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There are some questions on mathoverflow such as

with answers that tell us things such as:

Mathematicians prefer to use older books because of some old books are full of amazing ideas and some of them are comprehensive (such as books of Spivak).

Question: What older books (with low quality typesetting) would you like to see reprinted with high quality typesetting?

My question is not just a question. We are a group of math students (most of them are geometry students) that want to re-write popular old books using $\mathrm{\LaTeX}$.

One can search for most cited books such as: Curvature and Betti numbers (K Yano, S Bochner) or Einstein manifolds (AL Besse).

Update: We have some rules:

  1. After sending $\LaTeX$ and PDF file of rewritten books to main author or publisher, we delete it from our computer.

  2. We never publish it anywhere on internet (If publisher or author give an answer for re-typing).

  3. We don't want to earn money by selling these books (If publisher or author didn't accept to pay for our work we have no way but creating a donation page after author or publisher approval).

Note: See books in progress on my blog and encourage us by making a donation.

Update (April 30 2019): It would be great appreciate if you inform me about any grant that support this project.

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    $\begingroup$ wouldn't you run into copyright restrictions? (it typically takes author's life time + 70 years to expire...) $\endgroup$ – Carlo Beenakker Dec 17 '18 at 8:21
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    $\begingroup$ I'm afraid not without asking permission from copyright holders. $\endgroup$ – Carlo Beenakker Dec 17 '18 at 9:44
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    $\begingroup$ I'm surely not the only one who hopes you'll do it anyway. $\endgroup$ – Harry Gindi Dec 17 '18 at 11:21
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    $\begingroup$ Project Gutenberg (edit: a non-profit that exists to enable electronic access to public domain works) has a helpful FAQ about re-releasing works (in the US) without copyright restrictions. The "easy" standard is any edition published before 1923 is always fine, with some exceptions for more recent works. See gutenberg.org/wiki/Gutenberg:Copyright_FAQ and of course, consult a lawyer. $\endgroup$ – Ben Burns Dec 17 '18 at 14:56
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    $\begingroup$ Besse's Einstein Manifolds has excellent quality typesetting, so perhaps you would rather mention something older, like Bott's beautiful Lectures on Characteristic Classes and Foliations. $\endgroup$ – Ben McKay Dec 17 '18 at 15:14

50 Answers 50

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Hilbert’s Foundations of Geometry, with errata and better diagrams.

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    $\begingroup$ It is already done here. $\endgroup$ – user57432 Dec 18 '18 at 4:01
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Two collections of papers on category theory from the 70s:

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Grothendieck et al.'s SGA n for n >= 5. SMF has done SGA1,2,4, and SGA3.1 and 3.3, with a draft of 3.2 available online. I think it is difficult to overestimate how relevant these books still are.

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Rudin, W., Function theory in polydiscs, Mathematics Lecture Note Series. New York-Amsterdam: W.A. Benjamin, Inc., 188 p. (1969). ZBL0177.34101.

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Number Fields by Daniel A. Marcus.

That's my favorite candidate for real typesetting for two reasons: the book is great and the typewritten text is awful to look at. And it was so at the time the book came out.

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Leonhard Euler's Vollständige Anleitung zur Differenzial-Rechnung and his Vollständige Anleitung zur Integralrechnung.

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  • $\begingroup$ Wow! Did Euler ever publish in German? I thought he published all in Latin. $\endgroup$ – Allawonder Apr 30 '19 at 17:42
  • $\begingroup$ @Allawonder: those two books are translations from Latin to German by Johann Michelsen. $\endgroup$ – Michael Bächtold May 1 '19 at 8:47
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    $\begingroup$ @Allawonder I'm not aware of a good english translation of this. If there is one that would also be nice. $\endgroup$ – Michael Bächtold May 1 '19 at 9:14
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    $\begingroup$ @Allawonder Thanks! I had forgotten Blanton's translation but was aware of Bruce's. I haven't read much of Bruce's translation, but noticed in one particular case, that it was not of much help. $\endgroup$ – Michael Bächtold May 1 '19 at 10:06
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    $\begingroup$ I agree with you that Bruce's translation is sometimes difficult to understand. I hinted at something like that in my last comment. However, since there are no others... $\endgroup$ – Allawonder May 1 '19 at 10:17
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All eight volumes of Grothendieck's Éléments de géométrie algébrique, from 1960-1967.

