Stop Trying To Understand
Summary
TLDRThe 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
😖 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.
🤔 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.
🛑 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.
Mindmap
Keywords
💡Understand
💡Move on
💡Graduate school
💡Time management
💡Half understanding
💡Inequalities
💡Matrix
💡Revisiting
💡Efficiency
💡Struggle
💡Background
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
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