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I am an amateur mathematician. I am writing a research monograph in the field of abstract mathematics (general topology, specifically).

Should I publish it traditionally or self-publish?

There are many benefits of self-publishing (e.g with Lulu) an academic work:

  1. No need to tremble awaiting my book to be rejected by a peer review. No responses like "first publish in articles, only then make a book". I am in full control what I want to publish.
  2. I don't pay the publisher 80-90% of my revenue. (This also may make AdWords marketing of my book profitable and thus I can do a rather huge advertisement of my book myself using AdWords. I suspect, this may over-perform traditional publishers in the number of sales.)
  3. I am in a full control of my book. No forced need to change something, if an editor's opinion differs from my own.
  4. No need to convert it to LaTeX, I can use my preferred software such as TeXmacs.
  5. The book goes into Amazon and other distribution channels anyway.

I can pay a professional scientific editor to edit my book for paid, as a kind of business investment.

Peer review is intended to choose which books are published and which are not. I can do fine without peer review, allowing the buyers of my book to decide for themselves.

Well, a potential buyer may prefer books published by a big publisher, but it (in my opinion) can be well replaced with big red letters "Edited and checked for errors by professor XXX."

Drawbacks which I know:

  1. It may not be as good for my academic carrier as traditional academic publishing. (It does not matter for me anyway, as I am not a professional academic.)
  2. Not sure if my book goes into university libraries (please comment on this issue).

I've pointed many benefits of self-publishing. What are drawbacks (except of pointed by me)?


And one more specific question: Is the number of books sold if using a traditional publisher, likely to greatly overperform the number of books sold if self-publishing? If yes, why?

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    Why are you writing the book? Are you trying to make money, help the world, or improve your CV? Is it original research or a textbook based on research published elsewhere? Is publishing it in ArXiv a possibility? – Jukka Suomela Jan 29 '15 at 17:29
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    It's very unlikely that any university library will purchase your self published book unless (perhaps) a faculty member asks them to do so. – Brian Borchers Jan 29 '15 at 18:20
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    @porton: If you write to the managers of the arxiv, I'm sure they'll give you an explanation of why you cannot post there any longer. I can assure you that neither of your suggested explanations is the right one. Very likely it has something to do with the fact that one has to have institutional affiliation or specific endorsement from someone who does to publish on the arxiv. – Pete L. Clark Jan 29 '15 at 18:29
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    Your claim 'I am in a full control of my book. No forced need to change something, if an editor's opinion differs from my own' definitely clashes with 'but it (in my opinion) can be well replaced with big red letters "Edited and checked for errors by professor XXX'. – Massimo Ortolano Jan 29 '15 at 19:54
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    Maybe, they disliked my bold voice about superiority of my research in comparison with more traditional theories — Yeah, that would be my guess. There is very rarely room in mathematics for bold claims of superiority for nonstandard approaches to completely standard material. Your nonstandard approach might eventually replace general topology, but publicly making that claim on your own behalf only labels you a crank. Compare, for example, Wolfram's A New Kind of Science (crank) versus homotopy type theory (not crank). – JeffE Jan 29 '15 at 22:31
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Should I publish it traditionally or self-publish?

Why do you want to publish at all? You answered

I write the book to store down my research results and to spread my new knowledge. To make money is not the main aim, but it would be nice.

Given that: the answer is that you should certainly not self-publish your work. You can store your results and spread knowledge by having the material freely available on the internet, as I believe is already the case. The arxiv is one nice place to put work, but it is not the only one: you could put in on github or any number of other repositories. You can just put it on your own website and make sure that google indexes it. That means that billions of people can access it at any time.

Let me be clear with you: you are not going to make money self-publishing works of mathematics that you have not been able to publish traditionally. It is exceedingly rare for any mathematical text beyond the undergraduate level to make a profit that is worth the time taken to write it. (Maybe a few of Serge Lang's books qualify; probably not.) If you go self-publishing rather than traditional publishing, you will lose money, and what you're paying for is the vanity of being a published author.

The bar for interest by the mathematical community is much lower than the bar for the type of public interest needed to generate any real sales. The thought that you have "My ideas are too bold for the mathematical community, so I need to take matters into my own hands; they don't know the value of my work as well as I do" is not only crankish but actually specifically damaging to you: it makes you ideal prey for predators of various kinds. You told us in a previous question that you literally fell prey to a diploma mill and thereby lost money. The same mindset that you have now is going to cost you more money in the future.

I'm sorry to tell you this, but this has been going on for several years now, so I feel I should be plain: no one in the world has found your work to be of significant mathematical value. This means that, with probability slightly less than one, that your work does not have significant mathematical value. But in the unlikely event that your work does have value, you're not doing what is necessary in order to show it. Mathematical research is not about simply writing down structures that generalize other structures and proving results about them. You have to solve old problems or pose new ones that are of interest to the community. Bold statements of superiority would be a positive thing if they are specific and factual: for your work to be "superior", it should solve at least one problem that others have posed. If you've done that, please explain yourself properly and then your work can be published in the mathematical mainstream. If you haven't: please start to be honest with yourself about the value of your work. Your livelihood is at stake.

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I've pointed many benefits of self-publishing. What are drawbacks (except of pointed by me)?

