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Prof. Gilbert Strang from MIT giving a lecture on Linear Algebra - solving a system of two linear equations using a matrix. He really was a great teacher! I think he is now retired.

Martin

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41,808 views • 4 months ago •via X (Twitter)

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A 91-year-old professor is why Nvidia is worth $4 trillion. His name is Gilbert Strang. He teaches linear algebra at MIT. Every AI model on Earth runs on his course. The course has been free on YouTube since 2005. The videos have earned him nothing. MIT 18.06 opens with "The Geometry of Linear Equations." No advanced math. Strang takes a system of two equations, draws it two ways, and shows the class that a matrix is a picture, not an abstraction. The row picture is two lines that cross. The column picture is two arrows that sum to a target. Every neural network on Earth operates on the column picture. Strang first taught linear algebra at MIT in 1962. He wrote the textbook in 1976. It is on every serious engineer's shelf. Every quant fund, every ML lab, every rendering engine at Pixar is running his math. His central insight is that most people are taught matrices as bookkeeping. That is the first thing to unlearn. A matrix is a linear transformation. A linear transformation is a way of moving space. Once you see the space move, the math stops being algebra and becomes geometry. The Kalman filter is a linear system. PCA is a linear system. Every gradient step in a neural net is a matrix-vector product. GPT is a stack of matrix-vector products, each one a scene from MIT 18.06 running on a Blackwell GPU. He retired in 2023 after 61 years at MIT. The course is still up. Watched tens of millions of times. The chip is $40,000. Strang never asked for a royalty.

A 91-year-old professor is why Nvidia is worth $4 trillion. His name is Gilbert Strang. He teaches linear algebra at MIT. Every AI model on Earth runs on his course. The course has been free on YouTube since 2005. The videos have earned him nothing. MIT 18.06 opens with "The Geometry of Linear Equations." No advanced math. Strang takes a system of two equations, draws it two ways, and shows the class that a matrix is a picture, not an abstraction. The row picture is two lines that cross. The column picture is two arrows that sum to a target. Every neural network on Earth operates on the column picture. Strang first taught linear algebra at MIT in 1962. He wrote the textbook in 1976. It is on every serious engineer's shelf. Every quant fund, every ML lab, every rendering engine at Pixar is running his math. His central insight is that most people are taught matrices as bookkeeping. That is the first thing to unlearn. A matrix is a linear transformation. A linear transformation is a way of moving space. Once you see the space move, the math stops being algebra and becomes geometry. The Kalman filter is a linear system. PCA is a linear system. Every gradient step in a neural net is a matrix-vector product. GPT is a stack of matrix-vector products, each one a scene from MIT 18.06 running on a Blackwell GPU. He retired in 2023 after 61 years at MIT. The course is still up. Watched tens of millions of times. The chip is $40,000. Strang never asked for a royalty.

Ochob

130,880 views • 1 month ago

Gilbert Strang taught linear algebra at MIT for fifty years. His last lecture is on YouTube. It has fewer views than his worst lecture. Nobody told students it was the last one. He just walked in, said "the final class in linear algebra at MIT," and started reviewing old exams. Google built a $2,000,000,000,000 company on one concept from this course. He is 88 years old. He still answers emails. This is MIT 18.06. Linear Algebra. The most watched mathematics course in history. Then the Markov matrix. Strang writes a transition matrix on the board. Three states. People moving between them every step. After enough steps - the system locks into a steady state that never changes. That steady state is an eigenvector. Google's PageRank works the same way. Websites are states. Clicks are transitions. The importance of every page on the internet is one eigenvector of one enormous matrix. Then least squares. Three data points. No line passes through all three. So you find the line that minimizes total error. That is how every AI model on earth is trained - including the ones running inside Goldman Sachs trading desks. Then the projection. The closest point on a plane to a vector outside it. Strang draws it in 30 seconds. That same operation is how Netflix decides what to recommend to 280,000,000 subscribers. Watch the moment he gives back the final exam answer and asks students to work backwards to the question - the room solves it in silence faster than any other lecture all semester. A software engineer told me 18.06 was the course that got her from $90,000 to $200,000 in two years. Same company. Different title. Bookmark this and watch later - after this lecture every dataset you touch will feel like a geometry problem waiting to be solved. MIT 18.06 Lecture 34 | Linear Algebra Final Review | Gilbert Strang

