What to do if there is no book about a certain topic?

Question

I am currently researching the foundations of graph theory (math). I have noticed two kind of things in introduction books.

1. There are results seemingly so obvious nobody writes about it.
2. There are variants of the topic mentioned in almost any book, but covered in detail in none.

At the time of writing this question, the stack exchange community was unable to help me with my observations in my specific case. Since I think very highly of this network, I'm starting to believe that currently there are no suitable books about these topics.

But I feel like there ought to be books about it. The question is, what do I do in this situation? How can I "help" that such a book gets written? The most obvious answer would be "Write the book.". Although I like the approach, this is not possible. For simplicity's sake let's just say I lack the time. So what to do? Like, can I just mail a publisher "Why don't you already have this kind of book?", although I don't know anyone working at any publisher? Do I ask a professor at my university if (s)he would like to write one? Btw I'm a graduate student, but I don't think it is relevant for the question.

Please note this question is not about how I can research a certain topic. It is really about how books of some topic do not exist. Please assume for answering that they don't. If you happen to know about books about the exemplary example topic I provided here, please answer in my linked question, not here.

Answer 1

In reading the following, keep in mind that anything you can do personally will have at best a minuscule effect on whether such a book gets written, and you shouldn't expect it to happen anytime soon. For all practical purposes, you should plan on having to proceed with your research without the aid of this hypothetical book.

My impression is that these books usually get written on the author's own initiative, perhaps prompted by having them see a need for such a book. So I think the best thing you can do is to identify someone who you think could write such a book: someone who is a recognized expert on the topic and who writes particularly well and clearly. Contact them and say something like: "I've really appreciated reading your papers on topic X, but it strikes me that there are no books that could give a comprehensive introduction. Have you ever considered writing one?"

Unfortunately, your message alone probably won't do much, particularly because you are a grad student - these suggestions would have more weight coming from someone who would be recognized as a fellow expert. Someone who is more deeply acquainted with the existing literature and its gaps. But if the potential author starts getting a number of such suggestions, it might plant the seed that such a project could be worthwhile.

Of course, writing a book is a huge task (thousands of hours, I'd say) which is poorly compensated. Academic structures are such that researchers tend to have stronger incentives to write papers than books. If the book is to be published commercially, there is the additional question of whether it will be profitable - even if the book is fantastic, if the topic is too "niche", there may not be enough potential buyers to interest a publisher.

I don't think that contacting a publisher will have any effect. Again, the incentives are such that a publisher can't do much to encourage anyone to write a book, unless they already really want to do so.

Answer 2

Many times in my PhD I wondered: "Why has never anybody written down a thorough treatment of X? It would save so much time and hassle for Master and PhD students, and might attract more people to the field".

But the answer is rather obvious: Nobody pays for it. Writing a scientific book takes huge amounts of time, and you get very little reward for it (no grants, not lecturer positions, little positive feedback from the research community, sales are usually quite low). So writing a scientific book is largely an altruistic thing.

So if you do not write that book yourself, there is little to no chance that anybody will write it.

My personal advice: Get used to the fact that even for basic subjects, you need to state and prove many things yourself because you find no appropriate source to cite it.

Answer 3

Yes, you can write to the publisher and propose this as an idea. The commissioning editors I know are generally pretty happy to hear about such ideas because it saves them from having to do the work. Coming up with an idea is the hardest part of commissioning since one actually has to become sufficiently familiar with the field to identify a gap. After that things are algorithmic - identifying researchers in the field for example is simply a matter of searching Google Scholar or some similar database.

The people to write to are the commissioning editors. Some publishers list their commissioning editors on their website - for example, here's Springer's list of editors in mathematics. You can write to one of them with the suggestion. Alternatively you can also give me your email address and I'll put you into contact with some people I know.

I should say that the odds of failure are pretty high. First you have to convince them that there's a gap, and then they'll have to find someone willing to write the book. If you were someone with the pedigree to write the book yourself, or if you're able to persuade an established academic to write the book and put together a book proposal, you'd have a much higher chance of seeing the book actually published.

Answer 4

It looks like you are trying to connect your topic to the foundations of mathematics, which is a daunting task and often an ungrateful one. In particular, finite sets of explicitly enumerated elements rarely cause theoretical problems, so practitioners (in your case, people who invent and code graph algorithms) won't be willing to invest too much rigour in them. I think, it may be helpful to start by working out some basic proofs yourself, which will bring up more concrete questions, which you can discuss with your colleagues or on the Internet. This should attract attention of people who are interested in the same questions as you. Maybe, you'll find good company among theorem proving (e.g., Coq) community.