154

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).

C.F.G
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    wouldn't you run into copyright restrictions? (it typically takes author's life time + 70 years to expire...) – Carlo Beenakker Dec 17 '18 at 08:21
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    Is there any legal way to do this work? – C.F.G Dec 17 '18 at 08:24
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    I'm afraid not without asking permission from copyright holders. – Carlo Beenakker Dec 17 '18 at 09:44
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    I'm surely not the only one who hopes you'll do it anyway. – Harry Gindi Dec 17 '18 at 11:21
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    You could ask the people involved in the TAC Reprints series http://www.tac.mta.ca/tac/reprints/index.html how they approached the associated copyright issues – Yemon Choi Dec 17 '18 at 12:45
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    Not an answer since this already happened, but I would like to mention that Marcus' book Number Fields has rather recently been rewritten just like that. – Wojowu Dec 17 '18 at 13:27
  • Similarly, the 4 volumes of the Cabal series of proceedings in set theory are in the process of being reissued, with comentary, some updates, and new papers. Three have appeared already, the last one is expected in 2019. – Andrés E. Caicedo Dec 17 '18 at 14:16
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    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 https://www.gutenberg.org/wiki/Gutenberg:Copyright_FAQ and of course, consult a lawyer. – Ben Burns Dec 17 '18 at 14:56
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    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. – Ben McKay Dec 17 '18 at 15:14
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    Side note, Project Gutenberg is associated with Distributed Proofreaders which is a group converting very old (out of copyright) work into high quality electronic versions. Sometimes they have math texts for proofreading. https://www.pgdp.net/ – user3067860 Dec 17 '18 at 18:58
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    Elsevier notified Yves Meyer that the copies of his book "Algebraic numbers and Harmonic analysis" was to be destroyed. Because they do not want to store them. Some months ago an old copy was in Amazon for 1000$, now there are none. How can they ask for rights of copyrights? – juan Dec 17 '18 at 20:07
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    John Walsh’s book on spde. – shalop Dec 17 '18 at 22:06
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    In addition to "high quality typesetting", I hope you will aim for "high quality printing and binding". – Forever Mozart Dec 18 '18 at 01:25
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    @CarloBeenakker the OP didn't say what they intend to do after copying the books, but it would seem to fall under the fair use exemption if it is for criticism/classroom use and they don't distribute the copies that they make outside of the classroom. –  Dec 18 '18 at 03:31
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    Some advice, having seen projects like this started and abandoned: It's probably a lot more reasonable to 'remaster' a bunch of small works rather than invest time in one big one. This also allows you to do it in secret and put it up on one or another Russian website we all use before anyone inconvenient gets word of it... – Harry Gindi Dec 18 '18 at 12:01
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    I agree with Ben McKay, Besse's Einstein Manifolds is not really a good example. Its typesetting quality is as good as you can get. – Pedro Lauridsen Ribeiro Dec 18 '18 at 13:16
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    Our goal is not just high-quality for printed version. Electronic version that has clickable links and cross-references is a good feature. – C.F.G Dec 19 '18 at 07:08
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    Is this question potentially a duplicate of: https://mathoverflow.net/questions/64905/which-book-would-you-like-to-see-texified –  Dec 19 '18 at 17:29
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    Some answers seem to be misunderstanding the question as "what old books would you like to be freely available as a PDF with high-quality typesetting"... – Earthliŋ Dec 20 '18 at 18:38
  • I have too little rep to post an answer: "Riemannian Geometry, Fibre Bundles, Kaluza-Klein Theories and All That..." by Jadczyk and Coquereaux. – Mnifldz Dec 22 '18 at 14:47
  • Remember that there is a certain publisher who reprint the out-of-print math books for cheap. But they do it as an identical copy to earlier editions. Not telling the publusher to omit ads. – Oleg Lobachev Dec 22 '18 at 16:16
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    I would like to see contemporary books printed on the much thinner paper that was used long ago. – copper.hat Dec 25 '18 at 07:14
  • at the undergraduate level i'd love to see spivak's calculus on manifolds with a more refined edition – user153330 Dec 25 '18 at 14:31
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    I'll add that typing up the LaTeX yourself is probably a waste of time - there are automated computer vision solutions that will convert a scanned document to LaTeX for you, cutting down a large percent of the effort. – Nathaniel Bubis Dec 30 '18 at 08:20
  • @OlegLobachev I thought you meant Dover, but since that is such a commonplace word, you probably would not have had to worry about ads (same with Cambridge, Oxford etc.) So now I wonder which publisher I do not know about? Any hints? –  Mar 17 '19 at 22:14
  • I meant one of those you mentioned already. – Oleg Lobachev Mar 18 '19 at 18:23
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    von Neumann's Mathematical Foundations of Quantum Mechanics badly needed this for a long time (it was printed from a typewritten manuscript with handwritten math). In 2018, someone published a TeXified edition through Princeton Univ. Press. Unfortunately, it's ridiculously expensive (link). I wonder if this oldbookstonew project might have gotten to it first and gotten PUP to make it more affordable, and if there are other opportunities like that. – none Jun 02 '19 at 07:45
  • Maybe the real question is ... when will AI become good enough to OCR old math books? – Gerald Edgar Dec 04 '23 at 14:53

