Gilbert Strang: Linear Algebra, Teaching, and MIT OpenCourseWare | Lex Fridman Podcast #52

[@lexfridman]

I really enjoyed this conversation with Gilbert. Here's the outline: 0:00 - Introduction 3:45 - Math rockstar 5:10 - MIT OpenCourseWare 7:29 - Four Fundamental Subspaces of Linear Algebra 13:11 - Linear Algebra vs Calculus 15:03 - Singular value decomposition 19:47 - Why people like math 23:38 - Teaching by example 25:04 - Andrew Yang 26:46 - Society for Industrial and Applied Mathematics 29:21 - Deep learning 37:28 - Theory vs application 38:54 - Open problems in mathematics 39:00 - Linear algebra as a subfield of mathematics 41:52 - Favorite matrix 46:19 - Advice for students on their journey through math 47:37 - Looking back

[@syedabdul3462]

Useful 👍

[@tommygunhunter]

I really enjoyed your conversatiob with Gilbert. Never heard you laugh so much in a video.. he has a very subtle sense of humour.😊

[@zacharykraehling4363]

19:47 Terence McKenna

[@zacharykraehling4363]

Nassim Taleb

[@johnhogan6254]

Impressed with this podcast. You ask all the right questions.

[@bert88sta]

I remember emailing Dr strang after I self studied calc 2 for the AP test and passed using his material. He sent me a congratulations back, and that meant the world to me.

[@billyjames3046]

What you did probably also meant the world to him : )

[@davidsbeandip]

wholesome

[@julienyt1600]

High school dropout, joined the french army at 18. 15 years later, Took 18.06 and 18.065 using open courseware. Now I work in AI. I hope to be able to thank Dr. Strang in person one day.

[@JesusIsMySaviorILoveJesus]

What was his material on calc 2?

[@Cesar-th8hq]

@@julienyt1600 that’s fucking awesome, congrats man

[@NytronX]

Gilbert Strang single handedly made Linear Algebra my favorite branch of math. I have a signed copy of his textbook that I will keep until the day I die.

[@HL-iw1du]

Uditsinghparihar lol you both have the same profile pic

[@chrislimnios9180]

Absolutely in agreement with you that this author is amazing. I've got his linear algebra book and I have Apostols's calc book. Those are my two favorite math texts.

[@michaeldebellis4202]

Also, agree! I tried several other texts but his books and his online class made it so clear when things seemed so difficult in other books. His Socratic style is a model all university professors would do well to copy.

[@GlenWG1972]

Challenge accepted-

[@muttleycrew]

Nice!

[@yadavatsal]

Lex had a distinct smile on his face during the entire conversation. This was much more than just a interview for him, you can see the pride of just being in the same room with Gilbert in his eyes. This was beautiful.

[@bibimus5491]

Bless this man he is awesome 👍

[@sfincione2000]

I was thinking the exact same thing =)

[@Arghamaz]

U stole my words n my exact perception... no wonder why this man Strang is a profound maths genuis no doubt 🎉

[@NNCCCC63]

All hail. You have to love him. For those interested in academic lineage and apostolic succession - Gilbert Strang’s advisor was Peter Henrici, whose advisor was Eduard L. Stiefel, whose advisor was Heinz Hopf , whose advisor was Erhard Schmidt , whose advisor was David Hilbert, whose advisor was Carl Louis Ferdinand von Lindemann , whose advisor was Christian Felix Klein , whose advisor was Julius Plücker , whose advisor was Christian Ludwig Gerling , whose advisor was Carl Friedrich Gauss.

[@JousefM]

Makes me sad to see him getting old - he's a good guy. I love him!

