$$ \newcommand{\N}{\mathbb{N}} \newcommand{\C}{\mathbb{C}} \newcommand{\R}{\mathbb{R}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\ZZ}{\ooalign{Z\cr\hidewidth\kern0.1em\raisebox{-0.5ex}{Z}\hidewidth\cr}} \newcommand{\colim}{\text{colim}} \newcommand{\weaktopo}{\tau_\text{weak}} \newcommand{\strongtopo}{\tau_\text{strong}} \newcommand{\normtopo}{\tau_\text{norm}} \newcommand{\green}[1]{\textcolor{ForestGreen}{#1}} \newcommand{\red}[1]{\textcolor{red}{#1}} \newcommand{\blue}[1]{\textcolor{blue}{#1}} \newcommand{\orange}[1]{\textcolor{orange}{#1}} \newcommand{\tr}{\text{tr}} \newcommand{\id}{\text{id}} \newcommand{\im}{\text{im}\>} \newcommand{\res}{\text{res}} \newcommand{\TopTwo}{\underline{\text{Top}^{(2)}}} \newcommand{\CW}[1]{\underline{#1\text{-CW}}} \newcommand{\llbracket}{\mathopen{[\![}} \newcommand{\rrbracket}{\mathclose{]\!]}} % specific for this document \newcommand{\cellOne}{\textcolor{green}{1}} \newcommand{\cellTwo}{\textcolor{red}{2}} \newcommand{\cellThree}{\textcolor{brown}{3}} \newcommand{\cellFour}{\textcolor{YellowOrange}{4}} $$

“What are differential forms?” : A video series

mathematics
differential geometry
differential forms
video
English
Author

Luca Leon Happel

Published

October 12, 2026

Note

This post is a part of my ongoing series about differential forms. You can find more related posts here

I have been thinking about differential forms for quite some time now already. I still vividly remember 2022 when I was on the “Konferenz der deutschsprachigen Mathematikfachschaften”, where I was deeply intrigued by these mysterious objects. Most mathematicians do in fact not even know what these “\(dx\)” and “\(dy\)” and so on in \(\int f(x)\, dx\) are. But I wanted to know! Thus began my years long quest to find the truth (well, there are many different interpretations of \(dx\), like from measure theory or in this case differential geometry which I wish to inspect in here).

Previously I have written about these objects here: ../differential_forms/.

I have started a video-series as well though:

Part 1: 1-forms

Part 2: differential k-forms

Full playlist on YouTube