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I have had an idea for a year or two to write a book relating to the research I do. My specific field (in the mathematical sciences) is somewhat niche and no book currently exists that aggregates the big results into one place. Currently, all of the research is spread across multiple papers, journals and conferences.

I want to write a book about this topic so that future researchers can access basic definitions and results without having to hunt down individual papers. I don't want to write the book for fame/fortune since I recognize it would never be popular with more general audiences. I want to write it to improve my knowledge of the topic, to create a useful resource for others and (getting personal) to fulfill my dream of writing a book.

I have some original research on the topic and most of my current work revolves around the topic as well. But I've heard many people say that PhD candidates should focus on research instead of other pursuits like book-writing. Should I pursue this, or should I focus on research and leave the book for the future?

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    You could publish a survey in a journal, rather than a book – user2768 Oct 31 '17 at 8:43
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    No. Save it until later. Your advisor probably does not want you to lose your focus on anything but the project. – mathreadler Oct 31 '17 at 16:02
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    That is dont do lots of work on it, but writing down small notes and reminders for yourself that does not take up your working time could still be good. – mathreadler Oct 31 '17 at 16:20
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I think it's a very good idea to develop files/manuscript collecting important standard results in one place. To go to the additional trouble (which is much more than one might imagine) of publishing a book with that content, apart from vanity presses, would not be worthwhile for a young academic. Indeed, unless you can do a for-some-reason amazing job of organizing things, since you're not an established expert, have (presumably) no name-recognition, etc., good publishers would not see much reason to publish your book.

But you can assemble a PDF document and put it on-line. And you can revise it as you mature into your subject. Revision is much harder with physical books, or even official "e-books", because many publishers (especially better ones with an established base and style) re-typeset everything into their house style... so correcting typos is not a matter of correcting them in the TeX source, re-typesetting, and re-posting online. :)

EDIT: to clarify the last sentence: Yes, TeX is the current professional standard for mathematicians composing technical documents. It's a mark-up language created by Don Knuth, and donated to the community, in the late 1980s. (There are also WYSISWYG editors.) The older process of typesetting from TeX source documents created a "DVI file", device-independent file, from which postscript files were usually created, although there were DVI readers also. Nowadays, the usual output is PDFs. Further, although years ago it would take several minutes to re-run the typesetting after making changes in the TeX source, nowadays re-typesetting a 30-page document takes an imperceptible time, perhaps a second or two at most. And there are of course various ways of packaging the re-typesetting (as well as creating the TeX source file) in IDEs and so on.

  • To clarify for myself, by re-typesetting, you mean re-running the command to compile TeX into a PDF? (Or clicking a button in an IDE, or something else that does the equivalent) – Nic Hartley Oct 31 '17 at 15:49
  • @QPaysTaxes: Most publishing companies do not use Tex to set their books but different software (e.g. Adobe InDesign). While LaTeX is usually quite good at automatically formatting a manuscript, it is by far not perfect and the best way really is to do it carefully by hand. (Which you could theoretically do in LaTeX as well, however stuff like manually adjusting kerning is not something you want to do in there). – mlk Oct 31 '17 at 16:21
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    To add to the answer, before you write a book it also really helps to have given some lectures about the topic. As an expert one is usually to deep involved to note, which parts are easy and which are unclear. During my PhD, I also had the idea to transform some of my notes into a book, however after giving a few informal lectures to the rest of my group I noticed, that some things I thought obvious and intuitive actually need quite a lot of explanation, while other seemingly good ideas weren't as helpful as I thought. Maybe ask your group if they would be interested in something like this. – mlk Oct 31 '17 at 16:34
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    @mlk Definitely not always good advice. In certain groups there can be lots of rivalry and even commercial interests. – mathreadler Oct 31 '17 at 16:43
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    @mathreadler If your group is that bad, I agree that you should not do this but rather spend all available time writing applications to go someplace else. But apart from this I do not see the harm in talking to other people about already published results. If your group is that hostile, they will not be interested and even if they are, the only thing they could use it for is to write the book themselves. Which would be much more work for them for little to no return. We are talking about a niche field of research level maths after all. – mlk Oct 31 '17 at 17:10
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Of course talk to your advisor about it. Perhaps he will be one of those who says concentrate on your Ph.D. thesis and work the book afterward. Or perhaps he will tell you it is a great idea. He knows (much better than we do) what is involved in your particular case.

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    We should probably also not discount the possibility that his supervisor is female, in which case "she" might know better... – Owen Nov 1 '17 at 9:40
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Well, if ever there was a case when the classic "talk to your advisor" advice was applicable, this is such a case. So, obviously, talk to your advisor.

That being said, since you are in a mathematical science, I think I can predict with a high degree of confidence that if your advisor has any sense he/she will tell you that writing a book can only serve to distract you from your PhD research, and to engage in such a project would be damaging (potentially, fatal) to your prospects of success in finishing your PhD. In short, no, it's not appropriate.

The point is that both doing a PhD in a mathematical science and writing a book are very difficult and ambitious endeavors. A significant proportion of the people who undertake either one of those things do not end up achieving them. And yet, you seem to think that you can do both at the same time. Do you see the problem here?

The only time when writing a book would make sense would be either: (a) after you are an established academic with a proven track record and a tenured (or at least tenure-track, but on a clear path to tenure) position, or: (b) if writing the book was an activity that was synergistic with your normal research work to such a high extent (say, 80% or more overlap) that achieving success in your normal research and writing the book were two simultaneous goals that were realistically achievable with a similar probability to succeeding in just one of those goals. Based on your description it doesn't sound like that's the case here, but I can't say for sure based on the information you've provided.

Two more thoughts on this:

  1. I really like Paul Garrett's suggestion to collect your thoughts on your research area as organically evolving PDF notes that you make available online. I see this approach as much more beneficial to your normal thesis work and much less likely to derail your research. And maybe those notes can someday evolve into book-quality material, but what's the rush? Let them ripen like good wine; indeed, many world-class textbooks were created using just such a process.

  2. Another benefit to waiting until you are more established until writing your book is that by that point you will be a much better writer, and will have a much higher chance of writing a book that other people will actually want to read. But, regardless, even if you already are a great writer, writing a book would still very probably be a bad idea for the reasons I explained above.

  • What if that book is the research, it used to be a thing that these tasks were the same. – joojaa Oct 31 '17 at 14:30
  • @joojaa that would fall under category (b) in my list of exceptions, so obviously that would be a more reasonable idea. But it seems pretty clear that that’s not what OP is asking about. – Dan Romik Oct 31 '17 at 15:10
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You should consult your advisor, as how this would be perceived varies by field, and they will have a better notion of your progress than we do. And an undertaking like writing a book will inherently impact your progress - your advisor should absolutely know about it.

But I've heard many people say that PhD candidates should focus on research instead of other pursuits like book-writing.

I would also consider talking to any faculty in your department who have published a good as to the amount of work involved. In my experience talking to colleagues, it's substantially more work than any of them thought, even after writing.

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