What will be implications of not publishing officially? I am not a professional academic; I am an amateur mathematician.
I have developed an entirely new mathematical theory.
I have written a book about my theory and put it online at my web site.


I am considering whether to put it at an online Git hosting (such as GitHub.com) under a copyleft license instead of publishing in an official academic way. What could be the consequences of me violating the normal academic way?


I doubt whether professional mathematicians will refer to my work that is not published officially.
Since two objects cannot occupy the same place, I prevent others from publishing their own research duplicating my content.


This could have both negative and positive consequences:

The negative is that I may stall research in an entire part of mathematics, so that nobody could publish their own research on this topic.

The positive is that my little nail would be a nail in the coffin of continuing the existing way of disseminating scientific knowledge, as nobody would be able to step over my sharp nail. As an unbreakable obstacle on the way to do scientific research in the old way in an entire field of mathematics, this could crash the entire existing system (which is probably good).

My question: Please help me predict the implications of me disseminating my research in this rude way instead of publishing articles in math journals as most mathematicians do. Who would win in this struggle to integrate my research into the academic system: I or the rest of the world?

I want also to note that publishing with Git will greatly help in hunting possible errors in my book. It will also much ease publishing new revisions of the book.
It's difficult to answer this question effectively because it is premised on some incorrect assumptions.  Let me begin by correcting them:


There is no such thing as an "official" scientific publication.  There is no Board Of Serious Scientists who determines which publications are legitimate and which are not.  Science is a marketplace of ideas, and many things that have never gone through a typical peer-review process have gained high citations.  For example, the Agile Manifesto has hundreds of citations and vast scientific impact, but has never existed as anything other than a page on various websites.  Thus, you are not "violating" anything, you are just choosing an unusual and often less effective route for getting people to notice the significance of your work.
If you publish work, it doesn't prevent somebody else from publishing the same ideas if they don't know about you.  Parallel invention of concepts happens all of the time in science.  You cannot magically exclude people from working in an area by "getting there first."  If nobody has noticed the significance of your work, it's as though your work doesn't exist.  If they do notice you, then that doesn't stop them either: they'll just build on your work and cite your informal publication.


So, what are the actual advantages and disadvantages of publishing in this informal way?


Advantages: You don't need to convince any other researchers that your work has value, you can just publish it.
Disadvantages: Your work may simply lie unnoticed and disregarded.  Putting the source for an informal publication on GitHub isn't much different than sticking a PDF on your website. 


Let me also answer the question that you haven't asked: how do you get your work to have a scientific impact?  For this, you need to figure out how to engage with the scientific community.  Go to conferences and listen to other people's talks in related areas.  Figure out what questions can be answered by your work that cannot be answered by prior methods.  Above all, learn the language that other researcher use so that you can speak to them in a way that will not set off "crackpot alarms." You may well have created a fabulous new work of mathematical theory, but using words like "entirely new mathematical theory" sets off crackpot alarms, because they are frequently used by crackpots and rarely by researchers who actually have something to contribute.