Gilbert Strang: Linear Algebra vs Calculus

So planes in these multidimensional spaces, how difficult of an idea is that to come to, do you think? If you look back in time, I think mathematically it makes sense, but I don't know if it's intuitive for us to imagine, just as we were talking about. It feels like calculus is easier to intuit. Well, I have to admit, calculus came earlier, earlier than linear algebra, so Newton and Leibniz were the great men to understand the key ideas of calculus. But linear algebra to me is like, okay, it's the starting point, because it's all about flat things. Calculus has got, all the complications of calculus come from the curves, the bending, the curved surfaces. Linear algebra, the surfaces are all flat. Nothing bends in linear algebra. So it should have come first, but it didn't. And calculus also comes first in high school classes, in college class, it'll be freshman math, it'll be calculus, and then I say, enough of it. Like, okay, get to the good stuff. Do you think linear algebra should come first? Well, it really, I'm okay with it not coming first, but it should, yeah, it should. It's simpler. Because everything's flat. Yeah, everything's flat. Well, of course, for that reason, calculus sort of sticks to one dimension, or eventually you do multivariate, but that basically means two dimensions. Linear algebra, you take off into 10 dimensions, no problem. It just feels scary and dangerous to go beyond two dimensions, that's all. If everything's flat, you can't go wrong.