Stop trying to understand. Stop. Just stop now. I don't mean that you shouldn't learn mathematics, but stop trying to understand. Sometimes I think that this is something that has taken me a very long time to learn, and most people struggle with this immensely.

Immensely. When, when I first got to graduate school, I was assigned an advisor, a really brilliant man from Argentina. And I remember when I first went to his office, I walked in, he had a very large office and he had a desk bigger than this one, and it was covered

in papers. He had stacks of papers. We talked for a little while. He told me he was writing a book. Apologize for the mess, and he gave me some advice which I thought was great, but I didn't take it. He told me to not spend too much time

working on any one problem because I couldn't afford to waste the time. And I thought, wow, what a, what a great idea. I really like this guy. Yeah, he's right, this is great advice. So fast forward, maybe I don't know, three months, four months,

I'm waking up at 3 in the morning to work on a math problem that I've been working on for a week. Turns out there was a typo in the problem. I spent probably 50 hours working on one problem. What a waste of time! Now, I'm not saying you shouldn't

spend some time trying to focus and learn and understand math, but sometimes you have to move on. You have to stop trying to understand and move on and, and do something else. One of the things that plagues a lot of students, and I say this because I've had

thousands of students over the years is that they sometimes will get hung up on things, they'll get hung up on the why. They'll learn a formula in class and they'll want to understand where it comes from, the derivation. They'll ask the teacher maybe

the teacher gives them a response they don't want. They'll look in the book, maybe the book doesn't, doesn't explain it well. Sometimes they'll go home and they'll watch a video, it won't really make too much sense. They'll kind of half

understand it. Hey, that's okay. Half understanding is better than not understanding at all, right? And you tried, move on, right? Focus on your grades, focus on what's in front of you, right? Do what you can now instead of spending hours and hours and hours on

something that you might not be able to figure out for a very long time. A lot of times in mathematics when you revisit things that you've seen in the past, it's easier. And sometimes you just don't get it. When I was in pre-calculus, I was learning about

finding the inverse of a matrix, so you take a matrix and you put it into another matrix and you um turn it into what's called reduced row echelon form. It requires a lot of mental calculation, and I remember I had struggled with it because I always made silly

mistakes. And then the night before the test, I stayed up till like 1:00 a.m. I thought, 'No, I got to get this.' And you know what? I didn't. I kept making silly mistakes. Sometimes that's just how it is. Another example was, you know, learning

Mathematical induction with inequalities, this is a tough one. And it's funny because I know it's not hard for just me, it's hard for other people. And I know this well for a couple reasons: one, I've taught it in college; two, if I look at my

induction videos, I have more dislikes on the videos with inequalities. Why? Because they're harder to understand, so people get confused and they dislike the video. So maybe it's a bad video too. I don't think it is. I I don't think they are, but

I think it's because those people are having the same problem I was having, right? Even even though I try to explain, they still don't understand. So is it my fault? Is it their fault? Maybe it's no one's fault. The point is, sometimes you need to

revisit things later and they'll make sense. Now, you know, those those proofs are no problem for me, but I had to wait years, sometimes years, before revisiting something and then it comes to you, it clicks. So if you're hung up on stuff, if

you're hung up on some mathematics, or maybe physics, or whatever it is you're trying to learn, and and you don't get it, it's okay, right? It's okay to not understand. People always put this emphasis on understanding, which is important, like, oh, you know, if you take a

class, you should understand everything. And I've said this before, but I'll say it again, just in case you haven't seen my other videos, but typically for me, as a college student, I maybe understood 60 to 70% of what was taught in a class. 60

to 70% and that was it. That feels kind of low to me. I mean, it feels low. I felt like I should have understood more and it always bothered me. I felt like I wasn't that good, but then I knew I was good because I would go home and I would

study. I would figure it out and I would do well on the test, and that's how I, I guess, would prove to myself if that's a thing. I don't know, not really. I just knew I could do it, and so I worked hard and I did

it. The point is, a lot of times you're not going to understand everything. I don't, I don't think it's possible if you take a class. I mean, it's hard to understand everything. I, I had a student once, oh, he's a great guy. I just, just

remember this story, so I'll tell you really quick, and he was in my office once and he said something really interesting. He said, "Well, a C means you understand 70% of the material, right? So that's pretty good." And I was like, "Wow, that's, this guy's got something right."

