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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

45 Answers 45

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I have some experience resurrecting old math books and I want to make a few comments about copyright.

First, it is definitely true that except for very old books, someone owns the copyright. Typically it's the publisher, although sometimes it's the author. (If it's a collection of articles by multiple authors then the copyright may be shared in some complicated way.) In some cases, it's not actually clear who owns the copyright, e.g., because the publisher was bought out by another publisher and some of the paperwork was misplaced. But in any case, usually you should start by presuming that the publisher owns the copyright.

What are the implications of copyright? First, there's really nothing stopping you from creating a $\mathrm{\LaTeX}$ version of a book for your own personal use. It's only when you want to post it on the web or share it with someone else that copyright issues rear their head. So one approach you can take is to do all the work, and then approach the copyright holder and hope that they will agree to publish your new version. Note that if you do this, then the copyright holder is under no obligation to pay you for your work or give you royalties or anything like that.

Another possibility is to approach the copyright holder before doing any work and reach some sort of agreement ahead of time. The advantage of doing this is that you know what you are getting yourself into before you put in a lot of work. Be aware that even if the book gets republished and it sells well, you're unlikely to see much if any of that money.

Either way, be aware that the copyright holder is under no obligation to do you any favors. If they elect not to republish the book then legally there's not much you can do about that. If you've already created the $\mathrm{\LaTeX}$, they could demand that you hand it over (EDIT in response to comments: Such a demand will typically not be legally enforceable but they may issue it anyway as an intimidation tactic), and if you comply, they may then sit on it without publishing it or releasing the copyright to anyone else.

Having said all this, I don't mean to say that you shouldn't go ahead with your plans. I have successfully managed to get a couple of old math books republished. It was more work than I initially expected (even though I didn't have to do any typesetting) and I didn't ask for or receive a dime, but I did get the satisfaction of seeing the books resurrected.

Finally, as others have already mentioned, if you're going to all this trouble then you might want to consider not just re-typesetting but also correcting as many errors as possible.

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    $\begingroup$ The claims that they can "demand you hand it over" and that they have "no obligation to pay you" seems dubious. If you produce a derived work, the copyright holder for the original work does not automatically obtain rights to it, but of course you have no rights to reproduce or distribute it either. There is certainly room for negotiating compensation, although socially/career-wise it may be a very bad idea to try to do so. $\endgroup$ – R.. Dec 18 '18 at 5:19
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    $\begingroup$ Work on it in secret, release it anonymously, and the internet will make sure it never disappears. $\endgroup$ – Harry Gindi Dec 18 '18 at 6:45
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    $\begingroup$ @R.. : I think you misunderstand my point. In the U.S. at least, free speech is protected by the First Amendment. Therefore the publisher is not doing anything criminal by issuing a demand. That does not mean that the publisher can force you to comply with the demand. I'm just trying to tell you what kinds of behavior you might encounter. I've learned the hard way that publishers do not always behave reasonably. A lot of people are surprised at the behavior they encounter from companies when it comes to copyright and I'm just forewarning people. $\endgroup$ – Timothy Chow Dec 18 '18 at 21:03
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    $\begingroup$ @TimothyChow: OK, I misunderstood your sense of "can demand", as I think a lot of people would, as a claim that they have legal standing for a court to order you to do so based on their request, rather than just that they have the right to state the "demand". However I think the latter is also shaky. Free speech does not entitle you to make frivilous legal threats to mislead someone into waiving their rights. $\endgroup$ – R.. Dec 19 '18 at 1:08
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    $\begingroup$ I would edit this answer to make sure “demand that you hand it over” is not interpreted as legally enforceable. $\endgroup$ – user76284 Dec 19 '18 at 3:51
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Morse Theory by Milnor (and Spivak and Wells)

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    $\begingroup$ Yes, and with modern notation. $\endgroup$ – Michael Dec 17 '18 at 17:06
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    $\begingroup$ Isn’t the notation pretty modern? Or am I just too old? $\endgroup$ – Deane Yang Dec 18 '18 at 6:12
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    $\begingroup$ @C.F.G I think it would be most natural that you approach him yourself — it's your project/idea after all. You can ask him whether he would welcome such an idea and if he does, either he could talk to the publisher directly, or you could tell the publisher that the author of the books would support your project. $\endgroup$ – Earthliŋ Dec 26 '18 at 10:58
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    $\begingroup$ I think that the natural person to approach about undertaking such a project would be Michael Spivak. He still runs Publish or Perish, the last I knew, and he's a LaTeX guru who actually did typeset his Comprehensive Introduction to Differential Geometry. At the very least, I think that he'd give you some valuable advice. $\endgroup$ – Robert Bryant Jan 2 at 12:36
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    $\begingroup$ Michael Spivak told me that ``Morse Theory and Characteristic Classes may have been typeset''!!! $\endgroup$ – C.F.G Jan 8 at 13:49
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Characteristic Classes by Stasheff and Milnor. Morse Theory by Milnor was already mentioned. Lectures on the h-cobordism theorem would be a nice one. It is also rather short.