Gilbert Strang taught linear algebra at MIT for fifty years. His last lecture is on YouTube. It has fewer views than his worst lecture. Nobody told students it was the last one. He just walked in, said "the final class in linear algebra at MIT," and started reviewing old exams. Google built a $2,000,000,000,000 company on one concept from this course. He is 88 years old. He still answers emails. This is MIT 18.06. Linear Algebra. The most watched mathematics course in history. Then the Markov matrix. Strang writes a transition matrix on the board. Three states. People moving between them every step. After enough steps - the system locks into a steady state that never changes. That steady state is an eigenvector. Google's PageRank works the same way. Websites are states. Clicks are transitions. The importance of every page on the internet is one eigenvector of one enormous matrix. Then least squares. Three data points. No line passes through all three. So you find the line that minimizes total error. That is how every AI model on earth is trained - including the ones running inside Goldman Sachs trading desks. Then the projection. The closest point on a plane to a vector outside it. Strang draws it in 30 seconds. That same operation is how Netflix decides what to recommend to 280,000,000 subscribers. Watch the moment he gives back the final exam answer and asks students to work backwards to the question - the room solves it in silence faster than any other lecture all semester. A software engineer told me 18.06 was the course that got her from $90,000 to $200,000 in two years. Same company. Different title. Bookmark this and watch later - after this lecture every dataset you touch will feel like a geometry problem waiting to be solved. MIT 18.06 Lecture 34 | Linear Algebra Final Review | Gilbert Strang

Zyphor

56,603 views • 14 days ago

I got a viewer request to solve this system of linear equations

I got a viewer request to solve this system of linear equations

Howie Hua

17,239 views • 8 months ago

Rössler Attractor: A system of three non-linear ordinary differential equations.

Rössler Attractor: A system of three non-linear ordinary differential equations.

The Math Flow

39,417 views • 5 months ago

IN 1999 MIT FILMED A MATH LECTURE THAT QUIETLY BECAME THE FOUNDATION OF EVERY AI MODEL YOU'VE EVER USED AND ALMOST NO ONE WAS TAUGHT TO SEE IT THAT WAY 39 minutes from Gilbert Strang, who taught this at MIT for over 60 years -- the linear algebra course an entire generation of engineers and data scientists grew up on. -> The shift it creates: you stop seeing matrices as boring grids of numbers and start seeing them as the language of space, data, and motion itself. School drilled you to crunch matrices by hand and never told you why. Strang shows you what they actually mean. Every neural net, every embedding, every model you prompt is linear algebra running underneath. The math you skipped is the engine of the thing you use all day. Memorizing the steps was never the skill -> seeing what the numbers do is. This is where it finally clicks. Most people fear linear algebra and move on. The ones who watched this see straight into how AI actually works. Bookmark & Watch it today, this one's a legend ↓

IN 1999 MIT FILMED A MATH LECTURE THAT QUIETLY BECAME THE FOUNDATION OF EVERY AI MODEL YOU'VE EVER USED AND ALMOST NO ONE WAS TAUGHT TO SEE IT THAT WAY 39 minutes from Gilbert Strang, who taught this at MIT for over 60 years -- the linear algebra course an entire generation of engineers and data scientists grew up on. -> The shift it creates: you stop seeing matrices as boring grids of numbers and start seeing them as the language of space, data, and motion itself. School drilled you to crunch matrices by hand and never told you why. Strang shows you what they actually mean. Every neural net, every embedding, every model you prompt is linear algebra running underneath. The math you skipped is the engine of the thing you use all day. Memorizing the steps was never the skill -> seeing what the numbers do is. This is where it finally clicks. Most people fear linear algebra and move on. The ones who watched this see straight into how AI actually works. Bookmark & Watch it today, this one's a legend ↓

slash1s

434,785 views • 2 months ago

I took Gilbert Strang’s course at MIT, and it profoundly shaped how I think. One fun memory: an acappella group stormed into class on Valentine’s Day to serenade a student, Prof Strang was thoroughly amused! MIT CSAIL

I took Gilbert Strang’s course at MIT, and it profoundly shaped how I think. One fun memory: an acappella group stormed into class on Valentine’s Day to serenade a student, Prof Strang was thoroughly amused! MIT CSAIL

Pinar Yanardag

50,338 views • 2 months ago

New episode! Michael Nielsen joins tylercowen to discuss the beauty of the universe, quantum computing, Simone Weil, finding good collaborators, and...the status of linear algebra? COWEN: Is the status of linear algebra rising? NIELSEN: [laughs] That’s a great question. It probably has, yes. COWEN: It’s prominent in quantum, right? It’s prominent in AI. NIELSEN: Google is built on matrix multiplication. It’s prominent for a lot of reasons. COWEN: What should we infer from that about the whole nature of the world?

