't let the name fool you. This recent publication has more linear algebra than you can shake a stick at. It's a very comprehensive course of linear, and some abstract, algebra; very beautifully printed, lots of decorative markup. The book is very well structured, but is not easy and requires the reader to be fully aware of what's going on. It can be a bit of a mind wringer, but on the other hand that can force you to look at many things from the writers' - quite original sometimes - viewpoint. Tome 1 on the publisher's website

This is just a quick round-up of some good books in Mathematics. Hope this helps!

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Very interesting suggestions! While on the subject of "more linear algebra than you can shake a stick at", I'd like to mention Brieskorn's Lineare Algebra und Analytische Geometrie, volumes I and II (Vieweg 1983, 1985). This is the most fascinating linear algebra book I've ever seen, but very long and rambling. –  John Stillwell Apr 9 '10 at 22:11
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Another book I almost included in this list: Dieudonne - Treatise on Analysis Haven't included it because there's a (discontinued) translation to English from the 70s. Huge book: some editions have more than ten tomes. Huge amount of knowledge. All organized nicely in an easily understood structure, with hints on how to most quickly arrive at a certain theorem. Read it all and you'll know analysis the way a PhD student should. Dieudonne is the (often forgotten) co-author of Grothendieck's Éléments de géométrie algébrique - if one likes EGA, they'll enjoy this book as well. –  cheater Apr 11 '10 at 14:04
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Geometrie der Gewebe by W. Blaschke, and G. Bol

Geradenkonfigurationen und algebraische Flächen by G. Barthel, F. Hirzebruch, and T. Höfer

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Gesammelte Abhandlungen (Collected Works) of Carl Ludwig Siegel

(According to Amazon.com a trilingual version of this once existed, but I can't find it.)

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Bombieri's "Le Grand Crible dans la Théorie Analytique des Nombres"

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The Collected Work of Carl Ludwig Siegel.

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"Arithmetique Des Algebres De Quaternions" by MF Vigneras

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Over de Grondslagen der Wiskunde , L.E.J Brouwer, his thesis (in Dutch) on the foundations of mathematics.

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Joseph Louis Lagrange - Reflexiones sur la Resolution Algebrique des Equations. I've found lots of discussions and summaries of its contents (e.g. in Harold Edwards' book on Galois theory) and little snippets translated here and there (e.g. in Mathematical Expeditions by Laubenbacher and Pengelley) but haven't been able to locate a complete translation.

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Groupes Algebriques by Demazure and Gabriel. Someone tried to translate the first half of this book, but it's not very good (some of the mathematics is incorrect too).

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The following wonderful 54 page survey by O. Neumann on Kronecker's divisor theory could easily be turned into a book and would fill a very large gap in the English literature on such. I'm interested in helping if anyone is game for such (but, alas, my German is weak).

Neumann, O.(D-FSU-MI) 2003k:13021 13F05 (01A55 13G05 20M14)
Was sollen und was sind Divisoren? (German. German summary)
[What are divisors and what can we do with them?]
Math. Semesterber. * 48 (2002), no. 2, 139--192.

In the first part of this paper a survey is given of the development of Kronecker's theory of divisors. In the second part the author develops a theory of integral domains $R$ having a divisor theory in the following sense: there exists a monoid $D$ (i.e., a commutative semigroup with cancellation and a unit element) with the GCD-property for the associated group $G$ of quotients, and a homomorphism $\mathrm{div}$ of the multiplicative group $K^*$ of the quotient field of $R$ into $G$ with the following two properties:

(i) If $a,b \in K^*$ and $b/a \in R$, then $\mathrm{div}(b)/\mathrm{div}(a) \in D$, and

(ii) for every element $d \in D$ there exists a set $A \subseteq K^*$
such that $d$ is the gcd of $\{\mathrm{div}(a) : a \in A\}$.

The author states that a similar theory was presented in the thesis of F. Lucius ["Ringe mit einer Theorie des groessten gemeinsamen Teilers", Ph.D. thesis, Univ. Gottingen, Gottingen, 1996; Zbl 0901.13002]. After developing the fundamental properties of such divisor theory, relations to the approaches of Kronecker, Zolotarev and Dedekind are established.
--Reviewed by W. Narkiewicz

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There are two books on popular mathematics by Polish mathematicans Krzysztof Ciesielski and Zdzisław Pogoda (both from the Jagiellonian University in Krakow): the first one is Diamenty matematyki [Mathematical diamonds] (cover http://merlin.pl/images_big/3/83-7337-932-0.jpg), the second is Bezmiar matematycznej wyobraźni [The endlessness of mathematical imagination] (I could not find a better transaltion). Both aim at non-specialist, mostly high-school students, and are written in a unique, informal yet rigorous style. Both are very popular and out of print in Poland. A modified version of a chapter in Mathematical diamonds has been translated by Abe Shenitzer and was published in the American Mathematical Monthly as On Ordering the Natural Numbers, or, The Sharkovski Theorem in Vol. 115, No. 2 (Feb., 2008), pp. 159-165.

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Friedrich Levi, Geometrische Konfigurationen

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Chirurgie des grassmanniennes by Laurent Lafforgue.

http://www.ihes.fr/~lafforgue/math/M02-45.pdf

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2  
That sounds so much cooler in French. –  Pete L. Clark Mar 11 '10 at 7:22
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Chebotarev's "Grundzüge der Galois'schen Theorie"

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Catégories et structures by Charrles Ehresmann

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