An Interview with Gilbert Strang on Teaching Linear Algebra

SARAH HANSEN: Well, you have a
lot of followers of your 18.06 videos. GILBERT STRANG:
That’s wonderful. SARAH HANSEN: And I’ll
read this quote to you. “A commenter even noted
that this is not lecture, this is art.” GILBERT STRANG: Gosh. OK. Well, if you’re going to ask
what’s my system, I have none. I guess– well, first
I like students. And I want to help. And maybe the key point
is to think with them. Not to just say, OK, here
it is, listen, listen up. I think through the question
all over again as they do. And you have to give time. You can’t zip through a proof. Because this class has to be
sort of thinking with you. And that’s– yeah,
that’s my thought. I don’t know if I achieve it,
but I think it’s the goal. SARAH HANSEN: One
of our users on OCW noted that during
lectures you sometimes ask rhetorical questions, or maybe
feign confusion as a way– GILBERT STRANG: Feign confusion? I’m confused. SARAH HANSEN: Are you? OK. GILBERT STRANG: Well, no. Well, no, it’s probably true. That’s maybe part of
not rushing through it. But getting– so I’ll pause
at the critical point, maybe. You have to give time to see,
OK, what’s the next step? You know, mathematics
is beautifully ordered, and sensible, and logical. And linear algebra
is not too difficult. But still, you can’t rush. You have to sort of see
the idea a few times. First maybe on the
board as symbols. But not everybody
picks up on symbols. Then you say, what does it mean? And then finally you
say, why is it true? But you don’t say,
“Why is it true? Give the proof,”
the very first step. You want to make people
think, yeah, it is true. SARAH HANSEN: Others have noted
that you do this thing where you display your own
thinking kind of on the spot as you work through problems. GILBERT STRANG: Yeah. SARAH HANSEN: Is there ever
a risk in that for you? GILBERT STRANG: Oh, yes. And it happens, that
I lose the thread or I come up to a dead
end where I don’t know what I’m supposed to do next. But generally, especially in
18.06, The basic linear algebra course that many
people have watched, there I kind of get it OK. Yeah, I’ve taught
it enough times to have a good chance
of getting it right. SARAH HANSEN: Is this a strategy
that you developed over time? You know, lots of people
are nervous to do that, to make themselves vulnerable
in front of a large lecture class like that. But you’re working
problems in real time and demonstrating what happens
when you hit a dead end. GILBERT STRANG: Well,
that’s OK, because students are going to hit dead ends, so
it seems to me it’s OK for me to get stuck, too. And then if they see,
oh, OK, maybe this is the way to get
out of that corner. Yeah. So essentially I think the
thing is I like students. I like math. And putting them together is
just the best job in the world. SARAH HANSEN: Let’s talk
about humor for a second. GILBERT STRANG: OK. SARAH HANSEN: You
have been known to say things like, keep things
in their Gauss-given order. GILBERT STRANG: I see. SARAH HANSEN: And other really
funny things that people just love. So what’s the role of
humor in your teaching? GILBERT STRANG:
Well, maybe it’s– which is what I’m saying
here, maybe the key point is to make it human. You know, you’re a person,
like the student is a person. The book isn’t quite a person,
but it was written by a person. And to see that it’s just
like a natural thing to do. Yeah. Yeah. Yeah. SARAH HANSEN: So
one of our users was thinking about how you
teach complex material, how you convey it in ways that
are comfortable for students. And the user was
wondering, how do you know when to go into
detail and when not to? GILBERT STRANG: I suppose I try
to think it through once again. And then you sort
of automatically see the word– you recognize
what words you need to use, and what the steps are. Yeah. If you’re not
thinking it yourself, then you’re probably
going too fast and not connecting with
the thinking of the class. SARAH HANSEN: And
how do you connect with the thinking of the class
when it’s such a large lecture hall? And everyone’s at a different
point in their understanding. GILBERT STRANG:
That’s probably true. And of course, you don’t
know what everybody is thinking in that class. But overall, if you get– if you stay sort of conscious
of the class, conscious of where they are, that’s, I think,
the thing for any speaker, is to be conscious
of the audience and not just a A-B inverse. SARAH HANSEN: What
else would you like to add about teaching
18.06 linear algebra? GILBERT STRANG: Well, with
18.06 of course, I’m just– so, recently, Open
CourseWare, which I think was just such a great idea. Great idea for MIT. Great idea for faculty. So they did a count of the
number of viewers in 18.06, and it was 10 million. Which was like, woo. I never expected. But I do get nice,
really nice messages from all over the world. And I reply to
them far as I can. Sometimes they’ll ask what’s
a good way to learn math? I don’t know if I have
an answer to that. But anyway, I try
to be encouraging. So yeah. It’s been wonderful. Just having the video
lectures available allows everybody
to be in the class. Yeah. So, thank you all for
joining the class. Thank you.