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    $\begingroup$ What's wrong with the typesetting of these ones? The versions available via Numdam seem fine to me. $\endgroup$ – Fred Rohrer Dec 18 '18 at 17:56
  • $\begingroup$ @FredRohrer apologies; the only version I had seen before had much worse typesetting $\endgroup$ – Liam Baker Dec 18 '18 at 18:13
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There are many beautiful mathematical books, e.g. by Milnor, Serre, ... However, if I had to select only one, it would be by Emil Artin, Theory of Algebraic Numbers.

It should be allowed to make some minor editing. Indeed, the book is exceptionally elegant despite the fact that the note taker and translator were not always understanding the text. For instance, a marginal remark was called a theorem when the real result was stated as a regular part of the text. But then, who knows, possibly this is also a part of this charming and profound monography.

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    $\begingroup$ Perhaps this book is included as part of "Expostion by Emil Artin: A Selection", pag. 120-250, published by the AMS. $\endgroup$ – F Zaldivar Dec 20 '18 at 17:30
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Topics in multiplicative number theory by H.L. Montgomery. It is not out of print, but a version in LaTeX quality would be a significant improvement.

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I don't know whether the book mentioned in the question is readable or not yet; so I post it as an answer:

Curvature and Betti numbers by K. Yano and S. Bochner.

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Differential Geometry in the Large: Seminar Lectures New York University 1946 and Stanford University 1956 by Heinz Hopf.

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"Surface Area" by Lamberto Cesari, published by Princeton University press in 1956. It is similar to "Length and Area" of Tibor Rado, but the contents of the two books do not overlap and the book by Cesari has a complete bibliography that covers perhaps all contributions to the area problem from its beginning around 1900 up to its date of publication: also, it includes Cesari's complete solution to this problem, which is not easy to find elsewhere at all, since it was published in several large memories by the "Reale Accademia d'Italia" during the WWII.

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Stong, Robert E. (1968). Notes on cobordism theory. Mathematical notes. Princeton, NJ: Princeton University Press.

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  • $\begingroup$ Oh yes please... ! $\endgroup$ – elidiot May 10 at 19:32
  • $\begingroup$ Unfortunately this answer not highly up-voted!! So I don't think it is useful to do this. $\endgroup$ – C.F.G May 10 at 20:44
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Chern S.S. - Complex manifolds without potential theory (With an Appendix on the Geometry of Characteristic Classes)- Springer (1995)

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Antwerp Proceedings, ie Modular Functions in One Variable from 1972. Important historical testament with numerous classic studies (Deligne-Rapoport on moduli of elliptic curves, Deligne on $L$-function, Swinnerton-Dyer on image of Galois Representation, Serre, and Katz on $p$-adic modular form, Tate's algorithm, BSD conjecture, etc) and the volumes are so big that they can break apart physically upon casual perusal. Typeset on a typewriter unfortunately.

(I own the volumes previous owned by late Swinnerton-Dyer, who probably kept the set on the shelf, but they easily started to develop crevices once I started reading)

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Gekeler's Drinfeld Modular Curves, 1986

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I am very surprised no one has mentioned Sheaf Theory by B.R. Tennison. It is an awesome book : definitions and theorems are stated very precisely yet lucidly, and the proofs are detailed. It is a favorite of many Algebraic Geometers.

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A preprint of G. Perelman: Alexandrov's space with curvatures bounded from below II.

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The Homology of Iterated Loop Spaces (Thomas Joseph Lada, J. Peter May, Frederick Ronald Cohen),

The Geometry of Iterated Loop Spaces (J. Peter May), [EDIT: has been done by Nicholas Hamblet, pdf link]

$E_\infty$ ring spaces and $E_\infty$ ring spectra (J. Peter May),

$H_\infty$ ring spectra and their applications (R. R. Bruner, J. Peter May, James McClure),

Equivariant stable homotopy theory (L. Gaunce Lewis, Mark Steinberger, J. Peter May), and

A general algebraic approach to Steenrod operations (J. Peter May) which is not a book but an article essential to most of the mentionned books.

These are books and papers that I would love to have in a beautiful LaTeX version because they have major historical importance, are still important references which are quoted everyday, and present some proofs and computations that have not been fully exposed in one comprehensive reference as far as I know (and the recent documents very often cite these when it comes to technicalities). The article of May would deserve new modern notations also...

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Little & Ives 1958 Complete book of Science

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    $\begingroup$ That book was beautifully typeset (see rubylane.com/item/632271-007689/…). It is not hard to find a copy, and not expensive. Your answer doesn't seem to me to be in the spirit of this question. $\endgroup$ – Ben McKay Dec 18 '18 at 8:59
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