54 Answers54

61

Morse Theory by Milnor (and Spivak and Wells)

$\color{blue}{\text{Typesetting of this book has been finished}}$. Read it online here

C.F.G
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Neal
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    Yes, and with modern notation. – Michael Dec 17 '18 at 17:06
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    Isn’t the notation pretty modern? Or am I just too old? – Deane Yang Dec 18 '18 at 06:12
  • Is there someone here to talk to Professor Milnor for gaining permission for updating his books? – C.F.G Dec 24 '18 at 07:18
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    @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. – Earthliŋ Dec 26 '18 at 10:58
  • I sent an email to him already but I doubt that he read emails because of his poor eyesight. – C.F.G Dec 27 '18 at 07:55
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    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. – Robert Bryant Jan 02 '19 at 12:36
  • Thank you professor Robert Bryant. – C.F.G Jan 06 '19 at 06:06
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    Michael Spivak told me that ``Morse Theory and Characteristic Classes may have been typeset''!!! – C.F.G Jan 08 '19 at 13:49
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    Because Publisher and Author of this book Leaved my email without any response I'll Publish it freely. Download It from here: https://oldbookstonew.blogspot.com. – C.F.G Mar 16 '19 at 19:58
  • I wonder about the $\vdash$ notation in that book. – Michael Jan 23 '20 at 17:09
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    @Michael: I wanted to change $\vdash$ to $\nabla$, but the author argued in the footnote that his notation has more advantage than others. – C.F.G Mar 08 '20 at 16:40
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    A typo in your excellent version: page 26, S7 should be $\mathbb{S}^7$. – Ben McKay Nov 27 '21 at 17:41
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    Another typo: in the preface "Smale nave studied" should be "Smale have studied". – Ben McKay Nov 29 '21 at 17:12
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    p. 17 "391-4o6" should be "391-406" – Ben McKay Nov 29 '21 at 17:14
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    Wow, that's a beautiful job of retypesetting Morse Theory! – Daniel Asimov Dec 04 '23 at 20:01
57

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.

