Math is not properly explained or presented, especially at higher level
So its not one’s fault if they dont understand it after looking at material
Most versions you come across are not ideal, so to expect to grasp it quickly is erroneous
Rather you should just face multiple sources and not think any one of it is holy grail
All, even together, some times are insufficient
And the understanding can come only from you thinking about it enough + referencing the materials
Expectation that understanding can come without much thinking or single read is dumb
Same can be said about high level comp sci, ai, finance, math and physics too
So spending brain studying is only way ahead
Just exposure or reading cannot mean understanding at this level
It needs more
Essentially at higher level there are no learning sources just reference or cryptic inspiration sources
These are basically the epistemological limits of human work
The more number of people are exposed to concept the better documented it is and the better chance you will find something that is a intuitive explanation
But if it is something higher level then you are at mercy of people who touch that concept
If someone like feynman touched it then you will find good stuff
Or you will find incomprehensible, inaccessible bullshit
And I don’t know many feynmans
So when you’re trying to learn something complicated have patience because it is not a straightforward as trying to learn when you are in school
So even if I’m looking at someone’s work and I’m not able to understand it, it can be because they didn’t have any incentive to explain.
No one was gonna look at it other than the circle they are in, which already understands it
So even if the material had gaps it didn’t matter because the group understood and nor did it detect anything that was lacking
Essentially the material have become private material facing public
So wanting to learn something complicated is basically a solo venture
Because the people who have already learnt it they didn’t most probably make things for you
You are on your own and to blame yourself when you don’t understand the material is just bad
Realise the nature of problem and act accordingly
At that point you should not try to understand from the material
You would be better of trying to recreate mentally using the existing material as clues
Esentially at low levels you can completely rely on material and learn everything just from looking at it
But as your progress the reliance becomes dumb
And at higher levels sometimes the material can do nothing for you
As you go higher, the material was designed for a smaller and smaller audience, with more and more implicit context baked in.
Your reliance has to decrease proportionally, because the material is carrying less of the load,supplementing more with your own thinking.
This gap exists for something as popular as calculus also.
Take integration. You are introduced to it through rectangles, infinite thin slices stacking up under a curve, accumulating area. It is visual, it is intuitive, and it actually makes sense. Then a few chapters later someone hands you F(b) − F(a) and the rectangles vanish, never to be mentioned again. But even before you get to that formula, something breaks. If the whole point is infinitely many rectangles, how does that computation ever finish? You start slicing: 1, 0.5, 0.1, 0.001. Wouldn’t you just exhaust all computation chasing smaller and smaller pieces? The answer is that the infinite rectangles were never meant to be computed. They are the concept, not the calculation. The formula is just a faster road to the same destination, and the rectangles were never meant to be walked, only understood. No one tells you this. No one explains that both roads lead to the same place, or that the bridges between them exist, or that the confusion you are feeling is not yours. So you assume it is.
Every Youtube video trying to explain calculus uses it but when you get to the calculations you just cannot wrap your head around it. That this guy told me about infinite rectangles how does this formula do that? Or how would this formula the many curves this line is taking and thus affecting the area?
You are not out of the rectangle mood and these guys changed the whole flow.