How can I start trying to solve currently unsolved math problems?

Question

I'm sorry if this is a stupid question, but I really do want some guidance on this.

I really wanted to start helping solve unsolved math problems. (Like integer factoring, discrete log, etc. but I do want to expand to other problems too) How could I get a grasp of how far a particular problem is to being solved? How can I get a grasp of what math skills I would need to start solving a particular problem? Are there any good resources for problems like factorization?

Any help or guidance is appreciated.

Answer 1

Most if not all open questions in mathematics have at least some previously published work that can be found through a standard literature review. In fact, the first step in doing any kind of mathematical research is literature review, which addresses all of your questions:

0. Does this problem have a name? What do people call this problem?
1. What is the current state of knowledge regarding this problem or topic?
2. What are the mathematical prerequisites for research in this area?
3. Who has worked on the problem should I want to collaborate or ask questions?

If you do not know how to perform this type of scholarly review, then you're probably not in a position to make progress on most open questions, especially the more well-known ones. It is exceedingly rare that someone, either due to age, lack of prior experience, or lack of access to published research, can make meaningful headway on such problems in complete isolation. Even when young and inexperienced but extremely talented mathematicians make significant breakthroughs (one of which recently happened in the field of Ramsey theory), such discoveries do not occur in an intellectual vacuum.