I finished my bachelor degree in math and computer science (double major) recently and am applying for a PhD very soon. During this period I wanted to know how it feels to do research. Personally I am more interested in pure mathematics. As a result, I searched for around 20 open problems (not Riemannian hypothesis, small and unknown open problems) to see if I can achieve anything new about them to publish.
The problems did not need much to be understood, mostly in combinatorics, linear algebra and analysis. I was able to find new results about 2 of them, meaning that, I was not able to find any article that mentioned my results. However, I always feel my results are very bad and have low quality and I feel if I submit them to any journals I will only hurt myself. To explain a little bit more how my results look, I should say I was able to prove some special cases of the problem and find another elementary proof of one of the theorems that someone else found using advanced techniques. So by no means, I do not feel I did anything worthy of publishing.
However, when I am looking around the internet I see people publish results that are really easy to achieve, for example an elementary proof of Fermat equation for case 11. During my journey I found out achieving very good results will take years, those problems won't be solved easily and there is a reason that they are open for years if not decades.
So if we want to call a person a good pure mathematical researcher, does that mean solving very difficult conjectures only? It's really important for me because I am not sure if I want to go into the CS industry or do research on math and CS theory. Because I am afraid I am not a good fit for research and I feel that is because I have high standards.