your channel is one of rare ones in youtube. even about mathmatics . actually you guys introduce the true way of mathematical thinking ,not a bissed view of choosing  one of rigor or intuition alone. i my self follow my intution for establishing a new prove or concept ,and make it rigored to reach the point

I love your content sir ‚ you show the beauty of Mathematics and help people in getting rid of the mindset that Mathematics is useless ❤

Some deep PointCare principles here

A specific location in space. A location being one whole area distinguished from all others.

apart from enjoying your maths videos, you guys are also my “me and who” inspiration 😊

Great job, this video was very useful!

"When mathematic becomes rigorous, it forgets its historical origin"

THIS. I'm a 40 years old math enthusiast, I'm studying it (again) by myself but I'm taking a different approach than the rigorous one followed during the university (Politecnico).

I'm using a more intuitive and historical approach, considering the formal proof a consequence. The Russian authors are the best on this, because they focus on make the reader understanding, and because they have a different idea about time.

Understanding WHY in that historical period something had been formalized is understanding the whole picture, the reason, the intuition. And that's what is amazing for me.

its interesting that I was just watching the +30 year triple jump world record holder. a bachelor of physics from Great Britain. its so funny to see people try to break down the biomechanics. he just looks like a regular chill guy that non physicists athletes wish they could imitate. oh and the indoor world record holder is a phd in electrical engineering (not that he needs a job)

Right here at this part of the video where the fact is the experience is where it is always changing and now your looking for a answer in the displacements of your idea that these places you can figure out.😊

Love from Kerala, India.....such a good explanation. Thanks 🎉

Intuition is the creativity of moving into for finding the truth knowing what you understand that the fact presented in Knowing in some way it's real and exists.😊

The crazy thing is that the infinitesimal, the dot people imagine, is more like reality than a point, which is more like "a list of the energy and characteristics passing through this location" than an object.

Good 👍

Ваши видео всегда интересны

I only go to my catalog of experience.😊

A nice bridge to AI, where everything is treated with rigor. But if intuition cannot be fully captured or quantified mathematically, then what exactly is it? How is intuition determined in the first place?

That raises another question entirely.

I answered this by which I have discovered myself that ,, a point is infinitsely small circle with infinitsely small radius occupied by infinitsely thin length of lines inside it ...

We should keep in mind that we don't do "math" but rather "Law of Excluded Middle math". That's 1D and 2D math that excludes 3D math.

This is why we don't have 3D Number Theory (or 3D anything, really, since we exclude it entirely).

Now brings me to the point when someone creates something that no other has done I do not need to understand because I created it's reality at the experience in the experience all truths and facts are in the experience that can never be changed and that it happened to never happen again because is always moving and never to be the same that's how I know the truth to everything I say.example a leaf just fell off a tree and not one leaf is the say and the next one to grow is new even growing from the same tree and same hole the time is different the experience is different the conditions are different the circumstances are different in any kind of aspects and or any other.and no matter how hard you try to change the truth one leaf had its only time and a new one in it's.😊

In book  "On Certainty" Wittgenstein addresses mathematical certainty not as knowledge of absolute truths, but as rules and paradigms woven into our "language-game". He argues that math operations (like calculating 25 times 25 = 625 are empirical propositions that have hardened into rules, serving as the unquestioned foundation for our daily actions.