Math education rant

Published (click to see context) on 03/06/2021 by Morgan Bazalgette • 2 minutes
I always find it incredibly frustrating how hard it is to find "math intuitions" on the internet. There are a few resources, like betterexplained and 3Blue1Brown, especially in English, but a lot of the time even if you go and look at a lesson by a professor you found online there will be no clear intuition on the concept they're trying to explain.

I was trying to grasp onto the concept of what it means for two vectors to be linearly dependent. I tried looking up resources in Italian, and also a bit in English, only to resort to watching a video from 3B1B in his "Essence of Linear Algebra" series, where he gets right into the core of what I _actually_ needed to know:
- Two vectors are linearly dependent if they are parallel, AKA one is a scaled version of the other
- i, j, and k (for the third dimension) are examples of linearly independent vectors.
- If we are in 2d and have 2 linearly independent vectors, by scaling them by some number we can get to any point on the plane. Also, you can substitute 2 with any number of dimensions.

In the video, the animation that made me understand the concept. Talking about 3D space and how "if you remove one vector, you're basically removing one dimension from the space" is what really clicked and made me understand the concept.

This explains why educational maths videos (outside of Khan Academy) tend to be really good on YouTube and can get a lot of people passionate about the beautiful thing that it is. But I cannot help but feel sorry for the millions if not billions of students who were left helpless in class, at either high school or university, without a good teacher who could give a good spatial/geometric intuition about how linear algebra works.