## Books you would like to see translated into English.

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 2010 at 0:04
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 2010 at 0:36
At least I understood a meaning of your smile! – Petya Mar 11 2010 at 0:49

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"Introduction aux groupes arithmétiques" by Armand Borel.

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Paul Gordan Vorlesungen ueber Invariantentheorie" available here , both volumes. This is most worthwhile since the content of most other classics is well accounted for in modern texts whereas this way of doing algebraic geometry has been completely forgotten. Poor knowledge of Gordan's methods is a net loss for contemporary mathematics.

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Two volume introduction to Complex Analysis by B.V.Shabat. Actually, I have already translated about 150 pages of the first volume which is about as much as one can cover in Complex Variable undergraduate course offered by a typical U.S. university. I did give the translation as a hand out to my students last year when I taught Complex variables class. I did translation out of frustration with the book of Churchill and Brown.

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Durer's works on proportion, which take a Euclidean approach to constructing visible objects.

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Einfuhrung in die Algebraische Geometrie-B.L. van der WAERDEN

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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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Hilbert-Bernays's "Foundations of Mathematics", it's a shame that this classic work haven't translated yet!

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Abel's complete works.

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I agree that Abel's works are an excellent candidate. Like Riemann's, they are of stellar quality and not too long. In the meantime, you may be interested in the lengthy survey of Abel's work by Christian Houzel, which may be downloaded from the page: abelprisen.no/en/abel/fagligbiografi.html – John Stillwell Jul 1 2010 at 23:06
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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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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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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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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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I.N. Bronstein, K.A. Semyendayev - Mathematics Handbook - an awesome, very complete mathematics handbook for applied mathematicians, physicists, and engineers. Also useful for the pure mathematics researcher who just wants to quickly look up how a basic item in mathematics worked. This work has not lost any of its gleam since it was first written; numerous updates have been made; it is the reference compendium in Central and Eastern Europe. It has received prizes for being the best illustrated engineering book; indeed, the drawings are exact and even beautiful, and have not become outdated in the time of computer generated imagery. Definitely one of the books that put the Russians in outer space. Numerous German editions of the book on Amazon

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B. P. Demidovich - Problems on Multivariate Analysis (approximate translation). A very tough book about analysis on $\mathbb{R}^n$; in fact all problems 'can' be solved by first or seond-year students, but it's got lots of tricky questions that will not let you sleep at night. Only the best need apply - the book gives you the most basic definitions and then throws you out with a broken pontoon in the middle of the ocean, at night. I believe the writer is Russian or Belorussian, I have only encountered a few tattered copies that have been doing the rounds between students for a decade at least. Haven't found a better book for tough multivariate analysis.

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For every Demidovich there is an anti-Demidovich (proverb). – Victor Protsak May 21 2010 at 4:09
show 1 more comment

F. Prus-Wisniowski - Szeregi Rzeczywiste (Poland, Uniwersytet Szczecinski) - a monograph on real series. It can be read by first-year students while supplying the reader with very powerful tools for real (and sometimes complex) series; it might surprise the PhD reader. More importantly, it builds a good understanding of the way real series work. Publisher's website

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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 2010 at 22:11
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 2010 at 14:04

Catégories et structures by Charrles Ehresmann

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Équations différentielles à points singuliers réguliers, by Deligne.

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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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"Arithmetique Des Algebres De Quaternions" by MF Vigneras

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"Champs algébriques" by Laumon and Moret-Bailly.

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Chebotarev's "Grundzüge der Galois'schen Theorie"

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Teubner-Taschenbuch der Mathematik Teil II

The first part (Teil I) of this book was translated into English as the Oxford User's Guide to Mathematics

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Constantin Carathéodory's Vorlesungen über Reelle Funktionen. Why this book has never been translated into English is simply a mystery to me.

And while he's at it, let's get whoever's on that case to get Courant and Hurewitz's treatise on complex functions into English as well, so I can see finally if it's as good as Serge Lang always said it was...

2 last requests while I'm at it: Faddeev's 1984 Lectures In Algebra and the second edition of Kostrikin's 3 volume Introduction To Algebra. I'm such a sucker for Russian texts, they're so beautiful and concrete with connections to physics. We Westerners can learn so much from their approach.

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The Collected Work of Carl Ludwig Siegel.

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

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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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