Stop Trying To Understand

Summary

The speaker emphasizes the importance of not getting stuck on understanding every detail in mathematics, sharing personal experiences and advice. They suggest that it's okay to not fully grasp concepts immediately and recommend moving on when stuck, as revisiting them later can often lead to clarity. The speaker also discusses the struggle of students with understanding and the importance of managing time effectively, especially in the context of mathematical studies. They conclude by encouraging learners to persevere without getting hung up on every problem.

Takeaways

• 😀 It's important to not spend too much time on a single problem, as it can lead to frustration and wasted effort.
• 🤔 Sometimes, moving on from a difficult concept and returning to it later can lead to a better understanding.
• 📚 Students often struggle with understanding the 'why' behind mathematical formulas and derivations, which can hinder their learning process.
• 🕒 Time management is crucial, especially in subjects like mathematics that can be very time-consuming.
• 🔄 Revisiting past material can often make it easier to understand, as familiarity and new perspectives can clarify complex ideas.
• 🚫 It's not necessary to understand everything in a class; partial understanding is still valuable and better than none at all.
• 🤷‍♂️ Not understanding a concept does not mean you are incapable or less intelligent; it's a normal part of the learning process.
• 💡 Half understanding can be a stepping stone to full understanding, so it's okay to move on when you're stuck and come back later.
• 🎓 Even as a college student, the speaker understood only about 60-70% of what was taught, which is a reminder that complete understanding is not always possible or necessary.
• 👨‍🏫 The speaker's advisor's advice to not spend too much time on one problem is a lesson in efficiency and the importance of moving forward.
• 📈 The concept of understanding varying degrees of material can be applied to grading, where a 'C' grade could mean understanding 70% of the material.

Q & A

What advice did the speaker's advisor give them about working on math problems?

The advisor advised not to spend too much time on any one problem because it could be a waste of time.

What was the speaker's initial reaction to the advisor's advice?

The speaker initially thought it was great advice and appreciated the advisor's perspective.

What mistake did the speaker make after not taking the advisor's advice?

The speaker spent about 50 hours working on a math problem that had a typo, realizing it was a waste of time.

Why does the speaker suggest that students sometimes need to move on from a problem they can't solve?

The speaker suggests moving on to manage time effectively and because revisiting the problem later might make it easier to understand.

What issue does the speaker identify that many students face when learning mathematics?

Many students get hung up on understanding 'why' behind formulas and derivations, which can lead to frustration and wasted time.

How does the speaker describe their experience with learning to find the inverse of a matrix?

The speaker struggled with finding the inverse of a matrix due to making silly mistakes and not fully understanding the process despite staying up late to practice.

What is the speaker's view on the necessity of understanding everything taught in a class?

The speaker believes it's not necessary or even possible to understand everything taught in a class, and that it's more important to manage time and focus on what's in front of you.

What example does the speaker give about a concept that was difficult for them and others to understand?

The speaker mentions learning mathematical induction with inequalities as a concept that was difficult for both themselves and their students.

How does the speaker reflect on their own understanding of the material when they were a college student?

The speaker estimates they understood about 60 to 70% of the material taught in their classes, which they felt was low but still allowed them to perform well.

What does the speaker suggest is an appropriate response when faced with a difficult problem in mathematics?

The speaker suggests not spending too much time on one problem, but rather moving on and revisiting it later when it might be easier to understand.

What is the speaker's recommendation for managing time when working on math problems?

The speaker recommends spending a limited amount of time on each problem, revisiting them periodically, and not getting hung up on a single problem for too long.

Outlines

00:00

😖 Overcoming the Struggle with Understanding in Math

The speaker reflects on the difficulty of understanding complex mathematical concepts, sharing a personal anecdote about a mistake in a problem that led to wasted time. They emphasize the importance of not getting stuck on one problem and the value of revisiting concepts later, when they might be easier to grasp. They also discuss the common issue of students getting hung up on the 'why' behind mathematical formulas and proofs, suggesting that half understanding is better than none and that it's okay to move on to focus on other areas of study.

05:00

🤔 Accepting Partial Understanding in Learning

The speaker discusses their own experience as a college student, admitting to understanding only 60 to 70% of the material taught in class. They argue that complete understanding is not always necessary or possible and that it's more important to manage time effectively and not get hung up on individual problems. They share a student's perspective on grades representing levels of understanding and encourage viewers to keep trying, even if they don't grasp everything immediately.

10:02

🛑 The Importance of Moving On in the Learning Process

In the final paragraph, the speaker reinforces the idea that it's okay not to understand everything and that persistence is key. They suggest strategies for dealing with difficult problems, such as spending a limited amount of time on each and returning to them later with fresh eyes. The speaker also promotes their own math courses on Udemy, offering them at a reduced price for viewers, and concludes by reiterating the main message that it's normal and acceptable not to understand everything right away.

Keywords

💡Understand

The term 'understand' is central to the video's theme, emphasizing the struggle and the process of learning, particularly in mathematics. It is defined as the ability to comprehend the meaning or nature of something. In the video, the speaker advises against the relentless pursuit of understanding every detail, suggesting that it's okay to not fully grasp a concept initially, as revisiting it later can lead to a deeper understanding. The example of spending 50 hours on a math problem due to a typo illustrates the futility of stubbornly trying to understand everything at once.

