I will be completing high school at the end of this academic year. I have a strong love for Maths, and I am considering becoming a pure mathematician or pure mathematics researcher when I'm older. I have a few questions about the academic world of Maths in general:

1. I have discovered some formulae, or theorems if you prefer, about a quite specific topic in maths with apparently limited, if any, applications to any other areas of maths. I would like to write a paper about it and try to publish it in a journal, but I'm unsure if it's been discovered before, as it hasn't come up on any Internet searches I've conducted. I've also searched arXiv for it. My question is, is there some sort of archive or database that I could use to quickly check if something I'm investigating has been discovered before?

2. What exactly do research mathematicians do? Do they simply think all day and write/type their thoughts and results and progress as their job?

3. If I don't discover anything new as a maths researcher, would I still be employed or would I no longer be payed, ie is it a safe and steady job?

4. I would really enjoy being a pure mathematician/pure mathematics researcher, but is it a good job in terms of salary? I don't think job staisfaction would be an issue.

5. To be a research mathematician do I need to very good at maths or be spectacuar at it?

Thank you for your advice, it is really appreciated.

I will be completing high school at the end of this academic year. I have a strong love for Maths, and I am considering becoming a pure mathematician or pure mathematics researcher when I'm older. I have a few questions about the academic world of Maths in general:

1. I have discovered some formulae, or theorems if you prefer, about a quite specific topic in maths with apparently limited, if any, applications to any other areas of maths. I would like to write a paper about it and try to publish it in a journal, but I'm unsure if it's been discovered before, as it hasn't come up on any Internet searches I've conducted. I've also searched arXiv for it. My question is, is there some sort of archive or database that I could use to quickly check if something I'm investigating has been discovered before?

2. What exactly do research mathematicians do? Do they simply think all day and write/type their thoughts and results and progress as their job?

3. If I don't discover anything new as a maths researcher, would I still be employed or would I no longer be payed, ie is it a safe and steady job?

4. I would really enjoy being a pure mathematician/pure mathematics researcher, but is it a good job in terms of salary? I don't think job satisfaction would be an issue.

5. To be a research mathematician do I need to very good at maths or be spectacular at it?

Thank you for your advice, it is really appreciated.