[@qinlun6859]

I love him, too. I hope he can live forever. I'm sad to see him getting old

[@bookman9897]

He is immortal in our hearts

[@michaeldebellis4202]

Strang is one of my academic heroes. I started to take Andrew Ng's Machine Learning course on Coursera and Ng said "you don't need much linear algebra to understand this..." but not very far into the course he started talking about matrices, inverses, transpose of a matrix, etc. and I realized that I needed at least some linear algebra so I took Strang's online course at MIT. I very highly recommend Strang's course. It's one of the best online courses I've ever taken. I ended up taking the entire course even though I realized after about the first 3-5 that I had all the linear algebra I needed to go back to Ng's course. I also thought it was humorous that one of the things Ng says early in the ML course is something like: "you don't need the kind of theoretical math that people have who look at proofs and think they are beautiful" I thought "but, but,.. I do that!" Strang's course was definitely the kind of course where you see the incredible elegance and IMO beauty of a mathematical discipline. In fact, I've had different reactions from different people that I point to Strang's course. People who love math like me (even though I'm not very good at it) and love not just using it but understanding things at an abstract theoretical level love Strang's course. Engineering types (not that there's anything wrong with that, I earned most of my living as a software engineer) who just want to know the formulas and how to use them tend not to like his course. One of the things I loved about Strang's course was the way he started it. As simple as possible giving the most basic idea of solving two linear equations by finding the point in 2D space where they intersect, then expanding it for 3 dimensions (the line where two planes intersect) and then for n dimensions. Sounds trivial but that kind of basic grounding was what I had missed from other books I attempted on the topic and it made everything going forward so much more understandable. I also love his Socratic method of teaching where he pauses in the middle of a derivation or solving a problem to ask the class what the next step is, he really keeps you engaged that way.

[@michaeldebellis4202]

@@emir2750 It's a tough topic (at least for me) but really worth it. I wish I had something to offer you as far as tips. The only things I can think of are 1) Getting Strang's book Linear Algebra and its Applications. And 2) if you haven't already done so I recommend installing Octave (it's free). It's the linear algebra tool that Ng uses for his ML class but I found it helped me out quite a bit with Strang's class. It's great because unlike other ML programming environments like Python Octave is a direct implementation of Linear Algebra and it has an interpreted environment like languages such as Lisp and Python. So you can easily type in two matrices, multiply them, see their inverses, transpose, etc. I found that really helpful to make sure I was doing various calculations correctly, to practice matrix multiplication, etc. Hope that helps a bit.

[@FloppyDobbys]

Gilbert Strang is one of the most influential teachers in my life. Hands down. Thank you, Gilbert for being so inspirational.

[@ArchanaaDas]

Best update for a Monday. Thank you for interviewing Gilbert Strang.

[@muhammedshafi8704]

A humble person. " I am here to teach you math not to grade you "

[@agugyin]

Role model for all teachers!

[@DaveJ6515]

That's the one most important thing. Grading students is the worst thing you can do. Those who learn because of the grades should not be there at all. Those who have a real passion for the subject will see that passion overwhelmed by the need of getting a high grade. It's all wrong.

[@klmcwhirter]

Because he realizes - especially at the university level - that the responsibility of whether someone has absorbed the material lies squarely with the person themselves. Folks take your education seriously! And own it yourself.

[@TheEndlessslawter]

This man helped me so much in high school calculus, he is so incredible found my self looking for more stuff he taught even if I didnt need it.

[@joshuabonet]

Gilbert Strang gave the first series of videos of mathematics (specifically Linear Algebra) on KZbin for his class on MIT in 2000. I remember thinking I was blessed with these videos since they come directly from the colleges that I would dream about applying one day for my PhD. These videos shaped my perspective inside the connections that were being discuss inside his classroom and gave me a sense of connection with the audience. As if I was part of MIT students, I was equal to their intelligence because I was able to answer the questions correctly when he would ask them live. So I submerge myself and not surprisingly, it has been the core of my work with Deep Learning and Artificial Intelligence. What a beautiful podcast to watch, thank you Lex Fridman​.

[@DantheManMonty]

Started the Linear Algebra course back in 1806. Over 200-years of teaching under his belt, just incredible

[@PeeterJoot]

Prof Strang's lectures on SVD were awesome. That wasn't taught when I did my undergrad linear algegba ('92), and it wasn't in any of my old texts. After listening to his SVD lectures, I was so impressed, that I went back and listened to the rest of the course from scratch.

[@JeffMTX]

The SVD is so huge too…

[@sumanchaudhary8757]

Gilbert strang , My Hero too.

[@sinajahadi2973]

When I was in undergrad, I was starting to hate math until saw his course. It was everything I needed to recall the true beauty of math. Thanks Lex for interviewing one of my heroes.

