Does Mathematics research in proven problems have any importance?

It is not going look bad at all. It sounds like the Professor has given you a project that is achievable in the time frame, and satisfies your goals of improving your math and getting some experience in research. It should have a positive effect both on your CV and on your understanding of the research process.

In my PhD experience, much of the beginning was is exploring the topic, reading the literature, and trying to figure out a new direction. This can take many months, and can even change as your understanding improves or new information comes to light.

I don't think people will expect to see original research on new problems until the latter stages of your PhD.

In Finland, many bachelors' theses in pure mathematics are summaries of what is already known. Bachelor's thesis is required to get bachelor's degree. Master's thesis (pro gradu) might or might not contain original research.

From this perspective, it sounds like you are completing your thesis as an unpaid intern. You can presumably add this as work experience in your CV and it should be a positive at the beginning of your career.

If you are proving something with a new method, or writing down a folklore proof (something widely known, which is not in the literature), then your report might also have scientific merit. You should ask if this is the case from your advisor.