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I am an amateur (not affiliated with an academy) mathematician.

I have written a research monograph (see my site).

The current status of the book is that it is well written and is reasonably checked for errors. However there are serious errors in the last chapter. I may remove the last chapter and try to publish the rest of the book without it.

I sent my book (not yet including the last chapter) to several publishers. They all say either that my book is too original and rough for book form and should be published as articles first, or that my research is unmotivated. (I disagree and consider my work fully motivated.)

And now my book is in consideration of a publisher. After I sent my book to the aforementioned (last) publisher, I realized that before writing second volume of my book I need first create second edition of the first volume (which is in consideration now). I had two ideas how to rewrite it when it was already in publisher's review.

I doubt what to do with the last chapter (which as I've said above is currently erroneous). The simplest thing is just to remove it now, because it anyway should be rewritten in the second edition (and the rewrite is rather massive).

Should I for now remove the last chapter and leave this work to the stage when I will write the second edition of the first volume?

Or maybe should I stop any publishing attempts until I finish writing the second edition? (I'm afraid that if I happen to die, my work may be lost unpublished.)

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I'm sure this depends entirely on the specifics of the manuscript and chapter in question. I don't see how anyone here can answer this. –  ff524 Jul 19 at 19:58

3 Answers 3

I disagree and consider my work fully motivated.

This is a key point. The issue isn't whether there exists compelling motivation, and you may be right that there is. Rather, the issue is whether you have successfully communicated this motivation to readers who have spent far less time thinking about the topic than you have and who lack the perspective that comes from developing a subject from scratch. You'll have to work extra hard to articulate the motivation and communicate it successfully. If the readers still don't understand why are you doing something, then that itself amounts to a communication failure (regardless of whether you feel they ought to have understood). You don't need to communicate successfully with everyone, but you need to do so with a large enough audience.

I'd strongly recommend trying harder to address this before publishing the book. You can consider the editors who have looked over your submissions as a random sample of readers. Many of them fail to understand the motivation behind your work, which suggests that many readers would find it unmotivated even if someone agreed to publish it. Ultimately, the goal should be not just to get the book published, but to get it read and understood. The feedback from publishers is helping you identify what you need to work on to attract readers.

Or maybe should I stop any publishing attempts until I finish writing the second edition?

Are you proposing to publish the first edition while you are already working on a second edition, or to submit the first edition as a draft while telling the publisher that you are working on serious revisions? The latter could make sense, while publishers are unlikely to agree to the former. (Publishing a book takes time, effort and money, and nobody wants to commit these resources to a mathematics book that will quickly be out of date.)

But the fact that you already have large-scale changes in mind suggests that the book might not be ready to submit for publication. You don't need to have completed all possible revisions before approaching publishers, but your chances of acceptance go down if you aren't presenting approximately your best work.

Should I for now remove the last chapter and leave this work to the stage when I will write the second edition of the first volume?

What's the alternative to removing it? If you have in mind fixing the mistakes now, then I can't advise you on which approach is better (since I haven't read the book). If you mean keeping the incorrect chapter in the manuscript and not dealing with the mistakes until later, then that sounds like a bad idea.

I'm afraid that if I happen to die, my work may be lost unpublished.

I can understand that this is a depressing possibility, but I wouldn't worry about it now (assuming you are no likelier to die soon than other people your age). If it makes you feel safer, you could always ask a friend or family member to try to get your work archived somewhere if you died unexpectedly. I can't say they would necessarily succeed, but it couldn't hurt to try.

By the way, the publishers who suggest publishing research papers first have an important point. The mathematics publishing system is set up to work that way, and it is not particularly well adapted to publishing large chunks of unfamiliar research in book form. It's certainly possible to publish research monographs, but you may be making things unnecessarily hard for yourself. Unless you have a very strong reason to prefer a book, I'd recommend trying articles instead.

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"Are you proposing to publish the first edition while you are already working on a second edition". When I sent the manuscript to the publisher there was yet no idea to create second edition. This idea came later –  porton Jul 19 at 20:28

Yes, you should absolutely stop trying to get the book published until it is ready. Talk to the publisher who is considering your book, explain the situation to them and ask for their advice about what to do. In my opinion, a second edition is unlikely ever to be published because, as I understand it, mathematics research monographs don't sell well enough to justify a second edition.

Even if a second edition were to be published, what is the purpose of the first edition if it is rapidly superseded by the second? From the way you write your question, it seems that that the purpose, for you, is publication. Publication is not a goal: it is a means to an end. The goal is to make other mathematicians aware of your work and that is most likely to happen if you present the work in the best way you can.

Listen to what publishers say. You know more about your field than they do; but they know more about their field than you do and their field is books. It is unusual for advances in mathematics to be published as a book, rather than in papers. That doesn't mean it's impossible to publish as a book but it does mean that you should have a good reason for rejecting the conventional method of publication.

If the book you're talking about is the preprint "Algebraic General Topology" on your website, then I'm sorry but it is rough and unmotivated. You have a five-page introduction, of which less than two pages (the sections "Our topic and rationale" and "Earlier works") could be considered as motivation. That is followed by what is, literally, a 250-page list of definitions, lemmas, theorems and proofs. To write that much mathematics is without doubt impressive but, to get there, you must have read at least one or two maths books: this is not what a maths book looks like. If the technical content is good (I know nothing about topology) then you have a sound basis for a book but not yet a book.

Finally, make sure your family knows about your work so that, in the unfortunate event of something happening to you, they can try to get it published so it isn't lost forever. (And take your vitamins and look both ways before crossing the street! :-) )

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I would say you must keep trying and get it published, even if you end up paying for that because this is your hard work and should not be wasted or lost.

the best way is to go and talk to publishers and ask them what can be added or subtracted to meet their requirements and standards.

You can also convert the book into an e-book and upload it on paid libraries

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Do you have any evidence that paying to have a mathematics research monograph published and/or uploading an ebook version to paid libraries would achieve anything? Specifically, that any mathematicians would be likely to find and pay attention to a book published in that way. –  David Richerby Jul 20 at 10:32

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