[@ambujmittal6824]

Woah! I never expected or even imagined that Gilbert Strang will ever be a part of this Podcast series! Amazing job!

[@FoxInTheBasement]

Owe Gilbert Strang so much, 10 years ago i had to drop Linear Algebra. The textbook was unreadable and my professor's poor teaching and language skills made the abstract subject matter even worse. I genuinely believed I was incapable of understanding the material and switched from chem to biochem to avoid the course. Returning to school for a comp sci degree this summer with the same professor still teaching, Strang's lectures/textbook have carried me through to being an A student in the course. The 5th edition of his intro to lin algebra book brings so much clarity and the questions explore the broader implications of the introduced topics so well. Dr. Strang is an absolute gift to this world.

[@FoxInTheBasement]

update: got 100% on my midterm. Bless this man.

[@coal2710]

Prof. Strang has a Linear Algebra book I studied thoroughly, just because I heard that he said if students around the world can find an error in the book and send it to him, he would send the student an MIT keychain and a sweatshirt. I couldn't find any mistakes, but I passed the class with 9/10. He's a great teacher.

[@BrainKite]

THAT is awsome ! Remind me of how good and enyoyably positive his Linear Algebra MIT course is.

[@MrScattterbrain]

Yes, that is a positive definite course. Oh, I meant to say that is definitely a positive course.

[@MijeshDeuja]

One of the best maths professors. His OCW courses really helped me visualize concepts instead of just solving the problems.

[@leromerom]

I took his class online a few years ago, when I started my journey in A.I.. I’m so glad to see him in your channel!

[@xXxBladeStormxXx]

This is the best episode of your podcast. All your guests are very smart people but when the person has such clarity of thought and command over their answers as Gilbert Strang it's just magical simply listening to them speak. Kind of like listening to Richard Feynman speak. Beautiful talk, thanks for this Lex Fridman.

[@sterlingveil]

Gilbert Strang gave one of my favorite math quotes in the 3rd edition of his linear algebra book (he took it out in later revisions and I don't know why): "the contribution of mathematics, and of people, is not computation but intelligence.". That line made me feel so much better about all the careless mistakes I made solving the problems in his book and I'll never forget the picture of subspaces and transformations that he provided! Love to you Gilbert Strang!

[@brian_mcnulty]

This guy is awesome. I watched his entire linear class the summer before I took it last fall. Amazing concepts. I loved that class. It really made me understand that I don't need to visualize something to describe it.

[@koreypickering4583]

Did it help with the class. I am watching the lectures and reading the book now, I have the class this fall and it's suppose to be a particularly hard class at my University.

[@nabla_mat]

The humbleness of prof. Strang is astonishing. What a great man! Thank you for that interview!

[@OrionConstellationHome]

I absolutely Love love love Gilbert Strang! He is So Inspiring! He is my favorite American math professor! In Russia you start learning linear algebra at school very early. I learned it first at math-physics school #2 in Moscow, then at mech-mat MGU Moscow State Un. And loved it. Then I was teaching it all my life. And then I rediscovered it again with Gilbert Strang - it was So Beautiful and brilliant! I love the way he talks about it. Absolute genius! Great teacher! Thank You Lex for this interview. Please do it again. Spasibo.

[@dhiruhamal]

Well, I would say one of the best talks in this podcast. I am standing in this position as a researcher because of Gilbert Strang and Sal Khan like teachers because I never took calculus, Linear algebra even the statistics while schooling and if there is no mathematical foundation then no Machine learning. Before I used to think like I am kind of unlucky person because I missed the 1990's time period when the internet was booming, If I was studying at that time I would be doing great. But now I am feeling like this is the real golden time period ever in history because of the Artificial intelligence machines, robots, computers are getting vision and becoming more intelligent. And you guys are helping a lot to shape this community. Thank you and keep going... Hope next time you will bring Sal Khan.

[@kamrupexpress]

Prof. Gilbert Strang's lectures are not only for students but for math teachers and professional mathematicians. He has very deep insights. I can tell you this as a math prof myself. He is a hero for me too.