💡Move on

'Move on' is a recurring concept in the video, advocating for the idea that when one is stuck or unable to understand a concept, it's beneficial to proceed with other tasks or problems. It is related to the broader theme of efficient learning and time management. The speaker uses personal anecdotes, such as waking up at 3 a.m. to work on a math problem, to illustrate the impracticality of obsessing over a single issue and the importance of moving forward in one's studies.

💡Graduate school

Graduate school represents a higher level of academic study and is used in the video to set the context of the speaker's experiences and advice. It is a stage where students are expected to delve deeper into their fields of study, often requiring a higher degree of self-directed learning and problem-solving. The speaker's advisor from graduate school is mentioned as a source of wisdom on managing time and not getting stuck on single problems.

💡Time management

Time management is a key concept in the video, highlighting the importance of allocating time effectively, especially when studying complex subjects like mathematics. The speaker warns against spending excessive time on a single problem, which can lead to inefficiency and wasted effort. The advice to 'not spend too much time working on any one problem' is a direct call for better time management in academic pursuits.

💡Half understanding

'Half understanding' refers to having a partial grasp of a concept or idea without full comprehension. The video suggests that this state is acceptable and better than no understanding at all. It encourages learners to be comfortable with this level of knowledge, with the expectation that further understanding will come with time or re-exposure to the material.

💡Inequalities

Inequalities in mathematics are a specific topic that the speaker mentions as being particularly challenging. They are used to illustrate the point that some concepts are inherently difficult and may not be fully understood upon first encounter. The dislike of videos explaining mathematical induction with inequalities is given as evidence of the common struggle with this concept.

💡Matrix

A matrix is a mathematical concept that the speaker uses as an example of a topic that was difficult for them to grasp initially. It is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. The video mentions the struggle with finding the inverse of a matrix and the process of reducing it to row echelon form, which requires significant mental calculation and understanding.

💡Revisiting

Revisiting is the act of returning to a concept or problem after a period of time, with the expectation of gaining new insights or understanding. The video emphasizes the value of revisiting challenging material, suggesting that it can lead to a 'click' of understanding that may not have been possible during the initial learning phase.

💡Efficiency

Efficiency in the context of the video refers to the effective use of time and resources in the learning process. The speaker encourages learners to be efficient by not spending excessive time on a single problem but rather moving on and returning to difficult concepts later. This approach is presented as a way to manage time better and to enhance the learning experience.

💡Struggle

Struggle is a recurring theme in the video, depicting the common experience of difficulty and frustration when learning complex subjects. The speaker acknowledges that everyone struggles with understanding at some point and uses this to normalize the feeling of being stuck or not grasping a concept immediately.

💡Background

Background in the video refers to the pre-existing knowledge or experiences that a learner brings to their studies. It is mentioned in the context of why some students might grasp certain concepts more easily than others. The speaker suggests that differences in background could be a reason why some students struggle with topics like algebra, while others find it more accessible.

Highlights

The importance of not getting hung up on fully understanding everything in mathematics and the value of moving on when stuck.

Advice from an advisor about not spending too much time on one problem, as it can lead to wasted time and frustration.

The experience of spending 50 hours on a math problem due to a typo, illustrating the pitfalls of obsessing over a single issue.

The common struggle students face in trying to understand the derivation of formulas and the potential futility of spending excessive time on it.

The concept of 'half understanding' being better than no understanding at all, and the importance of moving forward despite incomplete comprehension.

The idea that revisiting concepts in mathematics later in one's education can lead to easier understanding and 'click' moments.

Personal anecdotes about struggling with pre-calculus and matrix inversion, highlighting the universality of learning difficulties.

The difficulty of understanding mathematical induction with inequalities and the commonality of this struggle among students.

The notion that it's not always the fault of the teacher or student when understanding is not achieved, but rather a natural part of the learning process.

The speaker's admission of typically understanding only 60-70% of class material, challenging the expectation to grasp everything.

A student's perspective that getting a C means understanding 70% of the material, offering a different view on academic performance.

The speaker's experience of struggling with algebra in 8th grade and how it didn't prevent later success in the subject.

The advice against spending hours on a single problem, especially when taking classes with multiple assignments.

Strategies for approaching problem sets, such as spending a short amount of time on each problem and revisiting them later.

The distinction between the approach to problem-solving in classwork versus research, where more time may be dedicated to a single problem.

The speaker's courses on Udemy and the recommendation to use links from their website for lower prices.

The final takeaway that it's okay not to understand everything, and the encouragement to keep learning and moving on from difficulties.

Transcripts

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 scho school I was assigned an

advisor 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 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 feel it feels low I

felt like I should have understood more

and always bothered me I felt like I I

wasn't that good but then I knew I was

good cuz 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 his 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 lock the background

or it could be that the time is just not

right you know when I was in eth grade I

remember trying to learn algebra copying

off this kid he would he would write

down stuff like communative you know and

X Plus yal 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 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 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 argentinan

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

timec consuming as mathematics is

extremely timec

consuming anyways if you want to Lear

mathematics I do have courses they're on

the udemy platform but please use my

links from my website math sourcer

docomomo me 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 take away 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