# 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.

• The Russian translation of Milnor's Morse Theory. That's a nice book. :) – Ryan Budney Mar 11 '10 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 '10 at 0:36
• At least I understood a meaning of your smile! – Petya Mar 11 '10 at 0:49
• Another interesting question along these lines: which books "lose" the most in translation? I can't read Russian, but apparently Kostrikin's "Around Burnside" is like that. – Steve D Mar 11 '10 at 2:32
• It was (during the 20th century) assumed that all mathematicians read English,French,German. Probably translations of French & German books from that period will (with few exceptions) happen only when computer translationn gets good enough to do it. – Gerald Edgar Feb 12 '14 at 15:00

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.

• I'd say that Diamenty matematyki should read The diamonds of mathematics. – Tomek Kania Feb 12 '14 at 15:45
• In their Monthly article mentioned above Ciesielski and Pogoda translate Diamenty matematyki as Mathematical Diamonds in the reference lists. – Dominik Kwietniak Feb 12 '14 at 16:03

Chirurgie des grassmanniennes by Laurent Lafforgue.

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

• That sounds so much cooler in French. – Pete L. Clark Mar 11 '10 at 7:22

Équations différentielles à points singuliers réguliers, by Deligne.

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.

• Why this book has never been translated into English is simply a mystery to me Solution to the mystery... it has been assumed until recent years that all serious mathematicians know German, French, and English. – Gerald Edgar Mar 31 '10 at 15:11
• I know,Gerald-but that's never stopped some great German texts from being translated into English-such as Courant's calculus lectures or van der Wearden's algebra texts. That's no excuse,I'm sorry.And times have changed,for better or worse.The language requirement-again,for better or worse-is fading in importance. – The Mathemagician Mar 31 '10 at 17:16

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 second-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.

• For every Demidovich there is an anti-Demidovich (proverb). – Victor Protsak May 21 '10 at 4:09
• Which brings us to the suggestion: Translate anti-Demidovič (Ljaško et al.). – Harun Šiljak Jun 22 '10 at 5:37

Friedrich Levi, Geometrische Konfigurationen

Riemannsche Geometrie Im Grossen by Gromoll, Klingenberg and Meyer. I remember this book being cited by Gromov in his famous green book for further details about connections.

Probably most of the works from Oskar Perron. It has been mentioned already Die Lehre von den Kettenbrüchen, both volumes, but we could also ask for Irrationalzahlen or any of the other works from Perron. Also worth being mentioned, for applied mathematicians, are the works of Grigory Isaakovich Barenblatt, previous to 1994; this is because Barenblatt has consistently worked about scaling phenomena, but from about the beginnings of the 1990's he began to do it on his own, whereas earlier work includes the participation of other marvelous mathematicians, like Z'eldovich; or even works on his own, but it is interesting to compare the evolution of his ideas. So, the name of books with his participation previous to the 1990's, and to my knowledge, not translated into English: * Ja, B Zeldovich, G. I. Barenblatt, V. B. Librovich, G. M. Maxvikadze "Matematicheskaja teorija gorenija i vsriva", 1980 * G. I. Barenblatt, "Podobie, avtomodelnoct, promezhutochnaja asimptotika: teorija i prilozhenija k geofizicheskoi gidrodinamike", 1982 * A. P. Licitsin, G. I. Barenblatt "gidrodinamika i osadkoobrasovanie", 1983 * G. I. Barenblatt, V. N. Entov, V. M. Rizhik, "Dvizhenie zhidkocteii i gazov v prirodnix plactax" 1984 * G. I. Barenblatt, "Analiz razmernosteii" . Uch. pos. M.: MFTI, 1987. 168 с. (I think this last work made it to English under the translation as "Dimensional Analysis", but in that case I saw it only once, at the library of the Department of Applied Mathematics and Theoretical Physics -DAMTP-of Cambridge, UK, many years ago and is likely out of print anyway, plus the edition, to my knowledge was not revised; on top of that, DAMTP changed from Silver Street to Wilberforce road, and I have no idea if that book survived the moving, if indeed was at that library).

Notice also, that in the Nachlass (the collection of manuscripts, left after the death of an academician, and of course in particular a mathematician) of people like Bernhard Riemann or Ernst Zermelo, there might be still some untranslated documents, but then again they also need to be interpreted in a way that could be meaningful, and this because they are not finished, published or even unpublished works, but sketches of something not fully developed.

Hilbert's collected works are not fully translated into English. E.g. his paper Ueber ternaere definite Formen". Acta Math., 17 (1893), 169–197 was only translated into Russian.

Weber's Lehrbuch der algebra, though I see this math underflow post that already expresses this wish: https://math.stackexchange.com/questions/438643/translation-of-webers-lehrbuch-der-algebra-vol-1-2-3

As a textbook bridging from elementary algebra to (then state-of-the-art) research, and coming right at the border between two eras of mathematics, it would be helpful for historians of algebra and mathematics to have this text in english.

I humbly thought I was up for it a year or so ago, but obviously someone more esteemed than I should handle such a monumental translation!

Re: For publication of EGA and SGA, see this: http://www.grothendieckcircle.org/

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

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

• Do you mean his Underweysung der Messung mit dem Zirckel und Richtscheyt (Instruction in Measurement with Compass and Straightedge)? – Phil Harmsworth Jul 9 '17 at 3:37

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.

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.

"Introduction aux groupes arithmétiques" by Armand Borel.

O. Perron - Die Lehre von den Kettenbruechen (Band 1-2)

Bourbaki "Théories spectrales Ch 1-2". This also related to the MO question here.

Etienne Ghys, Pierre de la Harpe, "Sur les Groupes Hyperboliques d’après Mikhael Gromov"

A detailed exposition of Gromov's ideas, outlined in his "Hyperbolic groups" article.

Arithmetique des algebres de quaternions http://www.springer.com/kr/book/9783540099833

Egbert Brieskorn’s Lineare Algebra und analytische Geometrie - the best textbook on the topic in my POV.

I would really love a translation of the third russian edition of "Number Theory" by Borevich and Shafarevich. It has updated notation, revised errata and has numerous new remarks and updated bibliography. Also, the AP english translation is full of misprints. Anyone knows if there is a project of translating this beatiful book?

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

• I happen to know Prus-Wisniowski personally, and he is a fluent English speaker who also translated several Russian papers for me in the mid 1990s. You might want to consider asking him about this. I suspect a translation would fit nicely into one of the MAA book series. – Dave L Renfro Jul 7 '17 at 14:33
• Dave, what is the MAA book series? :) – cheater Jul 7 '17 at 19:14
• I wasn't thinking of a specific book series, but since you asked, Classroom Resource Materials seems to be a good fit for the book. For example, the widely cited (on Math StackExchange) book Real Infinite Series is in this book series. – Dave L Renfro Jul 7 '17 at 19:36
• What is MAA though? – cheater Jul 8 '17 at 11:22
• MAA = Mathematical Association of America, which is mostly teaching and non-research oriented, in contrast to AMS = American Mathematical Society. – Dave L Renfro Jul 10 '17 at 14:35

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

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

Gerhard Thomsen's Topologische Fragen der Differentialgeometrie XVI: Über die topologischen Invarianten der Differentialgleichung $y^{\prime\prime} = f(x,y)(y^\prime)^3 + g(x,y)(y^\prime)^2 + h(x,y)y^\prime + k(x,y)$ Teubner Leipzig 1930.