[behnamoh]

I always liked geometry, but wasn't particularly talented in it. Still, I wonder whether geometry could explain certain algebraic concepts much more intuitively, or even lead to new discoveries that would be extremely difficult to do using math symbols.

[voldacar]

A lot of geometric results like trig identities come out most elegantly when stated using complex numbers. I always struggled remembering trig identites until I took complex analysis, and after that class they just seemed totally obvious.

[mathgenius]

I think "higher dimensional algebra" is some kind of attempt at doing this. String diagrams (for tensor networks) is one example. John Baez has written about this stuff.

[Frummy]

Maybe you would love linear algebra?

[behnamoh]

Why? I do like linear algebra but the way it’s taught in universities is often unintuitive.

[Frummy]

Well, if you stand on really strong foundations, you can picture everything that happens in your minds eye. It’s algebra with a geometric twist. Simplest example I can think of now is intersections of planes as solution spaces, thats the picture you could imagine from a bunch of equations. Sorry I had it 4 years ago but at the time I could have written better about it. I used contemporary linear algebra, howard anton. Another simpler example is span, the total space of points that you can get by adding and scaling specific vectors that you have. Imagine an infinite plane created by the configurations of two vectors.