Think about that. A C means you understand 70% of the material. So just think about any class you've gotten an A in. If I think about classes I've gotten an A in, I mean, well, I mean, at the end of the class, that I understand 90% or more

of the material. Maybe I just know that in that lecture I caught 60 to 70%, and I wonder how much people really understand when they're done with the class. Do they understand everything in the class? Probably not. So it's okay to not understand. Don't get hung up on

stuff you need to manage your time and move on, so just move on, don't get hung up on it. Everyone struggles and if you feel like other people are getting it and you're not, it's not because you're dumb, okay? It's not because they're

smarter than you necessarily. It could just be because you lack the background, or it could be that the time is just not right. You know, when I was in 8th grade, I remember trying to learn algebra, copying off this kid. He would, he would write down stuff like commutative, you know, and

X plus Y, Y plus X. I would just copy him. I didn't know what any of it meant. I went to the principal's office after class. I told the principal I didn't know what was going on. They put me in a class which was horrible, it was even worse, it's

like a lower level class and I didn't learn anything, so it didn't help. So that's a bad story, but the point was, the point is that at that time I didn't understand algebra, but later on I was able to do it. I had no good resolution

then, you know, going to the principal's office and telling the principal to put me in an easier class. I don't know if it helped me. I mean, I, I think I passed the easier class, but I don't remember learning anything. So stop trying to understand so

much and just move on when you're stuck. I'm not saying give up, but move on sometimes. And how long should you spend on a problem? You know, just depends how much time you have, depends on what you're, what you're doing, right? If you're

in grad school and you've got, you know, homework assignments with 10 problems, well you know an hour, two hours, I don't know, you can spend some time on these, right? But try to try to think about each problem within a short period of time so

at least you have the thoughts in your mind, read the problems, look them over, write when you get them and then the next day look them over again, you know, keep them in your mind, keep thinking about them, you know, so look at them all, read the questions, put some effort into

each question, see how far you get in the proof, put it down, then try again another day, but don't spend hours on one problem. Don't spend three hours on one problem. Don't do that. I mean, if you're doing research, that's different, but if you're

taking classes and stuff, no, you can't do that, right? You can't afford to do that. I should have listened to that Argentinian man, but I didn't. Hopefully, if you're watching this video, you'll take my advice and if not, that's okay, but at

least I'm trying, right? Stop trying to understand so much and move on. Manage your time, especially with something so time-consuming as mathematics is extremely time-consuming. Anyways, if you want to learn mathematics, I do have courses. They're on the Udemy platform, but please use my

links from my website, mathsourcer.com. Udemy takes a huge cut and, two, I've lowered the price on all my courses to the bare minimum, so when you click my links you should get a low price. I've got courses on algebra, calculus, abstract

algebra, some advanced calculus, and other stuff as well, differential equations, etc. Got a bunch of courses. Some have assignments, some don't. If you found any value in this content, feel free to hit subscribe if you want to. If not, it's okay too. The most important takeaway from this video

the most important thing you should take away is that it's okay to not understand. It's part of learning. And when someone tells you you should understand everything, I mean they have good intentions. If, if someone says that to you, I mean they're not wrong, they have good intentions, but realize

that as human beings, it's just not possible to understand everything you learn in a class. I mean it's just so hard, right? And, and if you're doing your homework and you're, you're stuck, just move on sometimes, you know? It's okay. Don't beat yourself up over it and don't

spend too much time on any one problem, right? Try to learn as much as possible, try to be efficient. It's okay to not get it, but it's not okay to quit, right? So come back to it later or move on and work on something else, right? But just don't get

hung up on stuff. Anyways, kind of a long video, but keep doing mathematics.

Stop Trying To Understand

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The Math Sorcerer

끊임없이 이해하려고 노력하지 말고 때로는 문제에서 벗어나야 할 때도 있습니다.

한 가지 문제에 시간을 낭비하지 말라는 연사의 조언에 대한 이야기입니다.

오타 문제로 50시간을 낭비한 일화를 통해 앞으로 나아가는 것의 중요성을 강조합니다.

많은 학생들이 '왜'와 공식을 도출하는 데 어려움을 겪습니다.

한 문제에 과도한 시간을 소비하는 것보다 성적과 현재 작업의 우선순위를 정하세요.

수학 개념과 씨름했던 개인적인 일화

어리석은 실수로 인해 행렬의 역수를 찾는 데 어려움이 있습니다.

수학적 귀납법, 특히 부등식을 다루는 데 어려움을 겪습니다.

동영상 싫어요를 기반으로 불평등에 대한 학생들의 어려움을 관찰합니다.

때로는 나중에 개념을 다시 살펴보는 것이 더 나은 이해로 이어지기도 합니다.

수업의 모든 내용을 이해하지 못해도 괜찮습니다. 발표자는 종종 60~70%만 이해했습니다.

학생의 관점에서 C학점은 70%의 이해도를 의미합니다.

A 학점으로 수업을 완료한 후 이해 수준을 반영합니다.

모든 개념을 이해하지 못해도 괜찮습니다. 시간 관리와 다음 단계로 넘어가는 것이 중요합니다.

8학년 대수학에 대한 개인적인 경험

8학년 대수학에 대한 이해 없이 같은 반 친구로부터 베껴 쓰기.

교장에게 도움을 요청하여 하위 레벨 수업의 효율성이 떨어집니다.

처음에는 어려움을 겪었지만 나중에는 대수를 이해하게 됩니다.

상황(예: 숙제 대 연구)에 따라 문제 해결을 위한 시간 배분에 대한 조언을 제공합니다.

제안된 접근 방식: 초기 시도, 휴식, 재방문, 한 문제에 지나치게 많은 시간을 할애하지 않기.

발표자의 온라인 수학 강좌를 홍보합니다.