  1. Gil Strang is a legend. I learned so much from him even though I never set foot on MIT's campus. Glad to see him still active after all these years.

  2. It makes me a little bit sad he has grown this old. I still want him to be teaching with that much energy and patience as we see him teach the class of 2005

  3. Man the energy … even though his body aged, his mind, movements and mimics are the same … I never attend to your class physically but probably I learned more efficiently than my 20 years education best wishes for you !

  4. The passion for mathematics and teaching it, shines through you and it is really infectious. Forever grateful. <3

  5. Sir you're a legend, and yet so humble. Thank you sir for your efforts and your love for mathematics. I will forever be grateful for the knowledge you've imparted to us. Stay healthy and cheerful like you always have been 🙂

  6. The most empathetic teacher towards students. His teaching idea is empathy. Though no school teacher could ever develop nor a college professor needs to, but great strang did.

  7. What you call "old school" teaching, when teachers actually cared about their students and worked hard at the black board, instead of just ripping through a bunch of slides at warp speed. It is sad that students these days have to pay such ridiculous sums of money for that nonsense when you can get a gem of a man like this here.

  8. I was almost done with the lectures but then today I saw that there were suddenly 36 instead of 35 videos in this series. I was confused and started scrolling through the video playlist to see what I missed and stumbled upon this gem 🙂 He looks different on the outside but he acts the same and is the same on the inside <3

  9. I've studied in university for 10 years and I haven't come across a better math lecturer. Best math teacher I've ever come across. He actually teaches but most lecturers just repeat stuff without connecting with students.

  10. Gilbert Strang is one of the BEST professors in the whole world! He has the power to really transmit knowledge and encourage students to learn more. He’s so charismatic and loves what he does. If a Nobel Prize of Mathematics existed it should be given to him for his great labour to the world of mathematics!!

  11. I watched the open course to renew my knowledge on linear algebra and I have to say Gil strange had helped me understand linear algebra much more than I was able to .

  12. What a gem of a teacher! A legend. I did not learn C of calculus in 5 years of my engineering studies way back in 1974-79. Then came the blessing in disguise and by the way I had to teach some calculus to my daughter in her graduate course in economics. And that is how I landed onto Professor Gilbert Strang's video and I fell in love with calculus which all these years was kind of a terror to me. What a beautiful and stylish way of teaching mathematics. I never have seen any teacher with such a vast knowledge and at the same time comfortable teaching beginners. God bless Professor Strang with health a d happiness.

    Anup Kumar Gupta

  13. He made me fall in love with linear algebra. I studied at an engineering college where the subject was taught very mechanically. His lectures were like a breath of fresh air.

  14. Fantastic advice, he is our elder he is really smart at this task and all the while he is level in head to realize what he knows you are learning so patients.
    I cannot do math, however he is really a pleasure to listen to and learn wisdom form regardless. I will still go watch his 18-06 course. humor is easy for all of us if we are the current one as the top in our skill set regardless the skill set we are sharing with others willing to learn that skill from each of us.
    Lance & Patrick.

  15. Sir, I wanted to thank you for your commitment to teaching. It's a great opportunity for me to watch those courses. I'm considering myself as one of your students and wishing you health and all the luck in the world.

  16. Why does the blackboard of a professor must be so badly made? Why are there so many impossible to be read notes???? Could he just make it readable for his students???? I ask that because I myself had already teachers and professors that made their blackboards impossible to read and messy! Despite that detail, this interview was awesome!!!!! This man is a legend to whom may like linear algebra!!!! I myself just love it!

  17. 要是没有他和YOUTUBE。我永远都听不到MIT的线性代数课。为什么他们要这么好呢?免费共享出来呢?

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