I'm 22 years old and studied 2 years of math before droping out to travel the world as an assistant of a friend who make commercials, documentaries and media creation in general.
I really love math and cs however I love to travel and learn about new cultures, so I can't go back to school in the near future, I'm getting more responsibilities and probably continue doing something similar for living like photography or videography.
I was wondering is possible to become an amateur mathematician doing relevant research independently? I can study 4 hr everyday, no more because of my work and because I have many hobbies. Also I can't work intellectually in a subject for more than 4 hrs. (I use to practice shogi and learn that 4 hrs distributed in a day work best for me).
I've liked algorithms since I'm a child, When I was in elementary school I liked this girl but I was super shy so I thought that if everybody in the class submit an ordered list of the people who liked we could make an algorithm to match people. I develop an algorithm who would make this possible and I remember that not was that simple, almost took me a whole year.
I think I have strong basics in abstract algebra, real analysis and linear algebra. I also have self study algorithms, computer complexity, basic computer theory and basic computational geometry. But now I don't know how to keep going. I also know to program because I enjoy making programs to solve problems like python scripts to automate download series or to automate the things I repeat a lot. For the things I learn I probably could get a CS degree since I'm interested in this themes since I was 12 and took one robotics course, I didn't learn much robotics but I was amazed with computers so I started programming.
I'm not interested in money, positions in universities or even social prestige (I probably would use TrashPanda as my penName like the boubarky school of math). Because I think academia has some big problems like the way academical publishing works. But as you probably has noted I really like fake internet prestige and I think don't would be cool that someone with no formal math education and with a pen name like trash panda started to publish in academic publications.
I admire profundy Erick Demaine and I after "reading"(I couldn't comprenhend many of the paper he have) some of his papers and the page in the CSAIL of MIT I think I'm interested in:
- Discrete and computational geometry: Folding and unfolding, linkages, robotics, motion planning, dissections, simple polygonizations
- Algorithms and their analysis: Adaptive computation, graph algorithms, string matching, randomized algorithms, approximation algorithms, fixed-parameter algorithms, streaming algorithms
- Combinatorics: Discrete mathematics, graph theory (matchings, minors, treewidth, …), combinatorial game theory .
My plan is to self learn combinatorics (With the books: Principles and Techniques in Combinatorics by Chen Chuan Chong and Brualdis book in combinatorics). Dominate the book CLRS of algorithm analysis. For CG I plan to complete Devadoss & O'Rourke's Discrete & Computational Geometry (I'm half way), the Springer published Computational Geometry: Algorithms and Applications, and David Mount's notes (Page on Umd) .
But I figurated that I can start reading some papers that are not that hard, I pass a lot of time in Mexico and in Chile so probably I can look from a professor there that could help me.
Or maybe someone here would like to mentor me. (I promise that I could research a lot here or in mathexchange before as you)
What you guys recommend? I feel like when you like a person so much but you can't see her/him.
Is there some papers I should read? How can I discover a proper theme acording my current level to try to investigate?
Thanks in advance to everybody and obligatory sfmbe.