These books are published by the Princeton University Press.

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  • $\begingroup$ After re-typing of Morse Theory ([Link][oldbookstonew.blogspot.com/]), I am waiting for what Michael Spivak told me: ``Morse Theory and Characteristic Classes may have been typeset''. Is there any new edition of this books? $\endgroup$ – C.F.G Apr 25 at 9:59
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Just for fun, Principia mathematica.

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    $\begingroup$ In modern notation, too? $\endgroup$ – David Roberts Dec 17 '18 at 20:49
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    $\begingroup$ Sure, so we could tell what it’s about. $\endgroup$ – Andrej Bauer Dec 17 '18 at 21:02
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    $\begingroup$ Not sure that would be a good idea @DavidRoberts. See, e.g., here (emphasis mine), "This article provides an introduction to the symbolism of PM, showing how that symbolism can be translated into a more contemporary notation which should be familiar to anyone who has had a first course in symbolic logic. This translation is offered as an aid to learning the original notation, which itself is a subject of scholarly dispute, and embodies substantive logical doctrines so that it cannot simply be replaced by contemporary symbolism." $\endgroup$ – user 170039 Dec 18 '18 at 4:14
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    $\begingroup$ Someone has already done this one: kickstarter.com/projects/1174653512/… $\endgroup$ – Joshua Frank Dec 19 '18 at 17:04
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    $\begingroup$ @JoshuaFrank: We are talking about Whitehead and Russell's Principia Mathematica. $\endgroup$ – user 170039 Dec 20 '18 at 3:27
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Many of the pamphlets produced by Mir publishers (USSR) called (if I recall correctly) the "Little Mathematics Library" were gems to be discovered by High School students. There is an attempt to collect these titles and others from the same publisher.

If these could be reproduced, that would be wonderful for students at that level and the rest of us as well.

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Mumford's Abelian Varieties. (It would also benefit from an expanded index.) However, as noted, you'd need to get permission from whoever holds the copyright.

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    $\begingroup$ There is a LaTeX-typeset edition of this book "published for the Tata Institute of Fundamental Research by the Hindustan Book Agency" and distributed internationally by the AMS. It is available on the AMS website at a list price of $75: bookstore.ams.org/tifr-13 $\endgroup$ – Bort Dec 17 '18 at 16:03
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    $\begingroup$ @Bort Thanks, I hadn't realized that Tata had reprinted it. I have two copies of the original edition, but they're falling apart! In terms of price, if you're an AMS members, it's only $60 with free shipping. OTOH, for some reason on Amazon there's no link to the AMS site, and lots of 3rd party sellers who are charging hundreds of dollars. $\endgroup$ – Joe Silverman Dec 17 '18 at 21:48
  • $\begingroup$ A friend bought it for me from Amazon India. The book itself costs about 5euro only. $\endgroup$ – Fang Hung-chien Dec 18 '18 at 21:52
  • $\begingroup$ The new edition of Abelian Varieties has quite a few typos; thankfully, Brian Conrad has compiled many of them into this list. An older version is available on the Tata Institute website. $\endgroup$ – Takumi Murayama Dec 19 '18 at 12:37
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A general theory of Fibre spaces with Structure sheaf by Alexandre Grothendieck

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  • $\begingroup$ Is this book used still? its citation is 167 due to Google that seems very low. $\endgroup$ – C.F.G Jul 9 at 6:11
  • $\begingroup$ @C.F.G it is not used much that is why I would like to get This reprinted. So, people can see.. $\endgroup$ – Praphulla Koushik Jul 9 at 13:03
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The 1978 book "Probabilities and Potential" by Claude Dellacherie, and Paul-André Meyer (and later volumes) is still a standard reference for man facts concerning probability theory, stochastic processes, and measure theory. Sadly, the typesetting is really ugly and newer reprints are just image copies.

Interestingly, the earlier 1966 book "Probability and Potentials" by Meyer alone, essentially the predecessor, was beautifully typeset.

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  • $\begingroup$ That timing would appear to match what Knuth found with TAoCP, leading to TeX $\endgroup$ – Chris H Dec 19 '18 at 15:40
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Complexe Cotangent et Déformations I & II by Illusie

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Borevich-Shafarevich in English or French. Without typos and with modern notation. Please.

