Veritasium
7 HN recommenders · recommended in 6 months, 2021–2023
23:29 · 23M views · Nov 1, 2021
Veritasium tells the history of how imaginary numbers arose from the quest for a general solution to the cubic equation, including the duels and secrecy among Renaissance mathematicians. It argues math had to give up the requirement that it mirror reality.
HN recommends it as a well-visualized, story-driven history of complex numbers, suitable for beginners; some quibble with its framing of algebra and geometry.
11 comments from Hacker News
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] this video
> 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] this 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: this 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 this video
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. this video