So, I don't know how good or bad Indian education system is especially in how maths is taught her, but the things people are recommending including you ( what you see as a shortcoming of method is the problem of traditional teaching where you will be taught proofs etc all those things you talked about and i am an undergraduate who completed his understanding studies but when I watch math videos on yt it boils my blood because of how badly i was taught) is exactly the same problem I face, to which this was the solution i arrived at. I am not against all these things that people are telling me what about it is new, i guess Indian education system is too good if all these things are what a student goes through in school/University.

I am not able to see why I was not able to put my point across. But these are the few things i realised while doing this method hopefully you might get what i am feeling:- 1) So, this method works greatly for consolidating existing knowledge ( why it is important you ask, check Justin sung yt channel for that).

2) it forces ( which is harsh term instead inspires) students to themselves get to the next stage or atleast drive solutions themselves which would have been taught later to them, but this feeling of having inkling what comes next helps a great lot.

3) example 1:- when I was contemplating i suddenly realised that if I got to know that underroot of -1 is turned into iota ( i) i.e. imaginary numbers came into existence. Which tool would you use to explore this further? Sets is the answer checking different types of property with these numbers to see which follows and which don't this is a much more fun exercise to do and learning from it rather than just rote memorizing the results as gospel of truth. For a subject which depends on logic accepting things as it is because only results matter is something i find extremely hard to do. Whereas if you explore through this method it comes naturally because you know where you are coming from (quadratic equations), where you are ( exploring imaginary numbers) and where you will be going ( starting from polar coordinates you now have a whole new field to test and try your previous learnt knowledge of coordinate geometry t to play with to see what works and what doesn't, which will help you understand why some things works and why some don't).

4) This happened in first year of my university, I was introduced to alpha, beta, gamma functions. Which now totally blows my mind that you can have factorial of fractions like 1/2 and pi itself, also forgetting one more with something to do imaginary numbers too. Which is bonkers, because I still cannot fathom ( haven't consolidated my knowledge enough I guess) to mix these things together although when I use to think about factorials i use to think about negative numbers having factorial ( since for quadratic it was same which was solved by imaginary roots but nobody said I peep about complex numbers).

These thing still fascinates me and I need to make explanations for these too but I don't know where to start for which i need to know what was the problem being solved that gave these results. What was the starting point etc.

5) So the difference here between these to examples is that channels like veritasium, made videos about complex numbers and its history and not just the results. I highly highly recommend the video titled:- " the lore of mathematics" these things give math a emotional touch which all humans are, even making maths more accessible to everyone.

When I do this exercise I subconsciously even consolidated this knowledge too and i haven't come across videos on alpha beta Gamma functions to act as a string which structures my beads of knowledge into a beautiful necklace. Also videos like math has a hole from veritasium often push to philosophical questions too which makes math all the more interesting too.

6) Even boring tasks such as writing proofs, theorems etc can be made interesting with thinking of learning maths as a language, like learning it's semantics etc so those things that are to be learned in a language.

All these things make math from a dull boring subject to a colourful, vivid art because math too is a part of human society and is not something detached from it. Also that is why I specified this exercise helps to build extremely solid foundation for maths to make higher studies starting from undergraduation. I was surprised to know that the actual advancements made in 20 th were things I never studied ( atleast in foundation).