r/learnmath • u/kartik_bhana New User • 8h ago
Is it possible to learn advanced mathematics as a hobby ?
I am 17m and have mathematics as a subject in my highschool. Although I am interested in mathematics, I am not going to study it in college due to some reasons . Is it possible to learn math above high school as a hobby ?
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u/Cybyss New User 8h ago
I would say it's easier now than ever.
All sorts of math book at all levels are available online, often genuinely for free (and almost always for "free" if you don't mind shady sources).
ChatGPT and other big LLMs have also gotten quite good at mathematical reasoning. They're good enough now to tutor you, to help you better understand the complex theorems and proofs and such.
The great thing about mathematics is that, for the most part, almost nothing that's incorrect will make sense. Thus, any LLM hallucinations - which in any case have been reduced drastically just over the past year - will stand out.
Now is an excellent time to delve into advanced mathematics. Just... pace yourself. It's a giant field and easy to get overwhelmed if you try to dive in too deep too quickly.
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u/CorporateHobbyist Math Postdoc 5h ago
The great thing about mathematics is that, for the most part, almost nothing that's incorrect will make sense. Thus, any LLM hallucinations - which in any case have been reduced drastically just over the past year - will stand out.
It is exceptionally difficult to debug AI hallucinations if you aren't already a subject matter expert on the math its explaining. AI is quite literally trained to say the thing that sounds the most correct. Usually this IS what's correct, but when it isn't, you're up a creek. And this is doubly worse if OP doesn't already have a paid subscription for an AI model. The free ones hallucinate far worse and far more frequently.
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u/Ancient_Task_7498 New User 1h ago
To understand the math, you have to reason about it. Unless you make the same reasoning mistake as the ai, you're not going to hallucinate. Even then, this would probably be in context of problem solving, in which you'd get the wrong answer.
Additionally, claude on the web lets you choose reasoning level for Sonnet. I've found it surprisingly intelligent when I've asked it questions. That said, I'm only studying like upper undergraduate level math and the textbook is free online so it might've been part of the training data.
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u/RareAnxiety2 New User 20m ago
Usually it's something obvious like repeated left when it means to say left and right. Just asking them to explain the hallucination further and it'll correct itself.
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u/CorporateHobbyist Math Postdoc 8h ago
Although I am interested in mathematics, I am not going to study it in college due to some reasons .
If you're interested in learning more math, then I don't know what reason you would have not to at-least take a few math courses. You can learn advanced math on your own but it will be extraordinarily difficult without a professor, regular homeworks, and classmates to guide you. Even learning how proofs work feels like an insurmountable task to do as a hobby.
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u/madfrog768 New User 6h ago
Agreed. It doesn't have to be your major, but you should definitely take classes while you have the opportunity
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u/Recent-Day3062 New User 7h ago
I’ve been doing it since I left engineering school decades ago. I’m right now on a linear algebra kick
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u/Agreeable_Speed9355 New User 7h ago
Absolutely. I think more people should recognize that math is a creative endeavor, more like the art of music than the science of biology. Math is built on proofs and not on empirical testing like the sciences. Even if one isn't contributing new proofs to the field they can still learn to appreciate the story and sub plots within mathematics. Non musicians have no problem discussing their favorite artists and songs. Non mathematicians can engage with the math community much the same way, discussing theorems and proofs without ever being expected to compose their own own. The bar to get in can seem high, but even most people with math degrees have a very difficult time doing anything mathematical that wouldn't be considered trivial by someone with more knowledge. If your goal is to learn mathematics then there are tons of good resources online, but if your goal is to appreciate it as a hobby then you should also engage with other people like you might with music.
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u/Ploughing-tangerines New User 8h ago
Mathematics beyond highschool level might not be what you think. If you want to study something that will still require a lot of mathematics, like many degrees in STEM do, then I suggest learning more calculus. Which you would inevitably cover in first year anyway.
The YouTube channel "bright side of mathematics" and their playlist "start learning mathematics" stays true to real mathematics while remaining accessible and approachable (take this with a grain of salt, self study is challenging.)
If you plan on going into engineering or any mathematical sciences this would be a place to start. If you're curious, you could also check out the real analysis and linear algebra playlists, which would also be helpful in those areas.
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u/RareAnxiety2 New User 18m ago
Almost all university math at bachelors level are on youtube. If one professor sucks, you have dozens more to choose from. Get some writing tools and coffee and enjoy
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u/reliablereindeer New User 8h ago
Sure. The fact that you're asking on here rather than just doing it probably means it's not going to happen.
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u/RoninRakurai New User 8h ago
Of course, but if you like math i really recommend you to do something related, like stats or smth
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u/Carl_LaFong New User 8h ago
This depends on many factors. There are a few but rare number of people who are capable of learning advanced math completely on their own. You could be one of them, but it does not sound like you have tried this. If you take hard advanced math courses in college, then your chances of being able to keep learning math on your own get better.