wchargin
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Timothy Chow
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    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. – R.. GitHub STOP HELPING ICE Dec 18 '18 at 05:19
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    Work on it in secret, release it anonymously, and the internet will make sure it never disappears. – Harry Gindi Dec 18 '18 at 06:45
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    There is an other point that may be important. If you also translate the book (e.g. from german into English) that may trigger additional interest from the publisher. I speak for semi-personal experience. Of course you need to know a bit of german, but not a lot is required for math books. – lcv Dec 18 '18 at 07:22
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    @R.. : They can certainly demand that you hand it over. That doesn't mean you have to accede to the demand. If you have done some unsolicited work, then they have no obligation to pay you. Of course if you negotiate a contract, then they are obligated to abide by the contract, on pain of a civil suit. – Timothy Chow Dec 18 '18 at 16:39
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    @TimothyChow: Under what law do you claim they can demand you hand it over? They can demand you not publish it (and take down and compensate them if you already did publish it) but they can't make you give them something you have in your private possession, nor can they make you give them permission to use what you illegally published - although they could certainly negotiate your doing so as part of dropping/reducing charges against you. – R.. GitHub STOP HELPING ICE Dec 18 '18 at 17:57
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    @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. – Timothy Chow Dec 18 '18 at 21:03
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    @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. – R.. GitHub STOP HELPING ICE Dec 19 '18 at 01:08
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    I would edit this answer to make sure “demand that you hand it over” is not interpreted as legally enforceable. – user76284 Dec 19 '18 at 03:51
  • @R. I'm curious - why exactly could it be "very bad" for your career to try and do this? If you're making sure to try and negotiate a deal with the author/owner and thus trying respect hir/their rights, what exactly would be the bad thing that happens? At worst to me it seems you just get told "No", and then as long as you don't try to impose yourself against that and desist, how is that a problem? – The_Sympathizer Dec 22 '18 at 06:39
  • And moreover I think trying to seek permission from the authors/owners is probably the best approach because it can save you a lot of work and also a lot of grief, or at least it will tell you that if you still do want to do the work, you have to be willing to be content with it for your personal enjoyment only. Whereas the consequences of actual copyright infringement that makes it to court really can be serious, with expensive lawsuits and a true reputation hit as a pirate. – The_Sympathizer Dec 22 '18 at 06:41
  • And depending on how strongly said author/owner values hir/their IP (and for better or worse how wealthy and/or well-connected with all the implications that has so as to be able to afford the wherewithal to pursue the case in court), that could be a very plausible thing to have happen, and especially if what you put out there becomes very popular, which is even more possible (if not even desirable if you think of yourself as doing a service) if your improvements are good. – The_Sympathizer Dec 22 '18 at 06:43
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    @The_Sympathizer: What I said could be bad for your career is demanding pay for unsolicited work typesetting someone else's paper in order to let them use the results you already produced. This is a hostile form of social interaction that's likely to feel like you're holding something for ransom. – R.. GitHub STOP HELPING ICE Dec 22 '18 at 14:05
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    @Timothy Chow: Would it make sense (besides the correction of errors) to update the "old" nomenclature to modern standards? – Moritz Dec 23 '18 at 22:41
  • @Timothy Chow: you noted that ``there's really nothing stopping you from creating a LATEX version of a book for your own personal use'', if so, all people can do this for their own personal use. They can 'request' LATEX file from someone that has done this before for saving time. So I think that copyright depends on honestness of people. – C.F.G Dec 31 '18 at 15:35
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    @C.F.G : I agree with you. More generally, a peaceful and stable society depends on the honesty of people. – Timothy Chow Dec 31 '18 at 15:58
  • @TimothyChow: in your opinion, do we live in peaceful and stable society? We live in 21st century but there are many wars in the world yet, for what? for nothing. Except mathematicians world, there is no peaceful and stable society. – C.F.G Dec 31 '18 at 17:48
  • @TimothyChow : Because you know about almost all copyright rules, Can you tell me that is it legal that I borrow any book that I need from a friend or a library and retype it for own personal use? – C.F.G Sep 15 '19 at 19:03
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    @C.F.G : You're not going to get into trouble for typing out a copy of a book for your own personal use. – Timothy Chow Sep 15 '19 at 20:24
47

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.

  • $\color{blue}{\text{Typesetting of ``Lectures on the h-cobordism theorem (V3 - 2023)" has been finished}}$. Read it online here

  • $\color{blue}{\text{Typesetting of ``Characteristic Classes" has been finished}}$. Read it online here

C.F.G
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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.

