# What are the problems that you tried to find their solutions and you did not know that it is impossible?

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 worked a project in which I was trying to develop a Fourier transform on some subgroup of the Lorentz group (where I was trying to express the group in terms of self-adjoint generators). After a few weeks of messing around with the generators, I realized it was impossible and it was a stupidly simple linear algebra argument. I was a little inconsolable for a couple of days haha. – Cameron Williams Jun 20 '14 at 2:54
• Well, to me it does not sound those were waste of time at all. – timur Aug 2 '14 at 21:12
• I think everybody has tried to find a formula for the n-th prime at some point(s) in their life. So far nobody succeeded – DenDenDo Feb 2 '15 at 22:54

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.