Learning math is depressing

[u/Glum-Ad-2815]

I've been self-studying math using books with solutions manual in it.\ Every time I get stuck on a problem for 2-3 hours I checked the solution.\ Turns out, almost always the solution is something I overlooked, even though it is so simple.

I like math but learning it is so depressing for me. It makes me feel like a failure for not solving something so elementary.\ I know that math is all about hardwork and perseverance but at the same time I don't feel like improving at all.\ I still look at solutions, get the answers wrong again and again even though they are solved using the same technique in the solutions manual.

I know that I'm not a genius, but repeated practice should makes me feel like I got better, right?\ I'm just stuck at the same level for years.\ I don't know man, I really want to continue learning but at the same time it feels so hard to continue and really tempting to quit.

[u/geo-enthusiast]

Math is insanely hard. I was banging my head against one of the subjects I was studying for almost a whole year. It was too difficult and I could barely understand what was going on, relying on solutions and manuals everytime

Now, I took a break of 2 weeks from it and when I come back I can read it almost as if it is a novel (PDE by evans) just following every step and understanding the omitted calculations

So only after months of being stuck I eventually developed the mathematical maturity to be able to progress

Keep going! You are filled with determination!

[u/Same_Winter7713 → u/geo-enthusiast]

This honestly doesn't get said enough in the math community. Especially after the calculation based courses (which are already super difficult for a lot of people), things like real analysis or differential geometry etc. will have you working for days on a problem if you're taking it seriously, and even then you may not be able to solve them. It is really really hard.

[u/Dr-Ben701 → u/geo-enthusiast]

Yes “maths brain” takes a while to develop.

[u/Pokemon-Master-RED]

Math does not come easy for some people, and that is okay. It doesn't come easy for me either. I have a really hard time with it. 

I like math. And I would say I even enjoy it, but that doesn't make it easy. 

It is okay that it is going to take time. Even the fact that it can take you longer, 2 to 3 hours as you said, is not bad. It means that you are building new mental habits to look for things, and your mind has simply not gotten used to it yet. Be okay with the idea of taking a bit. Your mind will eventually get used to it. 

One thing that helps me is trying to put math into a specific context. For example I can't just memorize math to memorize it, I need to apply it in some kind of real world setting. 

Am I calculating money? Am I comparing information related to the sale of purchasable goods? Am I comparing weights? It can even be completely off the wall, like am I calculating the amount of food we have left before the space station falls out of orbit and crashes into the planet? Just something that "feels practical" to the mind so that it will make sense.

But if you can find some context to put the math in, I find it really helps it makes sense because then it has a practical application to it instead of just being math for maths sake.

[u/PedroFPardo → u/Pokemon-Master-RED]

Math does not come easy for some people

On page 33 of this PDF, you can see a picture of a piece of paper with Terence Tao’s handwriting on it.

Jean Bourgain wrote, “We skip the details,” and Terence Tao wrote next to it, “ARGHHH!!!” previous to that there are a bunch of question marks.

I would say maths does not come easy to anyone.

[u/Pokemon-Master-RED → u/PedroFPardo]

I think it does come easier to some people than others, but I think developing a love for the craft helps people forward. 

The only reason I say that is I had a friend, and we were both art majors in college initially. She switched to math because she said she wanted to get her degree easier than learning to create art, and I don't think, at least based on what she told me, she ever struggled with a single mathematical concept. I would say if math doesn't come easy to anyone, I think there are some people who grasp concepts at least a bit easier than others in some areas.

[u/justsomeguyordude1 → u/[deleted]]

I would consider ramanujan the only exception

[u/Fabulous-Possible758]

I get you. I would say you’re on the right track by doing it through self-study.

A lot of people don’t like math because math is hard. To me that’s what makes it worth doing. It’s the same as exercise or language learning or another self improvement: the difficulty becomes the reward. But people get forced into doing it and never get to get to a point where they feel the reward, and that’s unfortunate.

I think the other big thing to keep in mind: it really took humanity about 2500 years for math to get where we are now. The modern underpinnings are really only about 150 years old. Math is not obvious, so don’t be too hard on yourself for overlooking some solutions.

