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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?

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  • $\begingroup$ Number theory is a fascinating area, but some questions are very difficult and some impossible to answer in general. Hilbert's tenth problem is a very good example : There is no general method to decide whether a diophantine equation is solveable. Prime numbers have intensively studied and noone discovered the "ultimate pattern", although much progress was made. It is not impossible that a newcomer discovers something really new, but you should not try to prove such conjectures like Goldbach's conjecture, Collatz conjecture or the Riemann-hypothesis. $\endgroup$ – Peter Mar 10 '17 at 13:58
  • $\begingroup$ This is a difficult item. On the one hand I would encourage you to follow your ambitions and learn about mathematics and maybe you are the one to solve certain problems. On the other hand, a decent mathematics student has studied mathematics for 5 years and has learned theories that took decades if not centuries to be formulated and proved. So a beginning mathematician has a vast knowledge of ideas that noone could have found by him/herself (by this I mean all those ideas). Of the many people there are with this knowledge noone seems to be able to solve the problems you mention. $\endgroup$ – Mathematician 42 Mar 10 '17 at 13:59
  • $\begingroup$ The danger to waste time is great and many false claims have been made. It happens often that someone is convinced that he/she has solved a famous problem. Nevertheless, it is well worth to study number theory. It is useful for example to learn proof methods like induction or infinite descent, And number theory really makes fun! $\endgroup$ – Peter Mar 10 '17 at 14:00
  • $\begingroup$ Good news: there is a pattern in prime numbers. To really see it you need to look at the numbers from your own perspective. Imagine if a mistake has been done on one of hypothesis' in mathematics in the past, then this problem is multiplied through other theories in time, and can only make a confusion for someone who is trying use existing knowledge to solve mystery conjectures. $\endgroup$ – usiro Mar 10 '17 at 20:01
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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:

https://www.google.com/search?q=elementary+problems+in+mathematics&ie=utf-8&oe=utf-8

https://www.google.com/search?q=recreational++problems+in+mathematics&ie=utf-8&oe=utf-8

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.

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