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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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3  
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

49 Answers 49

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

Chebotarev's "Grundzüge der Galois'schen Theorie"

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Catégories et structures by Charrles Ehresmann

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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 '10 at 4:09

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

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veit79 is referring to the following news: golem.ph.utexas.edu/category/2010/02/… –  Qiaochu Yuan Mar 19 '10 at 7:46

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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Équations différentielles à points singuliers réguliers, by Deligne.

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

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"Introduction aux groupes arithmétiques" by Armand Borel.

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"Quadratische Formen" by Martin Kneser.

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

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

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

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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.

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