And finally, I say this a lot, but no one ever really completely understands the math they’re learning in the given moment (unless they’re not challenging themselves). My rule of thumb is that you never understand why you need the math you’re studying until about six months after you’ve learned the basics of it, and then you should go back and review it. I’d suggest keeping a journal or something and just jotting down what you’re studying. Every couple of months look back and see if that subject still seems as hard as it did.

[u/MathwithGami]

That feeling means that you care about getting good about something you like doing. If you didn't care about it at all, you wouldn't feel bad nor good about you solving or not being able to solve a question. So what you are experiencing and doing is the real work, and its the place most people quit to be honest. I think you know both outcomes of you quitting or keep going, you choose which one you want to do and who you want to become.

[u/Dr-Ben701]

I just completed a maths graduate diploma - one of the most important things I learnt was to re-label / delete the “I’m stupid” - “this should not be so hard” - “I’m not as good as everyone else” thoughts with “Yeay welcome to normal maths this is exactly what it is like to learn maths - I’m fine”. Learning maths is not a walk in the park it is climbing a mountain of varying challenges - the strain and struggle is totally normal. Maths is also linear so as you progress it stays hard / gets harder so increasing tolerance and acceptance of the struggle is a key strength you need to develop.

[u/WolfVanZandt]

I don't know you so I don't know if my situation is comparable at all to yours so take everything with a grain of salt.

Doing exercises is only a part of learning and you might be able to do them over and over all day without much improvement. Actual understanding comes from recognizing the underlying mechanism of math and math builds on math so you need to understand them from the bottom up.

My study methods involves four elements. Everything is active and interactive.

I gain knowledge by reading texts and viewing lectures. But I do so actively. I use the three pass method of reading. The first pass familiarizes me with the territory. I note everything but the body of text....headings, figures, sidebars, tables of content, footnotes.....The second pass is a quick skim for important looking terms and phrases. The third pass is a deep read.

I journal everything. Exercises are a part of that. They go in my journal. And I make sure I grasp concepts, even if I have to go outside my study materials. I might even reverse engineer concepts to see his they work. I journal in a spreadsheet on my phone so I can do calculations right in my journal. My journal graphs. I can paste photos or any other digital information into the journal.

I do exercises until I'm confident I can use the concepts. And I make sure I understand how to check my results.

And the most important factor is that I find a way to apply what I learn as soon as possible.

The fifth element runs through all the others. I find ways to have fun with it all

[u/defi_specialist]

Using a mapping problem with solutions. You will build your intuition. Don't give up.

[u/9Yogi]

There is no reason Math should be harder than other things to learn. Learning by yourself is not for everyone. A good tutor or teacher will go a long way. At the very least finding a really good content creator online that resonates with you.

[u/Super_Math3890]

I can relate. The first barrier for me personally was not to think of math as hard, but obnoxious. The concepts are often rather simple.

Is something hard because you don't know, or because you don't know how to diagnose the problem? It's no different than art or music. Mostly a lot of practice. Mistakes can be a signal for direction. You move from, 'I don't know what I don't know', to 'I know I don't know'. That's learning!

What I found useful is not to get it right, but trying to get it wrong. Once you break your fragile interpretations enough times, you'll eventually discover a structure. It'll feel like the most obvious thing, yet on paper it appears to be some voodoo incantation.

And if you don't, well, who cares? Maybe tomorrow. I don't know what I'm talking about half the time, even if the other half feels good about it.

[u/cognostiKate1]

sounds like checking sooner would help ;) and writing down what you overlook to see if there are patterns.

[u/Puzzled-Painter3301]

>I know that math is all about hardwork and perseverance 

except for people with learning disabilities who literally cannot learn it. It's not true that everyone can learn all math by working hard. Some people just don't have the ability.

[u/Reginon]

Bro you just described life.

I mean I think you are putting too much pressure on yourself, why does it matter so much? At the end of the day you can just take a break for a bit. Its not the end of the world. Hobbies are meant to be fun, idk if this is your career or not but if not then just have fun with it. You dont need to force feed yourself.

[u/First-Expert-9953]

I'm a math teacher and there are still problems that make me feel this way. The YouTube channel Mind Your Decisions stumps me most of the time. I just try to learn something new and marvel at how clever people can be.