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  • $\begingroup$ It seems that this book has good quality typesetting. See here: amazon.com/Number-Theory-Pure-Applied-Mathematics/dp/0121178501 $\endgroup$ – C.F.G Jan 8 at 5:55
  • $\begingroup$ I have an original copy. Its not a disaster, but it uses some old (and sometimes) ugly notation, and it has many many typos. The book is a masterpiece and it should a pleasure to read in all senses :) $\endgroup$ – EFinat-S Jan 8 at 15:10
  • $\begingroup$ There is a scanned copy. Google "borevich shafarevich", the first link. $\endgroup$ – EFinat-S Jan 8 at 15:11
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Algebra for Beginners, by Todhunter.

It was first printed 1876, so it should be totally fine to make a typeset version of this. I got an original as a gift, and read it. For a research mathematician, it is elementary, but there is at least one trick that I learned from that book, that high-school (and undergraduate university) did not teach me:

How to simplify $\sqrt{7+4\sqrt{3}}$?

Also, the book is still being printed, latest I can find is from 2016, with a price of about $40 (when ordering from a Swedish company).

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    $\begingroup$ Does the trick have anything to do with period two points of a quadratic function? $\endgroup$ – JP McCarthy Dec 17 '18 at 12:07
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    $\begingroup$ @JPMcCarthy: The trick is very simple: assume the expression is of the form $\sqrt{x}+\sqrt{y}$ and square both sides, and then see what happens. $\endgroup$ – Per Alexandersson Dec 17 '18 at 18:56
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    $\begingroup$ @PerAlexandersson which leads to the lovely formula $$\sqrt{a+\sqrt b} = \sqrt{\frac{a-\sqrt{a^2-b}}{{2}}}+\sqrt{\frac{a+\sqrt{a^2-b}}{{2}}}$$ $\endgroup$ – Greg Martin Dec 19 '18 at 18:34
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    $\begingroup$ By the way, you can find Todhunter's textbook on spherical trigonometry typeset in TeX. gutenberg.org/ebooks/19770 $\endgroup$ – John D. Cook Dec 22 '18 at 16:11
  • $\begingroup$ @PerAlexandersson Euler explains this trick in his Algebra. Also, it's still taught to secondary school students who take Further Mathematics (in at least my country) under the title of surds. $\endgroup$ – Allawonder Apr 30 at 17:38
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Calculus on Manifolds by Michael Spivak in modern notation. Feels like everyone is saying this but: not sure about the copyright.

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    $\begingroup$ What notations are outdated in this text? I learned out of it, but I haven't seen enough other literature to know. $\endgroup$ – AlexanderJ93 Dec 18 '18 at 8:59
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    $\begingroup$ Calculus on Manifolds is not only a clearly written classic, but also one of the most beautifully typeset book I know (especially the original coloured version — the reprints seem to be in black and white). To be honest, I don't see how it fits this category — it would be hard to match the quality of the original typesetting... (Also, I wouldn't regard the notation as antiquated.) $\endgroup$ – Earthliŋ Dec 20 '18 at 18:30
  • $\begingroup$ Thanks, but I don't think they discuss typography of mathematics books there ^_^ $\endgroup$ – Earthliŋ Dec 20 '18 at 22:04
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Paul Cohen's Set Theory and the Continuum Hypothesis may be in print, but from the preview on amazon (dot) com it seems to be photographic copy of the one set by a typewritter, with hand-written diacritics.

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EDIT: The work has been done (thanks @jozefg for noticing). The tex version is available at the blog of one of the authors


The 1977 book of Makkai and Reyes "First-order categorical logic" is an amazing book and still the standard reference for the subject. But the typesetting, and especially the diagrams, are not good. It is readable, but it would be much better if we had a modern edition just for reference. This job has been done for example with some SGA volumes, as part of an ongoing project that aims to retype them in Latex. These are available online through the nlab page.

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Structures on manifolds, by Kentaro Yano and Masahiro Kon would be nice.

It is deep, broad, has been influential and as far as i know there is no other edition than the 1984, 1985 editions (which have rather low-quality typesetting).

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All volumes of Asterisque, from 1973 to about 1990.

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    $\begingroup$ Aren’t they finally available online? $\endgroup$ – LSpice Dec 19 '18 at 13:57
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    $\begingroup$ @LSpice: Yes, but in their original typesetting, mostly by typewriter. $\endgroup$ – Ben McKay Dec 19 '18 at 14:12
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    $\begingroup$ I feel like if people wanted to do this, they could possibly get an SMF grant. $\endgroup$ – Harry Gindi Dec 19 '18 at 17:26
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Curvature and Characteristic classes by J. L. Dupont.