Kapil
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    See also: https://archive.org/details/mir-titles?and[]=subject%3A%22mathematics%22 – ArB Oct 11 '20 at 15:48
24

Just for fun, Principia mathematica.

Andrej Bauer
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    In modern notation, too? – David Roberts Dec 17 '18 at 20:49
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    Sure, so we could tell what it’s about. – Andrej Bauer Dec 17 '18 at 21:02
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    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." –  Dec 18 '18 at 04:14
  • @user170039 it could contribute to the scholarly dispute though. A huge undertaking but if someone would do it, why not? :) – Prof. Falken Dec 19 '18 at 13:36
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    Someone has already done this one: https://www.kickstarter.com/projects/1174653512/isaac-newtons-principia-mathematica-reissue – Joshua Frank Dec 19 '18 at 17:04
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    @JoshuaFrank: We are talking about Whitehead and Russell's Principia Mathematica. –  Dec 20 '18 at 03:27
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    @user170039: my bad, thought it was Newton's. – Joshua Frank Dec 20 '18 at 14:30
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    FYI, see this site: https://www.principiarewrite.com/. – KConrad Dec 08 '21 at 04:26
21

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.

Joe Silverman
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    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: https://bookstore.ams.org/tifr-13/ – Bort Dec 17 '18 at 16:03
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    @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. – Joe Silverman Dec 17 '18 at 21:48
  • A friend bought it for me from Amazon India. The book itself costs about 5euro only. – Fang Hung-chien Dec 18 '18 at 21:52
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    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. – Takumi Murayama Dec 19 '18 at 12:37
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    @TakumiMurayama : The latest printing now incorporates Brian Conrad's corrections. – Timothy Chow May 29 '20 at 15:54
  • @Timothy Chow : I can't find this latest printing anywhere (AMS bookstore, online booksellers etc). Can you give a link ? – Matthieu Romagny Apr 28 '21 at 09:25
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    @MatthieuRomagny It's on the AMS website, but if you just search for "abelian varieties" in the bookstore, there are so many books with that title, it's not near the top. Searching on "Mumford" brings it up mid-page. In any case, here's the link:
    https://bookstore.ams.org/tifr-13/     – Joe Silverman Apr 28 '21 at 10:33
  • @Joe Silverman Thanks, I saw this but the page indicates the book published in 2012. In view of the comment of Timothy Chow on "the latest printing" I was expecting a mention like "reprint 2021". – Matthieu Romagny Apr 28 '21 at 13:13
  • @MatthieuRomagny Good point. But I'm not sure that the AMS bothers mentioning the date of latest printing on its website. They do have a "contact us" link at the bottom of the page with a phone number and email address where one can get product information. If you do find out anything, please do let us know via a comment or an edit to my answer. – Joe Silverman Apr 28 '21 at 13:54
20

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.

Denis Serre
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Michael Greinecker
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19

A general theory of Fibre spaces with Structure sheaf by Alexandre Grothendieck

Praphulla Koushik
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19

Complexe Cotangent et Déformations I & II by Illusie

zzz
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17

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).

Per Alexandersson
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    Does the trick have anything to do with period two points of a quadratic function? – JP McCarthy Dec 17 '18 at 12:07
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    @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. – Per Alexandersson Dec 17 '18 at 18:56
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    @PerAlexandersson which leads to the lovely formula $$\sqrt{a+\sqrt b} = \sqrt{\frac{a-\sqrt{a^2-b}}{{2}}}+\sqrt{\frac{a+\sqrt{a^2-b}}{{2}}}$$ – Greg Martin Dec 19 '18 at 18:34
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    By the way, you can find Todhunter's textbook on spherical trigonometry typeset in TeX. http://www.gutenberg.org/ebooks/19770 – John D. Cook Dec 22 '18 at 16:11
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    @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. – Allawonder Apr 30 '19 at 17:38
16