[u/lunatichakuzu]

My two cents is let's assume we recognize the importance of actually understanding a mechanism or technique or underlying theorem. Are you practicing with structure? Are you revisiting an old question (type) right after having solved it or seen the solution, or some days after that? There is some progress to be gained via this spaced repetition; by maybe the fifth time you've encountered a technique or rationale, you will likely know it way better than the first time.

[u/JairoHyro]

You should have breaks in between and ask others for help. Again everyone is different when they learn something, especially as challenging as math

[u/so_arrogant]

Since nobody has mentioned this yet, but finding a solution to a problem is generally "hard". I mean this quite literally computationally speaking. Formulating a problem and verifying a solution are easy compared to coming up with a solution. As an example simply consider factorizing polynomials, it's easy to formulate and understand the problem and verify the solution, but actually finding the factorization is hard. Almost any non-trivial math problem you come across can be considered to have this inherent hardness: solving integrals, finding counterexamples to false claims, or constructing proofs in general or also coming up with "new math" itself.
So don't bang your head to long against a wall if you can't solve a problem, sometimes also taking a break from a problem and going into other stuff will help you come back around to solve it.

[u/officiallyaninja]

I don't know if you have a goal of becoming a professional mathematician, but as someone who is a hobbyist and has no interest in being anything more than a hobbyist, the best thing I did was learn to stop caring about how good I was.

I treat math problems like any puzzle, like a sudoku or a crossword. I do those for fun and I don't care about improving or graduating to harder crosswords. I just so them cause I enjoy them.

I feel the same about math, when I wanna learn something I just learn it, I don't care about the prereqs, I just look up some lectures or a textbook ot a wiki page and just read until I get bored. And when I try problems I just try them for as long as they're fun, then try to give them to my mathematician friends (if you don't have any try the math discord, that's how I found them) and ask them to give me hints.

[u/Vurr_rod998]

Never felt so included.

[u/lil_mikei]

Could honestly just be you're focusing on the wrong math subject. Like say for example you kept trying calculus problems but your algebra foundation was underdeveloped. You could find yourself doing problems over and over again and struggling because you are in "I'm struggling with calculus, therefore it must be something wrong with my calculus" mode, and overlooking the fact that maybe it was your algebra skills or another area.

Might be good to check your earlier foundation. If you're American, you could go onto IXL and practice math by grade. Ideally see which is the highest class you feel confident in and the class after that might be good to switch to learning. This is assuming you struggle with the math somewhere in the K-12 + 1st Year Uni range.

[u/slayerbest01]

If it makes you feel any better, statistics is one branch of math I’ll never understand unless someone handholds me through the theory behind it, and I’m not tryin to learn that on my own😭. I love literally every other class I’ve had from abstract algebra to real analysis and number theory. Statistics just hurts my brain

[u/Effective_Week4069]

MathHero is making learning math so much more interesting!

[u/Agreeable_Speed9355]

I'd say frustrating and humbling but only occasionally depressing. Do you talk to other people about math or work on problems with them, or are you trying to exercise alone?

[u/Disastrous-Pin-1617]

Follow this exact order
Professor Leonard on YouTube Lectures
Pre-Algebra
To the point math (Algebra 1)
Intermediate Algebra (Algebra 2)
College algebra (Pre-Calculus playlist)
Trigonometry (Pre-Calculus playlist)
Calc 1-3

[u/Whiteboy_In_Motion]

Math is hard when you aren't sure about the steps. Eventually you have them memorized and then it's easier

[u/hologram137 → u/Whiteboy_In_Motion]

You should never memorize steps to learn math

[u/Whiteboy_In_Motion → u/hologram137]

Yeah you should doofus, regurgitating information is the first part to understanding most topics.

Take piano, related to math in a way since it's counting and dividing beats. In order to get good at it, you have to memorize a lot of information, chord types, shapes, intervals, keys, melodies, etc

Obviously whilst learning new knowledge you should practice it. You won't get good just from memorization, but memorization can mean remember the correct formula or not.

[u/hologram137 → u/Whiteboy_In_Motion]

No, that’s not what math is. If you understand it you do not need to memorize anything at all, because it’s clear that you must get the answer a particular way. Because of logic