[@eddiejennings5262]

Thank you, Dr. Strang. I was blessed to have several wonderful math teachers and mentors during my PhD in Mathematics.. You have left a beautiful impact that will influence several future generations. Thank you, Most Respectfully,

[@NadjaNiemann]

Oh yes, he made definitely a connection - I wish I had known his lectures during my studies. - And yes, - telling someone for the first time about an important concept is magic!

[@Wrathos]

Oh my god! Lex I love you. Interviewing Gilbert Strang is just an amazing choice. That man made me understand Linear Algebra. He is absolutely brilliant. Thanks for sharing!

[@mihailbalanici5392]

I really love the simplicity with which Lex is always approaching complex topics - be it deep learning, philosophy, or engineering as a whole. This makes your interviews always a joy to watch. Thanks for having Prof. Strang in this podcast!

[@sterlingveil]

Lex, I love that you asked him about the lack of math-literate representatives in Congress. That's such a rare question to pose but so important. I'm sure you're aware that it's one of Andrew Yang's talking points as well--he wants to introduce a neutral "Congressional technology office" to supply them with much needed expertise. And I just want to plug my favored solution to this problem which is almost never talked about and which solves many other problems at the same time: if we augmented the Senate with 50 additional seats that were not elected but chosen via sortition then statistically we are likely to get several engineers/mathematicians in office which would make a huge difference in the some of the Senate committees (and it would guarantee a working class voting bloc in the Senate which truly does not exist at the present moment).

[@janarthananpoornavel]

Lex is all smiles and happiness. There is something special about gilbert that lex exuded. Loved both of them in the conversation

[@williamerdman4888]

I received my MS in Electrical Engineering in 1984. I spent half of my coursework in Mathematics and took two semesters of Linear Algebra. We used the first edition of Strang's book. I worked almost every problem in that book (I couldn't do 10% of the problems). I still have that book on my shelf. I always considered the eigenvalue equation Ax=Lambda x as one of the most interesting equations in all mathematics. And it is so important for example when solving systems of differential equations. Thanks, Gilbert!

[@NeyVasconcellosJr]

Top-notch Professor. He is the best we can find, making LA enjoyable to learn. Thank You Lex

[@murraypatterson9190]

I am not a trained Mathematician. But I extensively used matrix algebra in my PhD (in energy modelling). Simply because it made intuitive sense and was insightful in regard to the problems I was dealing with. Much more so than calculus. And i agree with Gilbert Strang that Singular Value Decomposition is the best, though a lot a people including the journals are still stuck on square matrices and eigenvalues - for example I cant get a paper publushed purely because it used SVD rather eigenvalue-eigenvectors. By the way I emailed Gilbert Stang on another matter after watching many of his videos, not expecting a response but he got back to me the sane day,

[@akcj875]

these are the gems that make American education so unique and wonderful. And above all providing the world free lectures from a top university. Knowledge giving is a service to humanity that no amount of monetary charity can match. God bless Gilbert Strang and so many others who continue to give... it was truly a bold decision for MIT to give away this valuable 'product' for free.

[@lucyfrye5365]

Such a wonderful teacher. In two weeks he taught me enough about linear algebra to last a lifetime in computer graphics. He turned rotations in 3d space into things. That you can manipulate and work with as long as you follow a few simple rules. No longer this convoluted mess of sin and cos that makes your brain hurt. All online for free. Thank you so much.

[@stevecloutier9414]

Thank you both for this incredibly interesting discussion. I really like Gilbert Strang , he’s a superstar in so many ways. I’m starting to watch his lectures and enjoying them immensely , he’s calm , confident and poised. Thank you both for sharing your conversation.

[@samiehessi8163]

Every time I think this is last time I am being surprised by his choice of guest, I am proved wrong. Kudos to you and your guests!

[@klmcwhirter]

Dr Strang, thank you for all that you have done for all of us.

[@jimmygan801]

I don't thank Prof Strang enough... His open course of MIT legit got me through undergrad and grad... just insane level of explanation with such a depth and understanding... his textbook also very good study materials

[@noonesperfect]

Such a down to earth, humble man..... that's because all his wisdom , philosophy he carried out over the years. wonderful to hear him always.... Cheers

[@fearnobodyandtrustnoone]

Prof. Strang may God bless you with good health you are such a blessing for students worldwide.