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

Glorfindel
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efs
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  • It seems that this book has good quality typesetting. See here: https://www.amazon.com/Number-Theory-Pure-Applied-Mathematics/dp/0121178501 – C.F.G Jan 08 '19 at 05:55
  • 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 :) – efs Jan 08 '19 at 15:10
  • There is a scanned copy. Google "borevich shafarevich", the first link. – efs Jan 08 '19 at 15:11
  • The American Mathematical Society looked into "resurrecting" Borevich and Shafarevich and encountered serious copyright obstacles. Not to say that these can't be overcome, but just be aware that you may encounter the same obstacles if you try to resurrect the book yourself. – Timothy Chow May 29 '20 at 15:56
  • @TimothyChow Thanks for the update. This "almost resurrection" was a recent event? – efs May 29 '20 at 16:01
  • @EFinat-S : No, this was ten years ago at least, but I just happened to be browsing this MO question today for other reasons, and thought I'd mention it. – Timothy Chow May 29 '20 at 16:06
14

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.

godelian
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14

All volumes of Asterisque, from 1973 to about 1990.

Ben McKay
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13

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.

Michael Hardy
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12

Arithmétique des algèbres de quaternions by Marie-France Vigneras

12

Inequalities by G. H. Hardy, J. E. Littlewood, G. Pólya

Surb
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11

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

P.S. Many thanks to C.F.G. for delighting update!

მამუკა ჯიბლაძე
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10

Curvature and Characteristic classes by J. L. Dupont.

Praphulla Koushik
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10

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).

Konstantinos Kanakoglou
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10

Noel J. Hicks's charming little Notes on Differential Geometry, published by van Nostrand Reinhold in 1965 and reissued in 1971.

Edit (August 11th 2022): As reported by C.F.G in the comments and a previous edit of his, the $\mathsf{\TeX} \mathsf{\text{romancers}}$ group on Discord (cool name, by the way) $\mathsf{\LaTeX}$-ed Hicks's original 1965 issue and released it this year, it is now freely available in PDF format.

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.

Pedro Lauridsen Ribeiro
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    I was lucky enough to inherit this from my father. – Deane Yang Dec 18 '18 at 06:11
  • I've got an used copy of the 1971 issue, it's incredibly useful. – Pedro Lauridsen Ribeiro Dec 18 '18 at 12:29
  • I believe Hicks's little gem serves a different purpose. It's written in a lecture-note style that gets very quickly to the essential results of the subject (much quicker than the admittedly great books you cited - less than 200 short pages!), with minimal prerequisites and only introducing topological hypotheses at the right moment with proper motivation. It also proves some structural results which are difficult to find proven elsewhere - e.g. J.H.C. Whitehead's theorem on the existence of convex normal neighborhoods for (non necessarily Riemannian) manifolds with an affine connection. – Pedro Lauridsen Ribeiro Feb 08 '21 at 06:48
  • I had an undergraduate research student learn differential geometry for his project through that book alone. I don't think there really is a comparable textbook on differential geometry, if you take all of that into account. – Pedro Lauridsen Ribeiro Feb 08 '21 at 06:48
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    @PedroLauridsenRibeiro https://aareyanmanzoor.github.io/assets/hicks.pdf – C.F.G Aug 11 '22 at 04:37
  • @C.F.G Impressive, thanks a lot! I've entertained for quite some time the idea of LaTeXing Hicks's book myself, but that takes a lot of time... Glad to hear people are doing that. I only wish they had used the newer (1971) issue instead of the original (1965) one, although I don't really know how much difference there is between both since I only have the former. – Pedro Lauridsen Ribeiro Aug 11 '22 at 05:07
10

Seminar on the Atiyah-Singer Index theorem by Richard Palais

user90041
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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.

