YouSaid · the spoken record

Gilbert Strang

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48
first
2019-11-25
most recent
2019-11-25
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1
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podcast

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  1. “Well, that's a good question. I certainly feel good when I maybe I'm giving a class in 1806. That's MIT's linear algebra course that I started. So sort of as a good feeling that, okay, I started this course. A lot of students take it quite a few like it. Yeah, so I'm sort of happy when I feel I'm helping make a connection between ideas and students, between theory and the reader. Yeah, I get a lot of very nice messages from people who've watched the videos and it's inspiring. Maybe take this chance to say thank you.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  2. “Well, that's my topic, but oh, there's beautiful things in geometry to understand. What's wonderful is that in the end there's a pattern. There are rules that are followed in biology as there are in every field.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  3. “No. Yeah, that's hard. Well. I hope you have a teacher professor who is still enjoying what he's doing, what he's teaching. He's still looking for new ways to teach and to understand math. Because that's the pleasure to the moment when you see, oh yeah, that works.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  4. “Yeah, yeah. Maybe because of the approach in the past, they were discouraged, but don't be discouraged. It's too good to miss. Yeah, well, if I'm teaching a big class, do I know when I think maybe I do. Sort of I mentioned at the very start the four fundamental subspaces and the structure of the fundamental theorem of linear algebra, the fundamental theorem of linear algebra. That is the relation of those four subspaces, those four spaces. Yeah, so I think that I feel that the class gets it. When they sit. Yeah.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  5. “To give you a legitimate answer about learning, I should have paid more attention to the assessment, the evaluation part at the end. But I like the teaching part at the start. That's the sexy part.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  6. “That is hard. I'll have to admit here that I'm not really a good teacher. Because I don't get into the exam part. The exam's the part of my life that I don't like. And grading them and giving the students A or B or whatever I do it. Because I'm supposed to do it. But I tell the class at the beginning, I don't know if they believe me. Probably they don't. I tell the class I'm here to teach you. I'm here to teach you math and not to grade you. But they're thinking, okay, this guy is going to, you know, when's he going to, is he going to give me an A minus? Is he going to give me a B? What?”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  7. “Well, all the different ways it comes up. You see it in engineering, you see it as analogous in calculus to second derivative. So calculus learns about taking the derivative, figuring out how fast something's changing. But second derivative. Now that's also important. That's how fast the change is changing, how fast the graph is bending, how fast it's curving. And Einstein showed that that's fundamental to understand space. So, second derivatives should have a bigger place in calculus. Second matrices, which are like the linear algebra version of second derivatives, are neat in linear algebra. Yeah, just everything comes out right with those guys”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  8. “What's my favorite matrix? Okay. So my favorite matrix is square, I admit it. It's a square bunch of numbers and it has twos running down the main diagonal. And on the next diagonal, so think of top left to bottom right, twos down the middle of the matrix, and minus ones just above those twos and minus ones just below those twos and otherwise all zeros, so mostly zeros, just three non-zero diagonals coming down.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  9. “And very, very, very useful. That's what's happened in my lifetime is the importance of data, which does come in matrix form. So it's really set up for algebra. It's not set up for differential equations. And let me fairly add probability. The ideas of probability and statistics have become very, very important, have also jumped forward. And that's not different from linear algebra, quite different. So now we really have three major areas to me, calculus. Linear algebra, matrices, and probability statistics. And they all deserve an important place. And calculus has traditionally had a A lion's share of the time”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  10. “Right. Well, okay. The viewer is going to think this guy is biased. Not true. I'm just telling the truth as it is. Yeah. So I feel linear algebra is just a nice part of math that people can get the idea of. They can understand something that's a little bit abstract because once you get to 10 or 100 dimensions.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  11. “So the big fields of math are algebra as a whole and problems like calculus and differential equations. So that's a second quite different field than maybe geometry. It deserves to be thought of as a different field to understand the geometry of high-dimensional surfaces. So, I think, am I allowed to say this here? I think this is where... Personal view comes in. I think about undergraduate math, what millions of students study. I think we overdo the calculus at the cost of the algebra, at the cost of linear.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  12. “Well Myself, I'm probably a theory. I'm speaking here pretty freely about applications, but I'm not the person who really, I'm not a physicist or a chemist or a neuroscientist. So for myself, I like the structure and this flat subspaces and the relation of matrices, columns to rows. That's my part in the spectrum. So really science is a big spectrum of people from asking practical questions and answering them using some math. Then some math guys like myself who are in the middle of it. And then the geniuses of math and physics. Chemistry who are finding fundamental rules and doing really understanding nature, that's incredible.