These hard concepts were invented by people, so you can learn them too. Usually there are a few concepts you must learn as prerequisites before learning a particular concept, so learn those first. Then, if you put in the time and effort, you should be able to learn anything.

You Can Learn Anything

Intuition = your brain accepts a concept as a fundamental truthAs an example, think of concepts you’ve learned and mastered in the past, and see how now they are just second nature to your brain. A very simple example would be 2+2 - you do not even have to think about how to calculate that, so addition is an intuitive concept for you.On the flip-side, an unintuitive concept is one that your brain “rejects”, something that requires some effort for you to understand and learn.

What Is Intuition?

This means two things: <ol><li>Actually care about the concept - this is pretty important. If you are passionate or have a goal in mind (such as an exam), this is easy. If not, a good tip from the video is to see the concept as a challenge (it should bother you that you do not understand it)</li><li>Make your brain think the problem is important - think about why the concept is useful. Try to spend a lot of time playing around with the concept, so that your brain thinks it’s important. If you do so, your unconscious brain will help you internalize the concept better even after you are no longer focusing on it</li></ol>

Care About The Concept

After understanding a concept, there are a few ways to make it stick:<ol><li>Invent the concept yourself (when that is possible)</li><li>Practice - apply the concept to various things and use it solve hard problems</li><li>Explain - understand it well enough to be able to explain it to someone else (a great tip is to write about it and post it online)</li><li>Explore - think about various ideas related to the concept, try to change some parts of it and see where you end up, and question any assumptions you might have made</li></ol>

Reinforcement

The author of the video is a very good competitive programmer, so the advice might be more targeted towards science subjects, but I think it applies to learning any hard concept. The video is about how to learn concepts intuitively, which means remembering them for a long time, and being able to apply them in any context.

About The Video

When learning a new concept, first start with the big picture and then proceed to learn about each specific detail that is part of the concept. A good way to not get overwhelmed is to use the Black Box Method: assume that some parts are true without trying to understand why at first. I think a good analogy to this would be assuming that the gearbox of a car just works while you are trying to understand how the engine works.After you learn one detail, move on to the next, until you are able to understand how they all fit together and make up the concept.

Learning A Concept Intuitively

A few good tips for learning hard concepts.

A general learning method for learning and understanding hard concepts intuitively/deeply/obviously, and for long periods - up to years at a time. I’ve put in some easter eggs this time - enjoy finding them. Sources (probably not exhaustive): https://www.youtube.com/watch?v=glZLHLLalv0 https://betterexplained.com/articles/developing-your-intuition-for-math/ https://math.stackexchange.com/questions/23806/understanding-the-intuition-behind-math https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/ Music (not in order, I'm still lazy) Local Forecast - Slower by Kevin MacLeod Link: https://incompetech.filmmusic.io/song/3988-local-forecast---slower License: [yt dislikes this link, removed] Dreams by Bensound https://www.bensound.com Support by RFM - NCM: https://bit.ly/2xGHypM Sthlm Sunset by Ehrling https://www.youtube.com/watch?v=uoEhoGt4mIw (not exactly sure how to credit, the link is dead) Sunset On Terra by HYBRID V (Creative Commons License) https://creativecommons.org/licenses/by/3.0/ Support by RFM - NCM: https://bit.ly/2xGHypM Paradise by Ikson ( https://youtube.com/ikson ) Link: https://www.youtube.com/watch?v=Nhtj7_KaplM This Is For You (Prod. by Lukrembo) Link : https://youtu.be/GC0AhsnDMfc Timestamps 00:00 Intro (and about me) 00:31 What does “intuitively” mean? 01:41 Core principles 02:58 Abstraction barrier 05:10 How to understand a single piece? 05:41 Single piece - caring 06:51 Single piece - unleashing your brain 09:26 Single piece - reading the solution 10:01 Single piece - no need to solve it 10:33 How to reinforce? 11:16 Reinforcing - invent 11:27 Reinforcing - practice 12:05 Reinforcing - explain 12:56 Reinforcing - explore 13:58 Reinforcing - over time 15:09 Tying it all together 15:31 An ecosystem of learning 16:42 IQ 18:14 Final remarks

strategy

Strategy

education

Learning & Education

scienceandnature

Science & Nature

A general learning method for learning and understanding hard concepts intuitively/deeply/obviously, and for long periods - up to years at a time.

I’ve put in some easter eggs this time - enjoy finding them.

Sources (probably not exhaustive):
https://www.youtube.com/watch?v=glZLHLLalv0
https://betterexplained.com/articles/developing-your-intuition-for-math/
https://math.stackexchange.com/questions/23806/understanding-the-intuition-behind-math
https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/

Music (not in order, I'm still lazy)

Local Forecast - Slower by Kevin MacLeod
Link: https://incompetech.filmmusic.io/song/3988-local-forecast---slower 
License: [yt dislikes this link, removed]

Dreams by Bensound
https://www.bensound.com
Support by RFM - NCM: https://bit.ly/2xGHypM

Sthlm Sunset by Ehrling
https://www.youtube.com/watch?v=uoEhoGt4mIw
(not exactly sure how to credit, the link is dead)

Sunset On Terra by HYBRID V (Creative Commons License)
https://creativecommons.org/licenses/by/3.0/
Support by RFM - NCM: https://bit.ly/2xGHypM

Paradise by Ikson ( https://youtube.com/ikson )
Link: https://www.youtube.com/watch?v=Nhtj7_KaplM

This Is For You (Prod. by Lukrembo)
Link : https://youtu.be/GC0AhsnDMfc

Timestamps
00:00 Intro (and about me)
00:31 What does “intuitively” mean?
01:41 Core principles
02:58 Abstraction barrier
05:10 How to understand a single piece?
05:41 Single piece - caring
06:51 Single piece - unleashing your brain
09:26 Single piece - reading the solution
10:01 Single piece - no need to solve it
10:33 How to reinforce?
11:16 Reinforcing - invent
11:27 Reinforcing - practice
12:05 Reinforcing - explain
12:56 Reinforcing - explore
13:58 Reinforcing - over time
15:09 Tying it all together
15:31 An ecosystem of learning
16:42 IQ
18:14 Final remarks

General videos about learning and maximizing your brain's power (for now)

Some stats (competitive programming stuff):
Codeforces (max. rating): 2657 - international grandmaster
Codechef (max. rating): 2555 - 7 stars
ICPC progress: world finalist '23, ranked 3rd in NAC (all of US + Canada)
IOI progress: USACO camp
Best leetcode contest rank: 4th (weekly 323)
Best kickstart rank: 10th (twice)
