Has anyone here heard of this? What is Veeky Forums's take?

yes

>"It's so strange, and mysterious, and amazing, and doesn't come with an instruction manual! It's so awesome! It's unlike anything you've ever seen or conceived! And we can prove it's there, can you believe it? It is a simple complex thing, and very beautiful and mindbending."

Well, that cleared up all questions.

He's talking about Ehresmann connections, which are used to discuss curvature. Riemanning manifolds are used to discuss distances and angles. I'm guessing the guy is saying that in special cases Riemannian manifolds come equipped with a gauge group bundle and an Ehresmann connection.

Riemannian* obviously.

It's also somewhat interesting and perhaps worth mentioning that powers of two show up a lot in my work over the field on one element, where the algebra of inhabited subsets of a pointed set form the dual algebra, which happens to be equivalent to the Grassmann algebra of a vector space over F1. Maybe there are some artifacts of this duality higher up in Cartan geometry, which captures Ehresmann and Riemannian geometry. I don't know.

Go on then (I would actually like to know please thank you very much)

But he said QFT 'uses Ehresmann geometry INSTEAD OF Riemannian geometry'

I've only seen general Cartan geometries used to formalize QFT, but I don't know a ton about the field. Gauge theory is basicaly just Ehresmann geometry. As far as I know, Riemannian manifolds show up a lot in string theory, but I don't know how much they are used in quantum field theory.

bumping for superior explanation

It would probably take something like a year to really clear it up.

Take some object like a cube[show cube in hand], it has symmetries, in this case you can rotate it along x,y,z, by 90 degrees to get the same cube again. These rotations form a group where you can add to rotations to get another rotation that is a symmetry. [move cube around to show symmetry]. Some symmetries are continuous, for example if you take a ball you can rotate it in the same way, but now you can rotate it any amount in a direction and it remains a ball.

You arnt limited to just a 3D ball, there are all kinds of groups like this that describes some symmetries of some object in all kinds of dimensions. It was found out some time ago that all these groups are built up off only a handful of simple symmetries, any complex symmetry can be decomposed into a combination of these simple symmetries, we have 4 families of symmetries which are quite easy to understand, like the rotations of a spere, but for any dimension. But then we also find five exceptional cases, five groups that cant be broken down, yet are not part of these simple to understand families. We label them G2,E6, E7, E8 and F4.

Its important to note that we didnt invent them just to study them, there are a result of fairly basic assumptions of how a symmetry must act, for some reason they are the result of what we define as symmetries.

G2,E6, E7, E8 and F4 are the symmetries of very complex objects in very high dimensions, but E8 is by far the largest and most complex one living in about 250 dimensions, and what makes it even more uniue, is that its the only one of all of these which doesn't describe the symmetries of some other object, but it actually describes the symmetries of itself! [astonished le black man face to emphasize point].

what does it all mean?

are we an artificial intelligence, like the guy in the video said?

Mathematics is the language of god, obviously he is trying to leve us a message, we just don't know how to decode it yet