After 6 years, I finally get vector potentials

For 6 years, I didn't understand why vector potentials exist outside of being a mathematical trick. However, there can be a very vivid imagery of vector potentials that was hidden in a formula on Wikipedia. This channel is meant to showcase interesting but underrated maths (and physics) topics and approaches, either with completely novel topics, or a well-known topic with a novel approach. If the novel approach resonates better with you, great! But the videos have never meant to be pedagogical - in fact, please please PLEASE do NOT use YouTube videos to learn a subject. Files for download: Go to https://www.mathemaniac.co.uk/download If you read the description till here, please comment which YouTube videos you are currently watching that is entirely not informative / educational? My current addiction is Jet Lag: The Game. Sources and behind the scenes: I changed the narrative slightly from the way I actually discovered this intuition. Originally I was trying to make a video on Poincaré lemma, and I planned to visualise this: https://en.wikipedia.org/wiki/Poincar... https://math.stackexchange.com/questi... So I really need to visualise Cartan's magic formula and so on, which I did (but did not put in this final video). However, I really wanted to apply this to the vector calculus case, because it should be much easier. And using the supplementary sheet in the previous video (go watch it!) about the connection between divergence, curl, and differential forms, I came up with this intuition in the video. And then I thought, it can't possibly be just me discovering this, and indeed it was on Wikipedia all along (again): https://en.wikipedia.org/wiki/Vector_... However, that part in Wikipedia did not cite any sources, so I even went all the way to look at the Wikipedia edit history and see who edited that part in. Unfortunately that user did not provide an email that I could contact, and the username is also very clearly just a fictional name, so I figured that they just don't want to be contacted. But if you are Mentaro Ikeuchi on Wikipedia, and somehow watching this video, and reading this description, please add the references there. The explanation on gauge in physics is referencing the Aharonov–Bohm effect, which has a pretty nice explanation here: https://web2.ph.utexas.edu/~vadim/Cla... Video chapters: 00:00 Introduction 00:39 Chapter 1: Divergence and curl 04:23 Chapter 2: The construction 13:15 Chapter 3: Gauge freedom Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels: https://forms.gle/QJ29hocF9uQAyZyH6 If you want to know more interesting Mathematics, stay tuned for the next video! SUBSCRIBE and see you in the next video! If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I use PowerPoint, GeoGebra, and (sometimes) Mathematica to produce the videos. Social media: Facebook:   / mathemaniacyt   Instagram:   / _mathemaniac_   Twitter:   / mathemaniacyt   Patreon:   / mathemaniac   (support if you want to and can afford to!) Merch: https://mathemaniac.myspreadshop.co.uk Ko-fi: https://ko-fi.com/mathemaniac [for one-time support] For my contact email, check my About page on a PC. See you next time!