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  13. “Yeah, search for the rules. Yeah, exactly. And there will be a lot of random. I'm not knocking random because that's there. There's a lot of randomness built in, but there's got to be some basic”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  14. “Is looking for the rules. So that's another step. But if there are no rules at all that the computer could find, if it's totally random data, well, you've got nothing. You've got no science to discover”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  15. “Well, that's a good question. Yeah. So, I guess the whole idea of deep learning is that there's something there to learn. If the data is totally random, just produced by random number generators, then we're not going to find a useful rule because there isn't one. So, the extreme of having a rule is like knowing Newton's law, you know, if you hit a ball, it moves. So that's where you had laws of physics, Newton and Einstein and other great people have found those laws and laws of the distribution of oil in an underground thing. I mean, so engineers, petroleum engineers understand how oil will sit in an underground basin. So there were rules. Now the new idea of artificial intelligence is learn the rules instead of figuring out the rules with help from Newton or Einstein.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  16. “Well, you would have said a while ago that they're just computational limits. It's a problem beyond a certain size. A supercomputer isn't going to do it. But those keep getting more powerful. So that limit has been moved to allow more and more complicated surfaces”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  17. “I'm beginning to have a better intuition. This idea of things that are piecewise linear, flat pieces, but with folds between them. Like think of a roof of a complicated, infinitely complicated house or something that almost curved, but every piece is flat. That's been used by engineers. That idea has been used by engineers, is used by engineers big time, something called the finite element method if you want to design a bridge, design a building, design airplane, you're using this idea of piecewise flat as a good, simple, computable approximation.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  18. “Interesting because you're going to use that piece over and over a million times. So it has a fold in the graph, the graph two pieces. But when you fold something a million times, you've got pretty complicated function that's pretty realistic.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  19. “As one slope, one piece, the other piece has the second slope. And so that getting that nonlinear, simple nonlinearity in. Blew the problem open.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  20. “That's right. Linear algebra is a big part. Not all the part. People were leaning on matrices. That's good. Still do. Linear is something special. It's all about straight lines and flat planes. And data isn't quite like that. It's more complicated. So you've got to introduce some complication. So you have to have some function that's not a straight line. And it turned out. Nonlinear, non linear, not linear. And it turned out that it was enough to use the function that's one straight line and then a different one, halfway. So piecewise linear. Piecewise linear piece.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  21. “Structure of our new way to create a rule. We're looking for a rule that will take these training inputs to the known outputs. And then we're going to use that rule on new inputs that we don't know the output and see what comes.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  22. “Is deep learning? What is deep learning? Yeah. So we're trying to learn from all this data we're trying to learn what's important. What's it telling us? So you've got data. You've got some inputs for which you know the write outputs. The question is, can you see the pattern there? Can you figure out a way for a new input, which we haven't seen, to understand what the output will be from that new input? So we've got a million inputs with their outputs. So we're trying to create some patterns, some rule that will take those inputs, those million training inputs, which we know about to the correct million outputs. And this idea of a neural net is part of this.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  23. “Well, artificial intelligence, and particularly can I use the words deep learning. The deep learning is a particular approach to Understanding data. Again, you've got a big, whole lot of data where data is just swamping the computers of the world and to understand it. Out of all those numbers, to find what's important, in climate and everything. And artificial intelligence is two words for one approach to data. Deep learning is a specific approach there which uses a lot of linear algebra. So I got into it. I thought, okay, I've got to learn about this.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  24. “As president of a pretty small society, but nevertheless, it was a time when meth was getting some more attention in Washington. But yeah, I got to give a little 10 minutes to a committee of the House of Representatives talking about why Math. And then actually it was fun because one of the Members of the House had been a student, had been in my class. What do you think of that? Yeah, as you say, a pretty rare. Most members of the House have had a different training, different background, but there was one from New Hampshire who was my friend really. By being in the class. Yeah. So those years were good. Then, of course, other things take over in importance in Washington. And Math just. At this point, it's not so visible. But for a little moment it was.