Programmer,Mathematics and Science

bocios

Hi guys,

This is my first post here. I think that my question is a little-bit strange but sorry for that. I need to ask someone about this.

So I'am a programmer for ten years now. Not a big time..
I consider myself as a "jack-of-all-trades" programmer. My main area is Java enterprise development bit i know C,C++,a little-bit ASM and so on
Next to this i love math and i love to solve problems
I like optimization, algorithm.. i think that every programmer love these things (or should be)

My question is:
Could you please suggest me some areas of mathematics that is the closest for a programmer?
So.. there are mathematics topics like algebra, number theory, lineal algebra, discrete math., and so on.
Which pass for these:
- There are many-many problems to solve
- Need to write algorithm
- Maybe need to optimize

Okay i know that near every math things fit for these things.. But which area is closest for a programmer?

I would like to do this in my free time, for a hobby-like.. and for learn new things.

I think that maybe AI is the best for this. It has Genetic Algorithm, many-many problems to solve, and so on.


Edit:
Forgot one more thing.
Maybe i can join some math-science based research tasks at my work.
So you can suggest me math areas that pass for math research things.

Sorry if i'am not too correct or precise. Maybe neither i don't know what i want


Thank you,
bocios

bocios

So, to clarify..

Currently i learning a lots of math to use my programming knowledge other things.. not only for work.
Because i'am a hobbyist of astronomy i thought that i can use my programming knowledge in this very-very interesting and beautiful science.
Currently i have a basic telescope (it's a Luna-70) and i cannot stop to watch things with this, all the nights
Please help me to see how can i use programming thing with amateur astronomy. Is it possible to do programming things at home if i'am an amateur yet? I know that maybe the question isn't correct but hope that you will understand my question.
I'am open for new things, to learn things.