[@shoaibkahut]

It was my favorite ever talk . What a gentleman this HOST is . What a sweetheart this Professor is . Greetings from China 🇨🇳 . I loved this podcast

[@ninadghike8181]

I first time on youtube I liked someone promoting a sponsor. I have worked with Middle School First teams for past few years. Good to know that there are more who care about increasing STEM education among children. Thanks Lex!!!!

[@UltimateLuv]

Gilbert Strang really helped me understand what’s going on with his textbook and lecture videos while taking a class on Linear Algebra! His passion and calming voice made the subject enjoyable and educational at the same time. I hope to spread knowledge and improve the world like he does in my lifetime.

[@CharwakApte]

Delighted in all 10-dimensions

[@astropgn]

People, here is something wholesome to know: Professor Gilbert is very humble and kind. I once sent him an email, without any expectation to receive a reply from him. I just said his videos were very helpful and that I loved that I had the opportunity to learn so much, and I thanked him. A couple of days later he took his busy time to reply. What a wonderful person! I wish him well and I am grateful for what he taught me!

[@Ramachandran-i2j]

Great professor Dr. Gilbert Strand. Let him live long for his services in Mathematics.

[@shanghai_noon]

In my undergrad years I stuck in Linear Algebra. Stumbled upon his lectures on MIT open courseware and watched all of them. Fond memories!

[@samuelleung9930]

Really appreciate Mr Fridman, the questions are wonderful and the order of them is perfectly organized. We can see that prof Strang really enjoyed the interview.

[@richarddow8967]

I guess I need to start listening all the way through more often, that quote at end was so spot on. Love Prof Strang. I took LA in mid 80's and my Prof used topreach the column space and until I came across Gilbert never fully appreciated it

[@abdousayed3485]

Lex you look connected to him as everyone of us connected to a loving competent teacher who opened awesome paths in our lives through his/her teachings. It is beautiful to meet and debate with your teacher who one day gave you something valuable. An awesome discussion. Thanks Lex!

[@jasonabc]

Another homerun Lex, you have a knack for asking very thought provoking and interesting questions

[@obaidullahkhan797]

The way he blinks his eyes at the right instant is just awesome !! He is the guru of linear algebra ! What a man ..

[@ramzigaagai1000]

Thank you Prof. Strang for such beautiful insights in Linear Algebra!

[@oudarjyasensarma4199]

You never stop to amaze us Lex!!! with the guests you invite to your Podcast!!! Thanks a ton!!! :) And everyone's been waiting for the Geoffrey Hinton Podcast!

[@jakesorenson6152]

THANK YOU for bringing Gilbert on. What a score!! The visuals I got from his descriptions of linear algebra always gave me chills.

[@anaghpandey8805]

Mr. Strang is true love. He makes it so much fun to listen to him that I eagerly wait for his class to begin.

[@NANDUVENU-wt2lp]

At the age of 27, I came across his lectures. I considered myself to be very good at Math, having scored extremely well in every math exam of my life. His lectures humbled me to the point where I realized I knew nothing about the beautiful world of Math.

[@PetWanties]

This has made me excited to encounter linear algebra in my studies. I'll make sure to start watching his lectures as well. :) Thanks for the interview.

[@didierliango6402]

You were my favourite prof i watched during my undergrad Linear Algebra.. so elegant, especially the fundamental idea of 4 subspaces.

[@GeoPoly55]

Humble, down to earth, great professor of mathematics linear algebra.

[@robmcilroy1894]

Gilbert Strang strikes me as a teacher I would have loved to learn from. I certainly learnt some new knowledge in the last forty minutes or so, thanks.

[@JRush374]

You can learn from him. His linear algebra lectures are great.

[@reubenemmanuel3287]

It's always a pleasure to see Dr Gilbert Strang.

[@dmitriidatsenko]

84 freaking years and such passion, damn!

[@stapleman007]

Used Strang's Intro to Linear Algebra text in college in 2000. One of the best text books I've studies.

