Tinkering with mathematics

Hi lainons, I recently read "A Mathematician's Lament" and felt inspired to pursue math further. I want to explore mathematics not for the sake of researching X topic (i.e. not to follow the school curriculum for trigonometry), but for discovering and tinkering with math that links to my interests. Something like attempting a difficult proof or applying math to a hobby. Do any of you have any experience or resources with learning math in this way? I don't expect to discover a new mathematical law or theorem, but it might be interesting to write up my 'findings' for my personal wiki. Are there any good guides for learning to write in LaTeX or a mathematics editor of the sort? Thanks for your help!

> Do any of you have any experience or resources with learning math in this way? get a good book and do all the exercises. I cannot tell you what book to get because a) different people have different tastes b) I have no idea what level you're at Unlike art, mathematics cannot be appreciated by someone who does not have sufficient training. Since you're not bound by curriculum you can learn interesting things right away, but you will have to slog through exercises as well.

>>58870 I really recommend you to have a good foundations, that is, the basic real analysis, basic algebra, basic topology and basic geometry. After that, just learn whatever you want. The reason is that any other field will require some basic idea of those mentioned above and so you may waste time trying to understand something without the basis for it. For basic, I mean the kind you are going to see in any undergraduate level. Sadly, you can't just jump into commutative algebra and expect to understand anything if you have never studied algebra before. Same for many other math fields, which is why I recommend for you to get your foundations down. The problem on applying mathematics for other things is how good is your understanding of applied mathematics. By that, I don't mean you have studied a lot and more about if you understand how to create a model of something, how you go on breaking your model such that you can apply mathematical concepts to it, etc. It's sad that even in an undergrad math curriculum you hardly see any focus on this. In the case of trying to attempt some proof for any hard conjecture is that unless you know a lot of mathematics, you are bound to only learn about those really hard conjectures that requires a lot of background to even understand what you are supposed to prove. Book related have many interesting problems and even to understand most of them, if not all, you need to know more than just an undergrad math level. Anyway, you could just develop many math fields and even find out many theorems by yourself(even if you are unable to prove them, keep in mind that many people have used mathematics for centuries before they could prove any theorem), but you may waste a lot of time in something that you could use textbook to skip many levels and try new things in fields that interest you more. At the end of the day, mathematics is more about studying patterns than anything else. You are free to start without any help, get some foundations down or just try to apply it to something and use the internet to help with things you found out that may be related to some mathematical field already being studied.

You didnt say what level youre at. It is such a bad sign that you didnt consider this, so i'd guess you shouldnt try at all

Find interesting questions to guide and motivate your studies. The best math books are problem books. Too much explaining will rot your brain.

>>58918 please don't say that I recommend because you didn't say a level you find a tutor a website called preply is start

Lockhart's "Measurement" is good for an introduction to the thinking he champions in "A Mathematician's Lament" With regards to LaTeX, just google your way through it. Most online guides are ridiculously slow and assume the reader has no capacity for independent thought. Also, consider, if your text editor supports it, snippets such as these ones: https://github.com/gillescastel/latex-snippets If you want to get started right away, https://nrich.maths.org/ has both simple and advanced problems that require you to actually think. Not all of them are necessarily mathematical in nature, but they train critical thinking and reasoning skills, which is vital if you want to explore mathematics further.

>LaTeX I like Overleaf docs (https://www.overleaf.com/learn/latex/Mathematical_expressions) and the Wikibook (https://en.wikibooks.org/wiki/LaTeX). There are also some tutorials on YT: https://www.youtube.com/watch?v=NwnYHoNtfJ0&list=PL-p5XmQHB_JSQvW8_mhBdcwEyxdVX0c1T&index=1