When I was in High school, I really developed my interest in mathematics. From that time , I always had an ambition to become mathematician or to discover something in mathematics. Because of some reasons, I chose B.E. in electronics & communication and got a degree in that. Now I got a government job also. My work is some what less. In free time, I usually watch mathematics related videos about unsolved mathematical mysteries and sometimes I try to work on that. My favourite part is complex numbers. My most favourite thing is infinite number series problems like grandis series etc., From the beginning I always think that there must be something unified in mathematics like sometimes I feel like prime numbers , Fibonacci series , Pascal triangle , e, π, i are all related in some way. One day I watched a video about Riemann hypothesis which isn't solved yet. But solving it might give us better understanding of prime numbers. So here I come to my question part, instead of wasting my time everyday, I am thinking to achieve something. Mathematics is really that kind of item to work on it. I mean it just needs pen & paper. Also, I can get programmes to simulate my thoughts / ideas about numbers. Especially infinite series etc., Internet is there for me to get all information. so my question is which branch of mathematics is best for me to continue to work on that. Number theory?. I have decided yesterday that I should dedicate myself to mathematics in next 20 years. Now my age is 24. I hope I'll really get something positive result in future. Even if I fail also, I don't mind. I told this to my friend & he laughed saying "till now no one discovered pattern of prime numbers & you think you can discover something in mathematics, even PhD holder isn't getting results". sometimes crazy ideas come to my mind related to maths, & immediately I'll start working on that. After hours and hours ,I'll realise that this isn't simple thing to do. Can I really succeed in this? What is the best way to approach? Should I first start reading recent discoveries in maths & start working on that? Now I can't goto university & do PhD . With this internet, will I be able to do a reaserch in mathematics? Or else should I stop thinking like this non sense ? Can a person like me be able to discover?
Welcome to mathematics. You can have a lot of fun playing in this world. I think you'll have more fun if you start with easier problems than the Riemann hypothesis and the patterns of the primes.
You should count any problem you solve for yourself as "research", even if you're not the first one to solve it. Perhaps begin with easy ones - these searches suggests many places:
You may find that when you solve a problem you have an idea about how to change it slightly to make a new problem you will be the first to solve. Find a place to post it on the internet as a puzzle for others and you have begun publishing your own contributions to mathematics.