Math research as a high school student

[Ramanujan143]

I study and learn math independently but I was wondering if there was some kind of math research that I could do. I'm no where near a genius but I would like to take a shot. Obviously my math background is limited so this might be a stupid question all together.
A big reason why I'm asking is because if possible I would like to do something I can tell colleges about to help me standout and not seem like a liar when I say I'm passionate about math.

 

[Student100]

I study and learn math independently but I was wondering if there was some kind of math research that I could do. I'm no where near a genius but I would like to take a shot. Obviously my math background is limited so this might be a stupid question all together.
A big reason why I'm asking is because if possible I would like to do something I can tell colleges about to help me standout and not seem like a liar when I say I'm passionate about math.

There probably isn't any math research you can conduct that's publishable, no. The low hanging fruit in the sciences is all but gone.

You can show you're passionate about math by earning good grades in your current courses, taking as much math as offered, and possible enrolling in community college and taking math courses before you actually finish high school.

 

[IGU]

I study and learn math independently but I was wondering if there was some kind of math research that I could do. I'm no where near a genius but I would like to take a shot. Obviously my math background is limited so this might be a stupid question all together.
A big reason why I'm asking is because if possible I would like to do something I can tell colleges about to help me standout and not seem like a liar when I say I'm passionate about math.

Sure, there are lots of opportunities. Do you have any math circles in your area? If so, attend. You'll meet people who can answer your questions. There are also all sorts of math competitions that will give you an opportunity to distinguish yourself if you are interested in that sort of thing. Some, like USAMTS, can be done individually by mail. That isn't research though.

Research is also what science fairs are all about. You can get as real as you like. Significant results may be publishable. There are also various summer programs. Look into things like RSI and PRIMES.

On the other hand, if you're goal is to impress colleges rather than personal fulfillment, you're probably wasting your time. That's not a good reason to do something.