How Imaginary Numbers Were Invented

> Something that occurs to me is that most of us have a poor grasp of why we even teach school math One of my favorite math courses was a college class that focused on concepts - technically not an education class but intended for those in education majors. It covered 5th-8th grade math and showed me the why of so many things I had just taken for granted previously, and I'm sure if math was taught that way it would be much better remembered. Of course, it could still be argued over whether math should be intended for practical use or not, but I think it's important that math be taught from (at least one of) a conceptual basis, or a historical basis (eg. [0] on the creation/discovery of imaginary numbers - it explains why they were needed, as well as interesting historical background). (This was typed in a hurry, sorry if it's not entirely cohesive.) [0] [VIDEO]

It is a bit odd that the video really talks up the idea that complex numbers sever algebra from geometry, then without pause goes straight into a geometric interpretation of complex numbers [VIDEO] .

That is the reverse of this subject in botany, we have this method that we know works and is logical lets make our language more logical. The problem with that is the same reason we don't use imaginary numbers everywhere we can use them. Veritasium has a video description [1] with links to references about the history of imaginary numbers and polynomials. There are some great writing on this and understanding not the history but the problems that gave rise to imaginary numbers, this connection to taxonomy makes me want to read them again. There must be a study of this; failed attempts of taxonomy. [1] [VIDEO]

They're used in a generalised solution to cubic equations (analogous to the quadratic solution we all learn in high school), where they represent the side length of a square with negative area. [VIDEO]

Imaginary numbers simply represent a different and more powerful system like how integers gain power when you introduce 0 and negative numbers. Rational numbers (fractions) can’t represent irrational numbers like pi or e etc. It’s often useful because you can use complex numbers as an intermediary step in many calculations (such as solving cubic equations) while still ending up with a non imaginary number at the end. The history is actually fairly interesting: [VIDEO]

I think the sort of visualizations that are around on Youtube are great for those who don't "get" maths easily and need another angle to help them understand. Although 3Blue1Brown is not for beginners there are other beginner resources. For example, this goes right back to basic algebra but is a very well explained with the afore mentioned visualizations. Veritasium - How Imaginary Numbers Were Invented [VIDEO]

This is one video which shows history of imaginary numbers and their usefulness in current times. It's from Veritasium: [VIDEO]

For those interested I also highly recommend Veritasium's video[1] as an excellent explainer as well, especially regarding the roots of imaginary/complex numbers in geometry. [1] [VIDEO]

How about the really old days? How Imaginary Numbers Were Invented - [VIDEO] (jumped directly into the math battle part)

There's a good YouTube video on it that includes an epic math battle. Veritasium - How Imaginary Numbers Were Invented - [VIDEO] Solving the cubic was a physical thing back then. [LINK]

There is a video depicting the story of a search for a cubic equation solution and invention of complex numbers. Here it is described in a few sentences but really it was a novel, with secrets passed from dying masters to apprentices, duels (mathematical), broken oaths and suchlike. [VIDEO]