[@mmmmmark9751]

Gilbert is one of my favourite gentlemen.....I watch his videos and have some of his books, and I have more in my wishlist which I am getting v. soon.....I studied maths at UWA as a 40yr old, and took LA, but got a bit lost. Professor Gilbert has ignited something within me, and helped me see some things I missed 1st time around. Thank you Sir, for everything.....

[@andrapopa284]

There's beauty and harmony in his teaching as is in this interview...!

[@SloppyPastrami]

I had a big smile on my face watching this. Prof. Strang is a great teacher

[@dineshdevaraju6698]

Prof Strang is my Hero ...

[@nonesovile6019]

Gilbert Strang is a Great teacher made linear algebra easier to learn.

[@sitharthanmirudhul5411]

Cool guys! Thansk for the wonderful interview @gilbert strand & @ Lex Fridman.

[@kunaldongre9]

Wow how simply he explain difficult concept. SVD : ((Rotation ) stretch) Rotation. In his book he also provided layout for modern day Data Science.

[@winstonridgewayhardy]

I just saw this!!!! I just love this man... I did not realize that you had him on your interview series!!!!! Wooo Hooo Lex! You just keep getting more awesome the more I learn about you my good man!!!!! Gilbert Strang is one of my favorites of all time..

[@wildreams]

I love him so much. Thanks for reminding everyone every time, the simple joys of basic math.

[@atharvapagare7188]

What a delightful man!

[@robertwhite8194]

Just turned in my final exam in my first linear algebra course and I’m hooked on learning this kind of math. This guy helped me get primed for the course and I think I got an A!

[@abins641]

It is an honour to watch this series.

[@nativealien_14]

“Don’t be discouraged, it’s too good to miss.”

[@IvanGoncharovAI]

Such an immersive conversation! Really loved the energy of Gilbert!

[@samlol3]

This man's lectures saved my first university math course as I was on my way to fail, but then I made an epic comeback after I started skipping the course in order to watch the MIT courses online instead x)

[@jessiedeemarkgingo6074]

The way Gilbert Strang talks is an innocence like a baby. I can see that he is very warm and kind.

[@tractatusviii7465]

this is so nuts. This guy is plucked straight from the Pantheon. Wish Gilbert the strongest health!

[@RubenFTF1]

Gilbert is a great teacher! Thank you Lex for the interview, it was nice to hear.

[@mathhack8647]

I went through most of his course. What a pleasure to have a such gift from a such humble and generous person. @23:00 amazing answer. @43:50 " I am not a good teacher". La modestie par excellence. @45:00 "I am here to tech you Math not to Grade you". Hence, nobody looks at Marks the same way he did before.

[@wesw6787]

What a humble person. Absolutely great questions as well! Lovely!

[@Emboaba]

I’ve watched many lectures of linear algebra and how to solve systems of differential equations by LA Professor Strang is wonderful

[@DrHans-RudigerZimmermannTheore]

I love math and have dedicated as a theoretical physicist more then 30 years of my life to the math. Math is so beautiful and satisfying. And teaching is my economic professional work.

[@thebluriam]

"I don't think I'm a good teacher because I don't like the grading and exam part". Exactly why he's one of the best teachers

[@shellrox2878]

Strang! My hero!

[@dr.naveenakumarau.6811]

Thank you, sir, due to interview with great person Prof Gilbert Strang

[@vicktorioalhakim3666]

I am really curious why he didn't emphasize on the point that modern analysis, a step forward from calculus, is largely built on top of abstract concepts from linear algebra, i.e. normed spaces, Banach spaces, Hilbert spaces.. etc. In fact, the essence of calculus IS linear algebra, where we work with derivatives and integrals which are in fact linear operators working on the infinite dimensional vector spaces of functions. The key extra ingredient that we introduce there is the concept of a limit, which allows us to go from a finite dimension to the infinite. Linear algebra can go sooo much further than the simplistic view of matrices as rectangular arrays of data, and I firmly believe that it should be a prerequisite to calc.

[@focusEngineered]

Thank you so much Gilbert and Lex. ❤️❤️❤️❤️❤️

[@soheilsoltani713]

Gilbert Strang is the best math teacher I've ever had

[@helloimwill]

I love this so much. Awesome work. Thank you for making this content accessible.

[@alanarcher]

This man is a treasure in this world