In Fundamental Forms We Trust Differential Geometry Gang 2025 😤🤝♾️📐
https://bit.ly/amvmixtape
Today's video is officially the start of reading now at chapter 7 from Differential Geometry by Erwin Kreyszig on Absolute Differentiation and Parallel Displacement.
Leave a comment below and it might get featured on a future episode!
Catch up on past episodes in my Differential Geometry playlist: https://bit.ly/amvdiffgeoplist
Website: https://anthonymakesvideos.com
Get the Kreyszig Differential Geometry book I've been reading in these videos: https://amzn.to/3PhrWP3
📩 Questions/Business inquiries: anthonymakesvideos.info@gmail.com
DM me math memes on IG @anthonymakesvideos
Find links to my YouTube content recycled on X @anthonymksvids
TIMESTAMPS
==========
0:00 Beat: In Algorithm We Trust https://www.youtube.com/watch?v=5nHBugynHOI by Gemology https://www.youtube.com/@moji.flac1 @moji.flac1
0:51 Intro/Outline of upcoming video
4:58 Slides start; what motivates me personally to study differential geometry?
6:30 Why did I choose/buy Differential Geometry by Erwin Kreyszig in the first place? Consumer economic data on the price of the book on Amazon
9:20 The first paragraph of chapter 7 hits different as I’ve made more progress understanding differential geometry & general relativity over time
10:45 The difference between “classical” and “modern” differential geometry is perhaps at the heart of Gauss supervising Riemann’s habilitationsschrift
12:41 A wild Heidegger appears + Welcome back, Duns Scotus
12:59 Heidegger quote
14:00 What have I learned of relevance to general relativity so far if anything at all? Starting to look at Wald’s General Relativity and Intro to Smooth Manifolds by John Lee to really find out what kind of math is needed for GR
14:37 Intro to Smooth Manifolds by John Lee Table of Contents fly-by
17:03 If Ed Witten looked the way he sounded
17:26 The “Additional Textbooks” list for MIT OCW GR 8.962 is basically a short review list of the who’s-who of GR books
19:00 Wald’s General Relativity Table of Contents fly-by
20:07 The motivation necessitating the use of manifolds in GR is something as follows
21:37 What about Kreyszig’s Differential Geometry? 2 main valid criticisms of his treatment of differential geometry the way I see it
24:19 The motivation necessitating the use of curvature in GR is something as follows
28:21 Don’t forget about the preface of Wald’s GR: The mathematical appendices are prerequisites
30:00 Shoutout to a comment from @edwardsinger6493
30:50 Shoutout to a comment from @CovenantAgentLazarus
32:45 The viewer comment of the week @VanDerHaegenTheStampede
35:04 Aight Imma be 100 💯 witchy’all
38:35 Möbius
40:44 Recovering a previously missed opportunity to explain how a Möbius strip is related to the philosophy of Slavoj Zizek
45:27 Reading and Re-Reading the branches of key thinkers in the canon of Western Philosophy
48:12 What Zizek has to say about Kant in his work “The Parallax View”
56:40 Quote from Zizek in “The Parallax View” on what he sees as the fundamental lesson of Hegel
59:48 Time-travel
1:15:23 Review of related concepts from multivariable calculus: Div
1:17:12 Grad
1:17:40 Directional derivative
1:18:20 Curl
1:20:00 Finally starting to read §69. Concept of absolute differentiation
1:25:33 §70. Absolute differentiation of tensors of first order
study with me, talking, spoken word, reading out loud, read aloud, asmr, math lecture, math stream, math podcast, math audiobook, math influencer, math for physicists, general relativity, special relativity, ricci flow, grigori perelman, tensor calculus, riemannian geometry, curvature, torsion, osculating plane, osculating curve, osculating sphere, frenet frame, tpb frame, frenet formulas, frenet formulae, fresnel, non-euclidean geometry, how to learn math, congruence, allowable representation, arc, curve, tangent, principal normal, binormal, natural equations, first fundamental form, volume of revolution, topology, metric tensor, riemannian surface, riemannian manifold, Bergman metric, Bergman kernel, Carl Friedrich Gauss, Stefan Bergman, Bernhard Riemann, read along, should I major in mathematics, what's the difference between applied mathematics versus pure mathematics, math midterm exam questions, university math calculus exam problem step-by-step solutions, this video will make you fall asleep instantly, tingles guaranteed, yeti microphone, rode wireless go ii mic, learn advanced mathematics while you sleep, can AI do math better than humans, can AI learn math, string theory, dark matter, Ed Witten, quantum theory, chromodynamics