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  25. “Yeah, well, that's too bad. If you could make the connection, it would have to be people who understand engineering or science and at the same time can make speeches and lead”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  26. “Certainly somewhere in this system, we need people who are comfortable with numbers, comfortable with quantities. If you say this leads to that, they see it and it's undeniable.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  27. “Yeah, well, certainly many of us like to see examples. First, we understand it might be a pretty abstract sounding example like a three-dimensional rotation. How are you going to understand a rotation in 3D or in 10D? And then some of us like to keep going with it to the point where you got numbers, where you got 10 angles, 10 axes, 10 angles, but the best, the great mathematicians probably, I don't know if they do that because they, for them, an example would be a highly abstract thing to the rest of us.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  28. “What did you connect with most? Yeah. I'm somewhere between. I'm certainly not a Artist type, philosopher type person might sound that way this morning, but I'm not. Yeah, I really enjoy teaching engineers. They go for an answer. And yeah, so probably within the MIT math department, most people enjoy teaching students who get the abstract idea. I'm okay with, I'm good with engineers who are looking for a way to find answers.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  29. “Oh, wow Yeah, that's right. Well, I have to say, I'm not much of a philosopher. I just like numbers, you know, as a kid. This was before you had to go in when you had a filling in your teeth. You had to kind of just take it. So what I did was think about math, you know, like take powers of two, two, four, eight, sixteen up until the time the tooth stopped hurting and the dentist said, you're through.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  30. “It's wonderful, isn't it? I mean, I wasn't really aware of it. We're conditioned to think. Math is hard. Math is abstract. Math is just for a few people. But it isn't that way. A lot of people. Quite like math. And they like to. I get messages from people saying, you know, now I'm retired. I'm going to learn some more math. I get a lot of those. It's really encouraging. And I think what people like is that there's some order, you know, a lot of order things are not obvious, but they're true. So it's really cheering to think that so many people really want to learn more about math. Yeah.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  31. “Well, geometrically, as I freely admit, the action of a matrix is not so easy to visualize, but everybody can visualize a rotation. Take two-dimensional space and just turn it around the center. Take three-dimensional space. So a pilot has to know about, well, what are the three things one of them? I've forgotten all the three turns that a pilot makes. Up to 10 dimensions, you've got 10 ways to turn. But you can visualize a rotation. Take this base and turn it. And you can visualize a stretch. So to break a matrix with all those numbers in it into something you can visualize, rotate, stretch, rotate is pretty neat. Pretty neat”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  32. “Well, yeah, I didn't give the theorem. So here's the idea of singular values. Every matrix, every matrix, rectangular, square, whatever, can be written as a product of three very simple special matrices. So that's the theorem. Every matrix can be written as a rotation times a stretch, which is just a matrix, a diagonal matrix, otherwise all zeros except on the one diagonal and then the third factor is another rotation. So rotation, stretch, rotation is the breakup of any matrix.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  33. “Always pushing math faculty get on do it, do it, do it, singular values. So those are a way to find the important pieces of the matrix, which add up to the whole matrix. So you're breaking a matrix into simple pieces. And the first piece is the most important part of the data. The second piece is the second most important part. And then often, so a data scientist will like if a data scientist can find those first and second pieces, stop there. The rest of the data is probably round off experimental error, maybe. So you're looking for the important part.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  34. “Rectangle of numbers, a matrix is basic. So the big problem is to understand all those numbers. You got a big set of numbers. And what are the patterns? What's going on? So one of the ways to break down that matrix into simple pieces uses something called singular values. And that come on as fundamental in the last and certainly in my lifetime eigenvalues if you have viewers who've done engineering math or basic linear algebra eigenvalues were in there. But those are restricted to square matrices. And data comes in rectangular matrices. So you've got to take that, you got to take that next step.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  35. “Well, I'll stick with linear algebra here. I hope the viewer knows that really mathematics is amazing, amazing subject, and deep connections between ideas that didn't look connected. They turned out they were. But if we stick with linear algebra, so we have a matrix. That's like the basic thing, a rectangle of numbers. And it might be a rectangle of data. You're probably going to ask me later about data science, where and often data comes in a matrix. You have maybe every column corresponds to a drug and every row corresponds to a patient. And if the patient reacted favorably to the drug, then you put up some positive number in there anyway.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  36. “Yeah, everything's flat. 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.