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Arithmétique des algèbres de quaternions by Marie-France Vigneras

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    $\begingroup$ Yes, although John Voight is writing an encyclopedic masterpiece on Quaternion Algebras. $\endgroup$ – EFinat-S Dec 17 '18 at 14:53
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    $\begingroup$ @EFinat-S It is already written, as Ben likely knows. $\endgroup$ – Kimball Dec 18 '18 at 0:36
  • $\begingroup$ @Kimball Yes, I meant that in the sense that he is updating it constantly. $\endgroup$ – EFinat-S Dec 18 '18 at 0:45
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Noel J. Hicks's charming little Notes on Differential Geometry, published by van Nostrand Reinhold in 1965 and reissued in 1971.

I would also add Michael Beals's Propagation and Interaction of Singularities in Nonlinear Hyperbolic Problems, published by Birkhäuser in 1989. Its typesetting is absolutely painful to read - it looks like it came out of an old dot-matrix printer.

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    $\begingroup$ I was lucky enough to inherit this from my father. $\endgroup$ – Deane Yang Dec 18 '18 at 6:11
  • $\begingroup$ I've got an used copy of the 1971 issue, it's incredibly useful. $\endgroup$ – Pedro Lauridsen Ribeiro Dec 18 '18 at 12:29
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Masterpieces that deserve at least neat diagrams. After all these years, there is still a lot that one can learn from them and will probably not see it in quite the same extra convenient form anywhere else.

Don't know if any of these are republished - please tell me if they are.

Stable Homotopy and Generalized Homology by J. F. Adams

Just two instances from lots and lots of the brilliant early Springer LNM stuff:

Catégories Cofibrées Additives et Complexe Cotangent Relatif by Grothendieck

The Relation of Cobordism to K-theories by Conner and Floyd

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It's more of a book-length paper than an actual book, but I always wanted a LaTeX version of E. T. Jaynes' where do we stand on maximum entropy?. I retyped about 20% of it myself at some point, but never finished the project.

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    $\begingroup$ Perhaps you could make your partial effort available, say, as a git repository, so that others could build on it rather than starting from scratch? $\endgroup$ – LSpice Dec 19 '18 at 13:57
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    $\begingroup$ @LSpice if anyone seriously wants to continue the project I'd be happy to provide it to them. My version goes up to equation B20, and keeps the layout, numbering and punctuation as close to the original as possible. The references are not done yet. $\endgroup$ – Nathaniel Dec 23 '18 at 4:51
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Inequalities by G. H. Hardy, J. E. Littlewood, G. Pólya

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Seminar on the Atiyah-Singer Index theorem by Richard Palais

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History of Functional analysis by Jean Dieudonné is a very interesting book, but it is "set" with a typewriter.

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I would like a book, written in english typeset in LATEX and updated to modern notation, which includes some abridged form of the Polish journal Fundamenta Mathematicae up until World War II (this amounts to 32 volumes over 20 years).

enter image description here

They contain incredible amounts of beautiful topology there which is largely inaccessible due to language (mostly French I believe), notation, and occasionally poor typesetting. I feel that their knowledge and perspective is lost to most modern researchers. No book comes close to addressing their contents.

This of course would be a major project, but name your price as far as I'm concerned. It would be the type of book every mathematician should own.

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    $\begingroup$ Back issues of Fundamenta are freely available online. A project such as the one you describe would be rather expensive and not so easily accessible. $\endgroup$ – Andrés E. Caicedo Dec 17 '18 at 23:09
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    $\begingroup$ @AndrésE.Caicedo Yes, I'm aware. And admittedly if I were better at reading French those originals would probably be fine for me. $\endgroup$ – Forever Mozart Dec 17 '18 at 23:14
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Local Fields by J. W. S. Cassels. (Maybe even O'Meara's Introduction to Quadratic Forms).

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Dan Henry's "Geometric Theory of Semilinear Parabolic Equations". This 1981 text is (in my opinion) really well written, but can be a chore to read due to the typewriter math. As a runner up in the same category, I'd say Dodd et al., "Solitons and Nonlinear Wave Equations".

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Two collections of papers on category theory from the 70s:

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A Course of Modern Analysis by Whittaker and Watson

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    $\begingroup$ I think that one is pretty OK typeset, as is, at least my cooy. (The previous owner of my copy was a smoker, so I have the problem that it stinks. But it is a joy to read anyways.) $\endgroup$ – mickep Dec 23 '18 at 12:39
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Linear and Quasi-linear Equations of Parabolic Type by O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Ural′ceva

https://bookstore.ams.org/mmono-23

Linear and Quasilinear Elliptic Equations by Nina Uraltseva and Olga Ladyzhenskaya

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protected by Yemon Choi Dec 18 '18 at 12:39

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