advisor - How can I earn a professor's attention if I am not his/her student yet?

I am trying to find a professor to do my first research under his/her supervision. I am a high school student. However I have already self-studied all the BSc and MSc (Pure Mathematics) books [based on Melbourne Uni]. But I haven't done any research and I need to have some professor to help me to choose a topic, access to non-free-papers, publishing, etc. Most probably I won't need for the learning part, i.e. to ask professor on more understanding the texts (i.e., tutoring). Although not asking for teaching Mathematics to me may result in much less taking professor's time compared to professor's student, but professor prefers to not spend on someone off the street asked him/her to do research with.

I already have asked two professors to do research under their supervisions and in reply I have been rejected, saying "I would prefer to supervise my students" or similar, (one was just yesterday).

I am interested in doing research on Real Analysis and I know there might be some other professors to be interested in guiding me even a lot but they are not specialized on Real Analysis.

I should also add here what I am saying when approaching:

1. 
   

   As I quickly rejected in the first try by emailing, I decided to go to a professor's office in person with no previous meeting time; the result was a bit better in the beginning but no success.

   
   


2. 
   

   I speak: "As I found Mathematics the most supreme beauty, a true Paradise, I started and committed to Mathematics. I had a consecutive study plan and I have studied ... [name of books]. As I was keen to have a big impact on Mathematics, so I decided to analyze books (like what a critic does with a paper to publish) rather than studying. I know that I need a lot to learn before doing research (which I don't know what to study next) and afterwards I don't know how to proceed in research. It would be a great honor if you please help me in my journey..."

   
   

My questions are: What's wrong with my actions and speaking? and, what should I say or do in order to 'win' a professor's heart?

PS - I took your kind and helpful advises in the other question, and I decided not to be isolated from 'the system'. However, it's not that easy to find my way on my own. By the way, I truly appreciate for all your guidance.

Answer

As I found Mathematics the most supreme beauty, a true Paradise, I started and committed to Mathematics. [...] As I was keen to have a big impact on Mathematics, [...]

This is quite off-putting. What you say here is essentially that you want to be a great mathematician. Since there is no a priori reason to assume that you are better than many other students the professor you address has, such a statement is a little presumptuous.

I had a consecutive study plan and I have studied ... [name of books].

This is good. You give a more or less objective description of your abilities and show that you actually have done serious work.

What's missing is a description of your actual interests. If you say you are interested in mathematics or real analysis, you essentially say that you have not found something that really intrigues you. As research is largely internally motivated, this is not a good sign. Note that I do not say that you have no special interests, but that what you write in your question and what you state as your approach to a professor says so.

So a letter which should attract the attention of a professional mathematician could be the following:

I am (description + why you have no direct contact person).

I have read the following books.

I am fascinated by (special topic), because (honest reason). In particular, I would like to understand (something you are really interested in).

Can you recommend me further directions for my studies, e.g. textbooks dealing with (whatever)?

If you get a reaction like "read XYZ", and after half a year you pose a question which shows that you have worked through this book, you will probably be taken seriously.