  1. The scientific community will very likely ignore your contributions. That is, your book will have approximately zero impact. The combination of "I speak in a bold voice" and "I did not let my work get peer-reviewed" screams "crank" to professional mathematicians.
  2. Your business plan of "I get 100% of the profits instead of 10%, hence I make a lot more money" is a bit naive. If your book is not distributed and advertised by a known publisher, you can also expect to sell much less copies, so it is no clear that you will make more money (if any at all) using self-distribution.
  3. Relatedly, it is true that "the book goes into Amazon and other distribution channels anyway", but there is a large difference between "is hidden somewhere on Amazon" and "is advertised by Springer".
  4. You are in full control over your book, but you also don't get professional feedback. You seem to falsely assume that peer review is a mechanism to somehow suppress books and ideas. This is not the case - largely, peer review improves published work by forcing an author to take comments of other, independent researchers from the field into account. You seem to think that this is a bad thing, but most people would probably disagree.
  • If your book is not distributed and advertised by a known publisher, you can also expect to sell much less copies — [citation needed]! See, for example, Robert Ghrist, Radiohead, Louis C.K. Of course, your statement may be true if you are not already well-known in your field, but then you're comparing deltas to epsilons anyway. – JeffE Jan 29 '15 at 22:37
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    @JeffE Yeah, of course self-publishing can be great for some people that are already well-known enough to essentially do their own marketing, but the OP is presumably no Radiohead of maths. I still stand by my assertion that the OP will sell substantially less under a self-publishing model. – xLeitix Jan 29 '15 at 23:21
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I don't have time to look at your work in detail, but I have at least skimmed through parts of it. I would recommend against self-publishing if you hope for mainstream acceptance of your work (but if you don't care about that and self-publishing would make you happy, then go for it). What you write looks like mathematics, not the sort of nonsense one sometimes sees from amateurs, and it might plausibly be correct, but the motivation is absolutely unclear to me. To put it bluntly, I can't think of anyone who would want to read it, since I can't identify what they would learn or get out of it. I imagine this is the reason traditional publishers are reluctant to publish it, namely that there's no apparent market for this book in its current form.

Of course this doesn't mean your work isn't good. I don't know, since I haven't actually understood it, and it is possible that there are good reasons why it should be more popular than it has been so far. However, if you'd like your ideas to spread and be used by others, then you need to communicate them more compellingly:

  1. If you can address problems or topics other people have cared about in the past, in a way that couldn't be done without your work, then that will attract readers.

  2. It's important to give interesting or beautiful examples, whose attraction does not depend on already having an emotional commitment to this work.

  3. If you can't give great examples or make connections with previous work, then it will be difficult to attract readers, but at the very least you need to give clear, intuitive explanations of the concepts you deal with and why they are important.

In its current form, I don't think your book does any of these things. If you self-publish it, I do not expect it will sell many copies at all, and almost exclusively to people who are unlikely to contribute to mainstream acceptance of your work (such as friends or family). I would expect it to sell zero copies to professional mathematicians, and I'd be very surprised if it sold more than a handful.

One major contribution the publisher can make is to enforce clear and well-motivated communication. You are too close to the work to be an objective judge of this. You've spent years thinking about these ideas, so deeply that they now feel comfortable and natural to you, but nobody else has developed this perspective on them yet. If you want other people to take up these research topics, then you need to attract their interest. Reviewers or editors might be able to help refine an already attractive manuscript, but they can't add motivation from scratch (you have to convince them before they can help you convince anyone else). Until you reach the point where a traditional publisher would accept the book, I don't think it will have the impact you desire. So the fundamental questions are whether you can reach this point and whether you want to try.

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If you publish traditionally, you make it much more likely that the audience with the background to understand your work and an interest in the topic will find it and read it. The very fact of making it past the gatekeepers of traditional publishing serves as an advertisement of the quality of your work.

I say this based on personal experience from years of publishing philosophy non-traditionally. You can potentially reach a general audience outside of academia if your work is truly of broad general interest, but if you want to reach the experts in your field (or if you're working in a niche that is only accessible to the experts!) you 100% need to publish in the places they publish.

For a field like mathematics, even amateurs are unlikely to take a chance on reading something not peer-reviewed. If you disagree, ask yourself a question: When is the last time YOU purchased a self-published mathematics text by an unknown author?

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Your mathematics might be wrong, and since you're too close to it and too steeped in it, you might not notice.

  • You have not read the following paragraphs in my question: "I can pay a professional scientific editor to edit my book for paid" and "Well, a potential buyer may prefer books published by a big publisher, but it (in my opinion) can be well replaced with big red letters "Edited and checked for errors by professor XXX."" – porton Jan 29 '15 at 17:23
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    I read both of those things. A scientific editor is not likely to check your math, and a professor is unlikely to take money to serve as a named referee. I think you'll have better luck by following a more traditional route. – Bill Barth Jan 29 '15 at 17:24
  • I think Lulu publishing would even better to do with errors than traditional publishers, because if I (or my reader) find an error, it is easy to do a new edition of my book. Even if somebody found 100 errors, I can make 100 editions :-) – porton Jan 29 '15 at 17:28
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    What if your whole theory is wrong? I'm not talking about typos here and there. Self-publishing of new mathematics is often the sign of a crank, especially when it comes to amateurs working outside academic or industrial mathematics. It sends up red flags for professional mathematicians. I'm not saying you are a crank, but the traditional process has generally proved to lead to solid results over the 100+ years and self-publishing has not. – Bill Barth Jan 29 '15 at 17:34
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    I don't think it matters how big or small the theorems are. If you want people to take you seriously, you'll probably need to follow the traditional forms. If there's something groundbreaking here, you'll want it in the journals and to have it peer reviewed. If there's nothing groundbreaking, you're still more likely to have your work seen if it goes through the peer review process. You've already been banned from ArXiv, so you might want to consider playing by the norms of the mathematics community. – Bill Barth Jan 29 '15 at 18:01

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