independent researcher - What careers not requiring an academic degree might be open to a self-learner who wants to do research on pure mathematics?

I hesitated to ask this question since it may not relevant to this website, but I saw a question of same category here but still couldn't find an answer ...

Since childhood, I've had a sharp enthusiasm for Maths, studying books from an elementary level to ones suited for the level of a Masters of Science student at Melbourne University. I am currently 15, but the formal classroom setting feels like a waste of my time. Because of my passion for Maths, going through the formal procedure of education is making me severely depressed...

Here is my question:

What careers which do not require an academic degree (all research positions require a PhD) might be open (in Australia) to a self-learner who wants to do research on Pure Mathematics?

Salaries for a postdoc position are ~80k in Australia, but I am looking for a research career even of a ~15k salary because that would be enough money to survive while doing research. I have yet to published any paper to impress some institution to believe in me, if it helps at all.

EDIT - Thank you all very much for your very informative answers. To be more precise, I would like to write my main reasons of the 'horror' of university:

1. 
   

   Solving exercises or studying the texts in self-study themselves can (although difficult) be stopped for the duration of university affairs (classes, ...) but I believe that research can't be frequently stopped by other irrelevant things even with university affairs [university classes will be Math, but not be the research that I want to engross in, at least for first few years], since being creative requires to be much more engrossed (to put it simpler: 1 2-day is more efficient than 2 1-day for research).

   
   


2. 
   

   Even with prestigious universities it involves a lot of bureaucracy, which they may find necessary to obtain a degree but are irrelevant to Mathematics.

   
   


3. 
   

   Being very deep concentrated and having manic passion causes a lot sensitivity, that's why we have some recluse people (in Arts and Science) and most of them are suffering from Bipolar Disorder caused by their manic-enthusiasm. While there are many people with great achievements living in society with high-degrees UNFORTUNATELY I don't think it's impossible for me.

   
   

   3a. An example of negativity in university education is the focus on institutional ranking. Combined with job-seaerching being the main purpose of study for some, it could impact someone who just seeks the beauty of Mathematics faith in seeking a degree.

   
   



4. 
   

   University costs a lot for a Bachelors of Science, much more than it would to be a mathematician in solitude.

   
   

EDIT 2 - In my question, I have asked that from where I can get financial support for basic life expenditure, however many answers include enrollment in universities which costs A LOT for just BSc (supposing that I can survive with my mentioned conditions in first EDIT).

Thank you, everyone. I highly appreciate the brilliant advise in many of your answers, however my main question remains how would I pursue research in Mathematics without a degree? I know the path that is recommended for pursuing a research career, but the cost of university and not having peace of mind are too great of an expense for me.

Answer

The question you seem to be asking is "Can I be paid to do research, without any formal education, if I am very good?" The likely answer is no. I know many serious researchers across countless fields, and the only ones I am aware of who can make a living without any formal training are inventors who got quite lucky in terms of their ideas and their marketability. Many great artists, mathematicians, and scientists did other things to survive while doing the work they were truly passionate for, and we romanticise many very inspirational people. Research is probably much more a function of diligence and persistence, even when things are depressingly boring, than it is of intelligence or genius. I would suggest reading some of the good bits of advice many modern prodigies have given on the subject. Terence Tao in particular has several good pieces on accelerated education, working hard, and being a genius.

Yes, school can be terribly dull if you are quick. But being able to succeed in that environment is an invaluable human skill, which will prove useful in a research career when looking for funding, or when setting up research groups and similar things, as well as really showing that you have a sense of humility. We can complain about how slow and tedious bureaucracy can be, but if you really are quite good, it is worth your time to learn and understand how to survive in it. Mathematics is not simply something devoid of social interaction or human involvement. Pure and applied mathematics stem from human ideas and are inherently connected to social and cultural concepts, and these connections are often a part of what traditional formal education gives us. I would absolutely advise you to go further than what you see in a classroom, do independent and guided research as early as possible, and test out of whatever classes you can. But skipping the process entirely will handicap your ability to contribute meaningfully to mathematical research.