I have made my independent research available as a book on my website. Why is it not celebrated by the mathematics community? Some mathematicians said that general topology in general and theory of proximity spaces in particular are dead (meaning that no new discoveries appear in this field of mathematics).

I have discovered a theory which generalizes general topology in general and theory of proximity spaces in particular, opening a new major area of research.

It is described in this draft book.

So general topology "resurrected".

Where are the celebration and fireworks proclaiming: "General topology is alive!"?

I am an amateur mathematician and my speaking English (and also my purse to buy air tickets) is still not good enough to participate in scientific conferences.

I am not allowed to submit to either arXiv or nLab.

Something is wrong: There should be a celebration of general topology being alive, but this does not happen. What is wrong?

Well, one thing because which this does not happen is that I have not (yet) solved any specific open problem (not counting open problems which I myself formulated). But what else keeps the world off celebration?



My question is not a duplicate of Publishing vs. putting work online under a free license because at that question I ask about how citing (not acceptance in general) of my work may be influenced by its license and method of publication. Here I however ask about acceptance (not citing) of my work independently on its method of publication.

It is surely not a duplicate of I believe I have solved a famous open problem. How do I convince people in the field that I am not a crank?, because in this situation I have not solved a famous open problem.

It is not a duplicate of Creating a community around my research book, because in that question I ask what to do but in this question why does it happen. These are entirely different questions.
There should be a celebration of general topology being alive, but this does not happen. What is wrong?


The people who say general topology is dead are generally not unhappy about this conclusion: they feel it died a well-deserved death due to a lack of important connections with the rest of mathematics.  (They are wrong, both about whether it in fact died and about its lack of connections, but these beliefs persist.)  Your work does not challenge these beliefs, because it appears to be almost entirely self-contained, with minimal connections to other topics in mathematics.  If someone considers the field dead, then they will view your book as a zombie, rather than a sign of life.

This doesn't mean you have to try to change their minds.  It's perfectly reasonable to ignore them and focus on the mathematicians who do care about general topology.  But those mathematicians won't be surprised to hear that the field they work in is still alive.


  Well, one thing because which this does not happen is that I have not (yet) solved any specific open problem (not counting open problems which I myself formulated).


This is a major issue.  There are two ways you can attract researchers to a new research area.  You can show them how this area is connected to things they already care about, or you can convince them the new area is outstandingly interesting and important in its own right (more so than what they are currently working on).  The former is far easier, while the latter ranges from difficult to impossible.  If you can't build connections, then the chances of ever attracting much interest are low.


  But what else keeps the world off celebration?


Celebration is not the default state.  Every day, several hundred new mathematics papers are posted to the arXiv, some of them rather important.  On a typical day, none of them will get a reaction that could reasonably be described as celebration.  You should not expect it to happen here.

As a general rule, it can be difficult for authors to predict how their papers will be received.  Your book is exactly the sort of thing you like.  Maybe it's your favorite topic in the world, but that doesn't mean it will be everyone else's favorite too.  This can be really frustrating.  Some of my papers are much more popular and influential than others, and they aren't always the ones I'm most excited about or proud of.  I sometimes wish I could say to people "Hey, if you think X is so great, why aren't you twice as excited about Y?"  But ultimately people's tastes and preferences differ, and you need to make a case for your work in terms that other people understand and value.  This is not easy, but it's the only way forward.