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  37. “Well, it really, I'm okay with it not coming first, but it should. Yeah, it should. It's simpler. Because everything is fine.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  38. “I 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. 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 surfaces are all flat. Nothing bends in linear algebra. So it should have come first, but it didn't. Calculus also comes first in high school classes and 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?”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  39. “Perpendicular to those. So, like, if you have a plane in 3D, a plane is just a flat surface in 3D, then perpendicular to that plane would be a line. So that would be the null space. So we've got a column space, a row space, and they're two perpendicular spaces. So those four fit together in a beautiful picture of a matrix. Yeah, yeah. Fundamental, it's not a difficult idea. It comes pretty early in 1806 and it's basic.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  40. “Vector space, space of vectors. And my imagination is just seeing like a piece of paper in 3D. But anyway, so that's one of the spaces, and that's space number one, the column space of the matrix. And then there's the row space, which is, as I said, different, but came from the same numbers. So we got the column space, all combinations of the columns, and then we got the row space, all combinations of the rows. So those words are easy for me to say, and I can't really draw them on a blackboard, but I try with my thick chalk, everybody likes that railroad chalk. And me too, I wouldn't use anything else now. And then the other two spaces are...”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  41. “Well, probably I'm not a very geometric person, so I'm probably thinking in three dimensions. And the beauty of linear algebra is that it goes on to ten dimensions with no problem. I mean, if you're just seeing what happens, if you add two vectors in 3D, then you can add them in 10D. You're just adding the 10 components. So I can't say that I have a picture, but yet I try to push the class to think of a flat surface in 10 dimensions. So a plane in 10 dimensions. So that's one of the spaces. Take all the columns of the matrix, take all their combinations. So much of this column, so much of this one. Then if you put all those together, you get some kind of a flat surface that I call a...”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  42. “Yeah, that's right. In the lecture, I tried to, so if you think of two vectors in 10 dimensions, I'll do this in class and I'll readily admit that I have no good image in my mind of a vector, of an arrow in ten-dimensional space, but whatever. You can add one bunch of 10 numbers to another bunch of 10 numbers, so you can add a vector to a vector, and you can multiply a vector by 3. And that's if you know how to do those, you've got linear algebra.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  43. “So, a physicist would imagine a vector or might imagine a vector as an arrow in space or the point it ends at in space. For me, it's a column of numbers.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  44. “What's a matrix? Well, so we have a rectangle of numbers. So it's got n columns, got a bunch of columns, and also got an M rows, let's say. And the relation between, so of course the columns and the rows, it's the same numbers. So there's got to be connections there, but they're not simple. The columns might be longer than the rows and they're all different. The numbers are mixed up. First space to think about is take the columns. So those are vectors. Those are points in n dimensions.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  45. “To teach students. Okay. Well, on the teaching side, So it's not deep mathematics at all. But I'm kind of proud of the idea of the four subspaces, the four fundamental subspaces. Which are, of course, known before long before my name for them.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  46. “Well, knowing a little bit President Vest, it was like him, I think. And it was really the right idea. MIT is a kind of, it's known for being high level, technical things. And this is the best way we can say, we can show what MIT really is like because in my case, those 1806 videos are just teaching the class. They were there in 26 100. They're kind of fun to look at. People write to me and say, oh, you've got a sense of humor, but I don't know where that comes through. Somehow I've been friendly with a class. I like students. And linear algebra, the subject, we got to give this subject most of the credit. Really Come forward in importance in these years.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  47. “That was a wonderful idea. The story that I've heard is the committee was appointed by the president, President Vest at that time, a wonderful guy. And the idea of the committee was to figure out how MIT could make a Be like other universities market the work we were doing. And then they didn't see a way and after a weekend and they had an inspiration and came back to the present vest and said, what if we just gave it away? And he decided that was okay. Good idea.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source

  48. “I don't feel like a rock star. That's kind of crazy for an old math person. But it's true that the videos in linear algebra that I made way back in 2000, I think I've been watched a lot. And, well, partly the importance of linear algebra, which I'm sure you'll ask me, and give me a chance to say that linear algebra as a subject is just surged in importance. But also it was a class that I taught a bunch of times, so I kind of got it organized and enjoyed doing it. It was just the videos were just the class. So they're on open courseware and on YouTube and translated. That's fun.”

    2019-11-25 · Lex Fridman Podcast · Gilbert Strang: Linear Algebra, Deep Learning, Teaching, and MIT OpenCourseWare · IDENTIFIED FROM THE TRANSCRIPT · source