Although today I had other things to do (visit my relatives), on most Saturdays I'm planning to do some Math and try to do it offline without computers, if possible. Thus I would observe the "Sabbath" this way (ideally, I should not turn on my laptop on Saturdays, and Mathematics can be an ideal activity I could do on those days). What these Math activities can be?
- I've downloaded a lot of lecture notes and books about Mathematics from the Internet (mostly in English), but only those which have a good license like CC-BY, CC-BY-SA, GNU FDL, public domain, Project Gutenberg license or downloaded from "free Google books" (which I assume should be almost public domain). These files occupy about half the size of a DVD on my disk (and more, since I have more copies of them). Thus I'm occasionally also reading some of these books, or their printed versions, which I received as presents. (So they asked me what should they give me as a present and I wrote that they could print some of these books for me like university students print their lecture notes.) Earlier I also printed some of these myself, but those are just separate pages in folders.
- I've also picked some good-looking Math exercies from the website of KÖMAL (I linked the English-language version for you, but I picked them in Hungarian, of course), and I printed them. Thus I can think on them on Saturdays. Many people regularly solve crossword puzzles, Sudoku and the like, but in my opinion these KÖMAL exercises may be much more interesting and challenging than those. As a compensation, I'm planning to order 1% of my taxes to the foundation that runs KÖMAL (MatFund) in the next year (in Hungary, we can order 1% of our taxes to a NGO we choose, and another 1% to a Church we choose). In this year, however, I already ordered this 1% to an environmentalist organization (so 1% of my taxes for the year 2023 is given to Environmentalists, but 1% of my taxes for the year 2024 will probably be given to Mathematicians in 2025).
- Sometimes I am also thinking on really hard Math problems, like the Goldbach conjecture (by the way, I prefer those which can be formulated by relatively simple statements, so I'll probably not be thinking on the Riemann Hypothesis in the near future, because it is not "elementary"). Lately I had not many ideas for them, so they were neglected... also because I realized that the KÖMAL exercises are still hard for me, so it is not likely that I can solve these much harder problems in the meantime. (But I acknowledge that even if I cannot solve the Goldbach conjecture, I can become wiser if I try it and learn new things along the way.)
- ... and the following is what I am writing this blog post for: I've begun to think about new types of polyhedra, are they possible or not? This is what I could try to research. Thus I have some ideas as seeds (top secret), and I could try to do Math to decide if these ideas lead to new types of polyhedra or they fail. During this research I've found the Virtual Polyhedra website of George Hart, which is very interesting and well done! It lists a lot of polyhedra types I previously knew nothing about (although I knew the Archimedean solids and their duals, for example), and the interactive visualizations are outstanding. However, my ideas are not there, so they will either fail or they are still very well concealed by God. Mathematicians teach that the symmetry types of possible polyhedra may not be very different from what we already know about, but I would still like to check this myself. However, I may not be skilled enough in Mathematics to do it, so it is possible that I will use computers to help me... but then I should probably not do this on Saturdays. On other days, I still focus on writing a new book about the critique of Christianity, so it is possible that this polyhedra goal of mine will progress very slowly, and it will still be an open question for me in the next year... but at least I wrote about this today so that my readers know that I may be about to discover something, which may be more worthwhile for me than thinking on the Goldbach conjecture.
By the way, I could also do some other random things related to Mathematics not listed here. For example, I recently realized that I couldn't have beaten the best 8th graders in Mathematics on the Zrínyi 2021 competition for elementary schools (so I am probably weaker in this type of Mathematics than I was in elementary school). I've also recently mentioned some of my activities or plans related to Mathematics on my Hungarian blog (including some logic puzzles on computer or physically). Since then, I've also found a new game called "Chroma" in Ubuntu Linux, that is also looking nicely (if I had time for it)! On my Hungarian blog, playing chess is also mentioned, which I try to do regularly on LiChess (usually about one game per day). It would be good to level up my chess skills to be able to win a competition in my town, but I will probably not go to local chess competitions until I play good enough on LiChess or against a computer on Normal level.
By the way, knowledge in Mathematics is something that is good to have. Even if this World is evil, Mathematics is good, so we can build up knowledge about Mathematics in our brains, and this way we can get close to the universal values that are true in all possible worlds, not just ours. Thus I've also begun to read a book about Mathematics that contains many things I already know, but it was still good to read it, because it was organized in a special way. (E.g. it has chapters about the different proof techniques, which is a good summary of them.) Thus Mathematics is beautiful.
