Full episode with Gilbert Strang (Nov 2019): https://www.youtube.com/watch?v=lEZPfmGCEk0
New clips channel (Lex Clips): https://www.youtube.com/lexclips
Once it reaches 20,000 subscribers, I'll start posting the clips there instead. 
(more links below)

For now, new full episodes are released once or twice a week and 1-2 new clips or a new non-podcast video is released on all other days.

Clip from full episode: https://www.youtube.com/watch?v=lEZPfmGCEk0 If you enjoy these clips, subscribe to the new clips channel (Lex Clips): https://www.youtube.com/lexclips Once it reaches 20,000 subscribers, I'll start posting the clips there instead. For now, new full episodes are released once or twice a week and 1-2 new clips or a new non-podcast video is released on all other days.
(more links below)

Podcast full episodes playlist:
https://www.youtube.com/playlist?list=PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4

Podcasts clips playlist:
https://www.youtube.com/playlist?list=PLrAXtmErZgOeciFP3CBCIEElOJeitOr41

Podcast website:
https://lexfridman.com/ai

Podcast on Apple Podcasts (iTunes):
https://apple.co/2lwqZIr

Podcast on Spotify:
https://spoti.fi/2nEwCF8

Podcast RSS:
https://lexfridman.com/category/ai/feed/

Gilbert Strang is a professor of mathematics at MIT and perhaps one of the most famous and impactful teachers of math in the world. His MIT OpenCourseWare lectures on linear algebra have been viewed millions of times.

Subscribe to this YouTube channel or connect on:
- Twitter: https://twitter.com/lexfridman
- LinkedIn: https://www.linkedin.com/in/lexfridman
- Facebook: https://www.facebook.com/lexfridman
- Instagram: https://www.instagram.com/lexfridman
- Medium: https://medium.com/@lexfridman
- Support on Patreon: https://www.patreon.com/lexfridman

So planes in these multi-dimensional 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.

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.

Well, it really, I'm okay with it not coming first, but it should, yeah, it should.

Well, of course, for that reason, calculus sort of sticks to 1 dimension, or eventually you do multivariate, but that basically means 2 dimensions.

Linear algebra, you take off into 10 dimensions, no problem.

It just feels scary and dangerous to go beyond 2 dimensions.


Speaker 0: So planes in these multi-dimensional 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.

Speaker 1: 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. And that's.

Do you

Speaker 0: think linear algebra should come first?

Speaker 1: Well, it really, I'm okay with it not coming first, but it should, yeah, it should. It's simpler.

Speaker 0: Because everything is flat. Yeah, everything's flat.

Speaker 1: Well, of course, for that reason, calculus sort of sticks to 1 dimension, or eventually you do multivariate, but that basically means 2 dimensions. Linear algebra, you take off into 10 dimensions, no problem.

Speaker 0: It just feels scary and dangerous to go beyond 2 dimensions. That's all. If everything is flat you

See all Lex Fridman transcripts on Youtube

Gilbert Strang: Linear Algebra vs Calculus