EDIT 2022-03-16: This has now been typeset here: https://github.com/arxetype/jaynes78

Oscar Cunningham
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N. Virgo
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    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? – LSpice Dec 19 '18 at 13:57
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    @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. – N. Virgo Dec 23 '18 at 04:51
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    The paper has now been typeset. They didn't have permissions to edit this answer so they asked on reddit and I've inserted their link above. – Oscar Cunningham Mar 16 '22 at 13:51
9

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

mickep
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It's slightly prankish but I have to mention Felix Klein's "Riemannsche Flächen: Vorlesungen, gehalten in Göttingen 1891/92" (Riemann surfaces, lectures held in Göttingen 1891/92):

https://archive.org/details/riemannscheflch00purkgoog

The whole book is handwritten! I love looking at the page scans even though I have no idea what they say.

none
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Both Hejhal's books The Selberg Trace Formula for $\mathrm{PSL}_2(\mathbb R)$ are unique references for the classical version of the trace formula in high generality. It computes all the terms explicitly even for vector valued modular forms, including odd weights and nebentypus, and I cannot think of any other reference superseding it.

Unfortunately, these lecture notes published by Springer LNM are difficult to read: it is a very technical topic, with many one-page long formulas, and all the math is handwritten.

Desiderius Severus
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Local Fields by J. W. S. Cassels. (Maybe even O'Meara's Introduction to Quadratic Forms).

pavl0
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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".

Alex Jones
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A Course of Modern Analysis by Whittaker and Watson

John D. Cook
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    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.) – mickep Dec 23 '18 at 12:39
7

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

Truong
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Maybe it would be nice to put in one place pointers to projects aiming to retype old books:

  1. [WIP 10%; me] Adams's blue book [pdf] [source] [notes regarding the re-typesetting];
  2. [Complete (fixing some Tex issues); C.F.G.] Milnor's Morse Theory [link];
  3. [WIP 2%; C.F.G.] Characteristic Classes by Stasheff and Milnor [link];
  4. [WIP 95%; C.F.G.] Milnor's Lectures on the h-cobordism theorem [link];
  5. [0%; C.F.G.] Grothendieck's a general theory of fibre spaces with structure sheaf [link].
C.F.G
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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).

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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.

Forever Mozart
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    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. – Andrés E. Caicedo Dec 17 '18 at 23:09
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    @AndrésE.Caicedo Yes, I'm aware. And admittedly if I were better at reading French those originals would probably be fine for me. – Forever Mozart Dec 17 '18 at 23:14
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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.

Zhipu 'Wilson' Zhao
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A Discord group was recently created with the goal of re-typesetting some old books. We recently finished the first revision of Adams' Stable homotopy and generalised homology, which is now available on Doug Ravenel's website here.

We are currently doing Hicks' Notes on Differential Geometry. If you are interested in helping out, please join the Discord server through this link: https://discord.gg/2JjKvCqHhG. In addition to writers, we need artists to draw diagrams and proofreaders to make sure the writers and artists aren't messing around.

Proposed future books include:

  • H. Triebel - Interpolation Theory, Function Spaces, Differential Operators;
  • D. Rolfsen - Knots and Links;
  • D. Quillen - Homotopical Algebra;
  • H. Matsumura - Commutative Algebra;
  • D. Quillen - Homology of Commutative Rings.
andres
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Hilbert’s Foundations of Geometry, with errata and better diagrams.

