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My book was rejected by a publisher saying that my research is "unmotivated". To motivate it, should I solve some long standing open problem? Or are there other ways to motivate publishers?

This is despite I have some short sections in my book which describes my idea of motivation: "1.4 Our topic and rationale" and "1.5 Earlier works".

What motivation (except of solving long standing open problems) are?

Any text online on the topic of motivation in math research?

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  • math.ualberta.ca/mss/misc/A%20Mathematician%27s%20Apology.pdf was suggested by Terrence Tao in a chat – porton Mar 15 '14 at 14:21
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    It would be nice to see more about how your approach fits within the larger context of standard mathematics. Or, to explain how what you do is indeed more general. This is of course not at all an easy request. You might as a motivation for the proposed streamlining of proofs, show an explicit example to compare and contrast your proof verses the standard proof. – James S. Cook Mar 15 '14 at 17:57
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    The word "motivation" here likely has a special meaning. Rather than a general notion of why a person might be trying to get published, the editor probably means that a connection with past work by the author or others leads to interest in the problems investigated in the current work. Even if such a connection is evident to you (and perhaps even to the editor as well), omission of such introductory/historical material is unscholarly and makes the job of selling a publisher on your book much harder. – hardmath Mar 16 '14 at 16:33
  • I'll re-open temporarily to migrate to Academia. While this question is specific about publishing mathematics, I think there may be similar concerns in other fields making it potentially useful to have the exposure there. – Willie Wong Mar 17 '14 at 10:16
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    I see several reasons why this will not be published: The work introduces way too many objects that are unfamiliar, AND has not passed peer review. Looking at your book, it has lots of definitions, and one-line proofs, but lacks motivation and flow; this looks more like something that a computer would automatically generate. See page 44 example. It is completely unreadable, and there are no motivations for the proofs. I suggest that you familiarize yourself with mathematical WRITING, not just what symbols LaTeX manage to produce. – Per Alexandersson Mar 21 '14 at 23:11
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What the publisher is looking for is a book that will attract many readers. If crowds are already clamoring for a book, then the decision to publish it is easy, but that's uncommon. Instead, the publisher generally has to try to predict whether an audience for the book will materialize when nobody knows they want to read it yet.

The "motivation" the publisher refers to is anything that makes people want to read the book. You need to demonstrate to potential readers that the material is interesting and exciting, that reading the book will be useful, that it connects to a larger scholarly conversation, etc.

Right now, it's clear that you feel the book is valuable and would like many people to read it, but you aren't giving potential readers a lot of motivation. For example, in Section 1.4 of the current draft, you write

Somebody might ask, why to study it? My approach relates to traditional general topology like complex numbers to real numbers theory. Be sure this will find applications.

and

This book has a deficiency: It does not properly relate my theory with previous research in general topology and does not consider deeper category theory properties. It is however OK for now, as I am going to do this study in later volumes (continuation of this book).

Basically, this amounts to saying you don't yet know how it will be useful and you aren't connecting it to the literature. The lack of applications is a serious disadvantage, but not necessarily decisive by itself (some things can be published in mathematics just because they are beautiful or seem like they should be useful). However, not explaining the relationship with previous research is a major problem. It's nearly impossible to get an academic book published under these circumstances.

I don't mean to be overly discouraging, but my impression is that writing a book on your work is premature. Instead, I'd focus on connecting your work with the rest of the field, with the goal of getting a group of other researchers building on your papers. Once you start to get more citations, you can bring them to the attention of publishers as evidence for a community that values your work and would benefit from a systematic presentation in the form of a book.

  • A small technical note: "general topology" (even if we add "traditional") is not about complex and real numbers. That sentence alone is already a flag that may worry potential editors. It suggests that you are not aware of what the fields you are mentioning are really about, and suggests that your work is an isolated eccentricity. Not saying this is or is not the case, simply pointing out how your words may be perceived. – Andrés E. Caicedo Mar 17 '14 at 16:26
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    @AndresCaicedo: I think what porton meant by that sentence is that the relationship of his "approach" to general topology is analogous to the relationship of the complex numbers to the real numbers. I think the more serious red flag to editors is the following sentence, which very clearly suggests that the hoped-for applications have not been found yet. – Mark Meckes Mar 17 '14 at 17:26
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    Oh, I see. That's too vague, then. There are very specific relations between complex and real valued theory, and it is not clear other than in the vaguest of senses what plays the role of those relations in the new context. – Andrés E. Caicedo Mar 17 '14 at 17:28
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Now that you have started the field of Algebraic General Topology you may want to convince other people that it is worth their while to learn about it.

Looking through the slides I see lots of words whose definitions I do not know. I have not read your paper and I am ignorant of the terminology in the fields you are generalizing. Perhaps there are theorems in two different fields that when generalized by your techniques turn out to be the same theorem. If you are lucky no one will have previously realized that they are the same theorem. If something like this is the case. I would pick such theorems, place them at the top of each of two columns on (digital) piece of paper and then use your general proof for each of the theorems but use the language of the field from which the particular theorem comes. This way people will be able to see what you have accomplished without learning lots of new language.

  • What about this theorem for both topological, proximity, and uniform spaces: The product space is the maximal space for which all projections are continuous (respectively, proximally continuous, uniformly continuous). Theorem(s): product of continuous (respectively, proximally continuous, uniformly continuous) is continuous. Also this theorem holds for (di)graphs and discrete continuity. Would this four-fold theorem proof be interesting? – porton Mar 20 '14 at 23:45
  • Note that this theorem is not included in my book (it is scheduled for volume 2). – porton Mar 20 '14 at 23:45
  • Dear Jay, how can I write my proof in the language of a particular field, when prior to me my "composition" operation was not defined in topology? Writing proofs without composition I would need to split the definition of composition into logical formulas with quantifiers which define it. The proof would become less than clear. This way reading the specialized proof people would not be able to catch my (more algebraic that before) proof idea. – porton Mar 21 '14 at 0:00
  • Perhaps. I do not pretend to be an expert in any of these topics. I think you should look at Lowen's Approach Spaces. It may be that there is some overlap with what your work. – Jay Mar 21 '14 at 0:04
  • I've looked into Lowen's Approach Spaces. I am unable to find a common generalization of Lowen's and mine research. Thus (as it seems for me!) reading Lowen would be not useful for me as a researcher. (I may mistake on this however.) – porton Mar 21 '14 at 0:06

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