The Oxford Advanced Learners Dictionary defines a Mathematician as a person who is an expert in mathematics.
The Cambridge Advanced Learners Dictionary defines a Mathematician as someone who studies, teaches or is an expert in mathematics
I wouldn't take Oxford's definition too seriously but according to Cambridge's
- If you study Mathematics, you're a Mathematician.
- If you teach Mathematics, you're a Mathematician.
- If you're an expert in Mathematics, you're a Mathematician.
Personally, my love for Mathematics came $12$ years ago when I took my first $97\%$ score in Mathematics home to my father and I saw the look in his eyes. Since then, it's been Mathematics everywhere. Mathematics has been my life and even right now, Mathematics is paying my college fees, feeding and clothing me, so I think I can call myself a Mathematician, but
- Do I deserve to be referred to as one?
- Do I feel like one?
The first question is something I can't answer because the society has what its own image of a Mathematician. The likes of Euler, Newton, Euclid of Alexandria, Fibonacci etc. that I can't even imagine comparing myself to. So I can't answer that question because the society already has one and it's a NO.
For the second question, the answer is also a NO most probably for the same reason I stated above for the first question. I don't feel like one, I may be in a reasonable percentile for my age but I most definitely do not feel like one because there're Mathematicians I know that I may never measure up to. But does that mean I do not know enough?
Here is another interesting part. What Mathematics should I know so I can feel, or deserve to be referred to as a Mathematician. The answer to this question depends on the question
Why do you love/do Mathematics?
Is it because you want to make a change in the world? Is it because you want to achieve something huge and become famous? Or is it simply because you love it so much, you can't spend a nano-second of your life without it?
Depending on your response to this question you will know whether to try and be the best in one area of Mathematics or learn as much as you can in any area that you can.
In all cases, one cannot always depend on the majority/society to answer our own questions. even though the majority carries the vote, the majority can still be wrong.
In whatever you do, don't forget that
- To be conscious that you are ignorant is a great step to knowledge.
- A little learning is a dangerous thing
- You never know, until you truly know.