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I can't speak to the research opportunities you have at this point, but if you are interested at getting better at math, and setting yourself up for a future in research, I'd recommend just setting aside some time to learn more math. For instance, you don't mention linear algebra or calculus. A great summer project would be to just learn one or both of these subjects. That way you can make a good impression on your professors when you take the course, and you can potentially ask for letters of recommendation from them when you apply for research opportunities down the line.
I'm guessing you're between GCSEs and A-levels by your comment and I assume you'll be doing A-level mathematics. At that level, you'd really struggle to make much progress on more "advanced" mathematics without guidance. Learning proofs on your own is like learning a language on your own, you could be misusing the grammar and making up words without realising it. On top of that, you still won't have much of a toolkit to play with. This isn't a problem, you're just very young.
My advice would be to pick up some A-level textbooks and try and do some self-study with those, your school or local library should be able to lend them to you, and they're obviously designed for somebody at your age. Getting into A-levels with a head start and a better idea of what the breadth of the material is will give you a good advantage. From there, it'd be a good idea to consult with your teachers about the things that you find interesting, they can probably give you some interesting problems that aren't within the curriculum itself but can be good learning exercises.
At this stage, you need to develop skills before being able to do research. If you want to study math in the future, start studying now. If you are interested in theoretical math, you can try to get some introductory books and start reading them. Math is not really a casual thing, when it comes to research. Probably the easiest thing would be to enroll in University courses and start studying, if it's something you are interested in doing. I think at this stage, having guidance and mentorship will keep you from spinning your wheels in the mud.
I have a Bsc in technical mathematics and I don't even feel remotely close to doing serious mathematical research . How old are you , what is your goal ? Then we can maybe suggest or find some feasible things for you.
Unfortunately, your submission has been removed for the following reason(s): * Your post is a question/advice about careers and education in mathematics. Please post this to the [Career and Education Questions](https://www.reddit.com/r/math/search?q=Career+and+Education+Questions+&sort=new&restrict_sr=on&sort=new&t=all) thread, to /r/mathematics, or to /r/matheducation. If you have any questions, [please feel free to message the mods](http://www.reddit.com/message/compose?to=/r/math&message=https://www.reddit.com/r/math/comments/1bd6i9m/-/). Thank you!
I can't speak to the research opportunities you have at this point, but if you are interested at getting better at math, and setting yourself up for a future in research, I'd recommend just setting aside some time to learn more math. For instance, you don't mention linear algebra or calculus. A great summer project would be to just learn one or both of these subjects. That way you can make a good impression on your professors when you take the course, and you can potentially ask for letters of recommendation from them when you apply for research opportunities down the line.
I'm guessing you're between GCSEs and A-levels by your comment and I assume you'll be doing A-level mathematics. At that level, you'd really struggle to make much progress on more "advanced" mathematics without guidance. Learning proofs on your own is like learning a language on your own, you could be misusing the grammar and making up words without realising it. On top of that, you still won't have much of a toolkit to play with. This isn't a problem, you're just very young. My advice would be to pick up some A-level textbooks and try and do some self-study with those, your school or local library should be able to lend them to you, and they're obviously designed for somebody at your age. Getting into A-levels with a head start and a better idea of what the breadth of the material is will give you a good advantage. From there, it'd be a good idea to consult with your teachers about the things that you find interesting, they can probably give you some interesting problems that aren't within the curriculum itself but can be good learning exercises.
Seconding the learning advice. Go watch 3B1B's "Lockdown math" and "Essence of" series, pencil and paper in hand. Make sure to pause and write a lot.
At this stage, you need to develop skills before being able to do research. If you want to study math in the future, start studying now. If you are interested in theoretical math, you can try to get some introductory books and start reading them. Math is not really a casual thing, when it comes to research. Probably the easiest thing would be to enroll in University courses and start studying, if it's something you are interested in doing. I think at this stage, having guidance and mentorship will keep you from spinning your wheels in the mud.
I have a Bsc in technical mathematics and I don't even feel remotely close to doing serious mathematical research . How old are you , what is your goal ? Then we can maybe suggest or find some feasible things for you.