Dour High Arch
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5

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

Mike Shulman
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5

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.

lhf
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4

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

András Bátkai
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Ryan Tully-Doyle
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4

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

Edit Dec. 2023: LaTeX'd versions of Euler's Institutiones calculi differentialis can be found for:

  • Vol. 1 on the homepage of the Euler-Kreis Mainz (German translation by A. Aycock)

  • Vol. 2 on arxiv (English translation by A. Aycock)

Michael Bächtold
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  • Wow! Did Euler ever publish in German? I thought he published all in Latin. – Allawonder Apr 30 '19 at 17:42
  • @Allawonder: those two books are translations from Latin to German by Johann Michelsen. – Michael Bächtold May 01 '19 at 08:47
  • Oh, I see. You want the German editions. I was implicitly assuming this project is only about English translations. Sorry. – Allawonder May 01 '19 at 08:50
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    @Allawonder I'm not aware of a good english translation of this. If there is one that would also be nice. – Michael Bächtold May 01 '19 at 09:14
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    Oh, but John D. Blanton has made a translation on the first nine chapters on the one on differentials, published by Springer-Verlag as Foundations of Differential Calculus. It's sad that Blanton doesn't complete the work. However, Ian Bruce has commenced on an ambitious translation project, where he has translated both books completely -- however, I cannot say it reads as nicely as Blanton's translation, but since I'm not able to read Latin I have to do only with what's available. See Bruce's project at http://www.17centurymaths.com – Allawonder May 01 '19 at 09:41
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    @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. – Michael Bächtold May 01 '19 at 10:06
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    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... – Allawonder May 01 '19 at 10:17
  • I noticed that my claim that both book were translated by Michelsen is wrong. The integral books were translated by Joseph Salomon – Michael Bächtold May 11 '19 at 09:00
4

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

C.F.G
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All eight volumes of Grothendieck's Éléments de géométrie algébrique, from 1960-1967.

Liam Baker
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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.

Wlod AA
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    Perhaps this book is included as part of "Expostion by Emil Artin: A Selection", pag. 120-250, published by the AMS. – F Zaldivar Dec 20 '18 at 17:30
3

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.

Jan-Christoph Schlage-Puchta
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3

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.

C.F.G
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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.

Daniele Tampieri
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3

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

C.F.G
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2

Chern S.S. - Complex manifolds without potential theory (With an Appendix on the Geometry of Characteristic Classes)- Springer (1995)

C.F.G
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2

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)

Zhipu 'Wilson' Zhao
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2

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...

David Roberts
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elidiot
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Not so bad quality but I'd like to see the following recent books in new typesetting:

  1. do Carmo, Manfredo Perdigão, Riemannian geometry. Translated from the Portuguese by Francis Flaherty, Mathematics: Theory & Applications. Boston, MA etc.: Birkhäuser. xiii, 300 p. (1992). ZBL0752.53001.
  2. Helgason, Sigurdur, Differential geometry, Lie groups, and symmetric spaces., Graduate Studies in Mathematics. 34. Providence, RI: American Mathematical Society (AMS). xxvi, 641 p. (2001). ZBL0993.53002.
  3. Guillemin, Victor; Pollack, Alan, Differential topology, Providence, RI: AMS Chelsea Publishing (ISBN 978-0-8218-5193-7/hbk). xviii, 222 p. (2010). ZBL1420.57001.
C.F.G
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1

Gekeler's Drinfeld Modular Curves, 1986

Liam Baker
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1

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.

user90041
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A preprint of G. Perelman: Alexandrov's space with curvatures bounded from below II.

C.F.G
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Selected volumes from the Interdisciplinary Mathematics series. written and published by Robert Hermann (1931 - 2020). Good starting points:

Geometric Theory of Non-Linear Differential Equations, Backlund Transformations and Solitons (XII part A and XIV part B)

Toda Lattices, Cosymplectic Manifolds, Bäcklund Transformations, and Kinks (XV part A, XVIII part B)

Cartanian Geometry, Nonlinear Waves, and Control Theory (XX part A, XXI part B)

Interesting ideas, some of which remain to be explored. Being privately published and decades old, the books are hard to obtain, too.

Phil Harmsworth
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Little & Ives 1958 Complete book of Science

Dean Humphus
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    That book was beautifully typeset (see https://www.rubylane.com/item/632271-007689/1958-Little-Eves-Complete-Book-Science). 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. – Ben McKay Dec 18 '18 at 08:59