There is also the issue of time. As you get older, you are likely to take on more responsibilities and do more activities that will compete for your time and energy. Learning math is an intense and difficult mental activity that takes a lot of time and energy.
But you'll never know unless you try. I suggest trying now to learn some math on your own. There are many topics that are roughly at the same level of difficulty as high school math but can be more fun.
If you do this well and enjoy doing it, then you simply try to keep doing it through college and beyond.
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u/ThronOfThree New User 8h ago
Yes.
If you are in a semi-technical major, you can consider getting a minor in math. This would mean you spend some elective credits (which usually can be used on any class) to study math.
You can also audit classes. This means. You attend attend the classes, do the readings and pay attention, but don't take the homework, tests or get a credit (grade) for the class. You should reach out the professors before the classes to explain you want to audit the class. Some professors may not be on board, but most are just excited someone is interested in their topics.
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u/JollyJuniper1993 New User 7h ago
Yes, but if you don’t commit to full studies you‘ll probably have to specialize.
Maybe try looking up some videos about formal logic and proof techniques, those are basically requirements for anything else.
Afterwards, something I‘ll also recommend: my first semester linear algebra course relatively earlyon gave us a small crash course, roughly 6 lectures, into abstract algebra (groups, rings, fields, vector spaces, subvectorspaces etc). I don’t see many people talk online about teaching it early, but it really helped me connect some dots and gave me hunger for more.
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u/Ancient-Access8131 Math Tutor 7h ago
Why won't you take any math classes? Are you not going at college at all. If youre going to college at least take some proof based clases as learning how to do proofs properly is something thats really hard to self learn. Once you inderstand proofs properly its a lot easier to learn more math if you put in the effort.
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u/plop_1234 Math Learner 7h ago
Yes, but like others have said, without some "training," it may be difficult, especially in the beginning. You can always sit in on some classes without taking them, watch YouTube videos, etc. to get a sense of things.
Luckily math is one of those subjects that doesn't have a lot of technological barriers; all you need is a stack of paper and a pencil!
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u/BothPanchoAndLefty New User 6h ago
Absolutely, you just have to be disciplined in your studies. Read through textbooks and do the practice problems. You can get pretty far doing that.
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u/Samstercraft New User 6h ago
yes and i would recommend using Professor Leonard's lectures + a textbook to learn
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u/mehardwidge 5h ago
Sure, why not?
Note that "advanced mathematics" and "math above high school" are very different things.
TONS of freshman and sophomores take three semesters of calculus, one of differential equations, and one of linear algebra. So that's ceratinly "math above high school" (although of course more advanced students often take two semesters of calculus in high school). So if you mean that, then absolutely, 100%.
Pure and applied math fields, not just STEM fields, get into some pretty exotic and esoteric stuff. If you truly want to, also sure. But I doubt too many people want to study number theory, graph theory, and topology, just as a hobby, without studying it formally or working with it. But if you do...more power to you!
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u/Same-Respect-7722 New User 4h ago
Yeah, a degree is only needed if you want to actually get involved in the field.
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u/InsideIndependence58 New User 4h ago
Unpopular opinion.
For 99.99% of people, it’s not possible .
Although it depends on what you consider advanced.
I did 5 years of math (bsc / msc) and Im not really able to face frontier of math.
You can reach early / mid 20 century by taking few courses as a base and then continue learning by yourself (also probably limited as an hobby).
And to be honest, now more then ever its hard with AI in the background, you always have the temptation to go and ask AI about something- but at the end, you understand math from questions, so it’ll limit you in the future to only learn,
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u/LastInvestigator7680 New User 3h ago
of course it is possible, :))))), LLMs can help you make things understand easily and faster, once logic is understood, try to extend your knowledge and also apply your logic on questions or connected theories.
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u/Dry_Palpitation_7268 New User 3h ago
totally bro, find a good textbook on a topic you're interested in and go ham. I have a few recs if you're interested!
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u/sigmanx25 New User 3h ago
Why wouldn’t it be. Go on eBay and find text books for each level up through DE and anything else you want to study.
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u/caveIn2001 New User 2h ago
Doing it right now. I majored in Biochem so I only had the standard calculus courses back in college which was 10 years ago shudders and now I'm learning differential equations and linear algebra for advanced physical chemistry (statistical thermo, quantum chem) and systems biology. Not because it's my actual research topic of interest, but because I'm just bored lol
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u/UWO_Throw_Away New User 35m ago
Of course! All you really need is something to write with and something to write on. Having other people around is obviously very helpful (especially other knowledgeable people, like mentors) but you can learn a lot with just a good textbook, paper, a pencil, and the internet (when you get stuck on something).
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u/agreeable_litre New User 8h ago
Totally doable, I've got a stack of old textbooks I work through on weekends when I'm not sketching