I recently received a bachelor's degree in Computer Science (which I pursued for pragmatic reasons) and would like to contribute to Mathematics as a mathematician would. My challenge is not knowing what there is (the cutting edge) and which direction to take in order to one day contribute.
A. Is it possible for one without all the knowledge from the formal path and with a C.S. background to contribute directly to maths as a researcher? If so, how and in which fields? (How about combinatorial set theory?)
B. At the heart of it, I want to do research in maths and contribute to this magnificent discipline because I love maths. It has brought structure to my thoughts and I now want to expand its structure. i.e. I do not mind this project of mine taking 10+ years because it is a labor of love. (Favorite book: How to Solve It by George Polya)
Therefore, putting aside A., what advice would you give to someone in this situation?
Thank you
In brief, do what you love. Don't worry about "the cutting edge". There are many ways to contribute to "Mathematics" that don't require advanced degrees. Only you can decide what work you want to do and how to do it. Learn more about areas of mathematics that you are interested in. You may want to read books that give a broad view of what Mathematics is. For example, The Princeton Companion to Mathematics. Formulate and work towards solving problems you find interesting.
In the past it was much harder for someone to do mathematical research without going through the traditional route. Now we have LaTeX, CAS, web browsers, arXiv, and powerful computers. These change the theory and practice of doing mathematics in significant ways.