Tell us your story about Mathematics. Have you dream one day to do a big contribution in Mathematics because you are curious and love challenges. What are things that you tried to prove which then shown to be impossible.
For me, I will tell you a little story about me:
When I studied second order equation $ax^2+bx+c$ and learned how to get the solutions, I was thinking that the solution to the cubic equation $ax^3+bx^2+cx+d$ can be found by me. I tried to do the steps and after some experience and learning I noticed that I was just wasting my time (because the solution already exists).
Another example is when I studied Riemann series and when I saw $\lim_{N\to\infty}\sum_{n=1}^{N}\dfrac{1}{n^2}=\dfrac{\pi^2}{6}$, I tried to apply the technique used to get the general formula for geometric and arithmetic series to obtain a general formula for $\sum_{n=1}^{N}\dfrac{1}{n^2}$. After some times, I noticed that I was wasting my time too (because it could not be found).
Another one is I tried to get a closed form formula of this integral $\int\,e^{x^2}dx$ because I wanted to found something new that people did not found yet. It was also a waste of time (after seeing Liouville's theorem).
All of this and more happened to me because I was curious and I love challenges about mathematics in my first levels of studying.
I would like to hear from you.
I would suggest (read the questions, not the answers)
A bijection between the real and the irrationals
x^y=y^x
and one I couldn't find (and answered) but loved: if you order the rationals, what is the smallest gap you can achieve between neighboring elements. So among all functions $f(n)$ from $\Bbb {N \to Q}$ what is $\inf \left(\max_{n \in \Bbb N} |f(n)-f(n+1)|\right)$? This is a favorite because I was trying to prove one answer and found a different one.