New episode! Michael Nielsen joins tylercowen to discuss the beauty of the universe, quantum computing, Simone Weil, finding good collaborators, and...the status of linear algebra? COWEN: Is the status of linear algebra rising? NIELSEN: [laughs] That’s a great question. It probably has, yes. COWEN: It’s prominent in quantum, right? It’s prominent in AI. NIELSEN: Google is built on matrix multiplication. It’s prominent for a lot of reasons. COWEN: What should we infer from that about the whole nature of the world?

Conversations with Tyler

94,765 views • 2 years ago

This is a great lecture at MIT by David Shirokoff on Markov Chains. He covers the fundamentals of Markov Chains using a simple particle movement example. He starts by explaining how a particle moves between two positions, A & B, with different probabilities. From there, the talk converts the problem into matrix form using a Markov matrix. The main topics covered are: - Transition probabilities - Markov matrices - Probability vectors - Matrix multiplication in Markov Chains - Finding probabilities after n steps - Eigenvalues and eigenvectors - Matrix diagonalization - Long-term steady state distribution

This is a great lecture at MIT by David Shirokoff on Markov Chains. He covers the fundamentals of Markov Chains using a simple particle movement example. He starts by explaining how a particle moves between two positions, A & B, with different probabilities. From there, the talk converts the problem into matrix form using a Markov matrix. The main topics covered are: - Transition probabilities - Markov matrices - Probability vectors - Matrix multiplication in Markov Chains - Finding probabilities after n steps - Eigenvalues and eigenvectors - Matrix diagonalization - Long-term steady state distribution

𝗿𝗮𝗺𝗮𝗸𝗿𝘂𝘀𝗵𝗻𝗮— 𝗲/𝗮𝗰𝗰

141,930 views • 3 months ago

When I got into a huge Student Debt, but some random dude on the Internet is using Linear Search instead of a Hash Table! Absolutely infuriating!

When I got into a huge Student Debt, but some random dude on the Internet is using Linear Search instead of a Hash Table! Absolutely infuriating!

Тsфdiиg

52,621 views • 2 years ago

Set Yourself on Fire is now available on Steam A linear visual novel. A quiet town awaits death. Stagnation is the default state of being. Two aimless young women fall in love.

Set Yourself on Fire is now available on Steam A linear visual novel. A quiet town awaits death. Stagnation is the default state of being. Two aimless young women fall in love.

Denhop

255,318 views • 4 months ago

Gilbert Strang, a quiet MIT professor, picked up a piece of chalk and explained the one skill standing between you and every account you have ever blown. MIT put the entire course online. it has been free for over twenty years. almost nobody finishes it. His point: the market never pays in certainties. it pays in probabilities, and a human gut can barely hold one straight. the math that holds ten thousand at once, weighs them, and collapses them into a single call is linear algebra. it is the branch Citadel and OpenAI both pay $400K to hire for. he is not a trading guru. his 18.06 lectures are the most watched math class on the planet. Skip to where he turns a wall of numbers into one vector. a single object carrying a thousand odds at once, in notation a beginner can follow. No slides. no jargon. one piece of chalk. a quant I know rewatches lecture one every year before he sizes a single position. You do not have a strategy problem. you have a math problem. the fix has been free for two decades, and you are still guessing.

Gilbert Strang, a quiet MIT professor, picked up a piece of chalk and explained the one skill standing between you and every account you have ever blown. MIT put the entire course online. it has been free for over twenty years. almost nobody finishes it. His point: the market never pays in certainties. it pays in probabilities, and a human gut can barely hold one straight. the math that holds ten thousand at once, weighs them, and collapses them into a single call is linear algebra. it is the branch Citadel and OpenAI both pay $400K to hire for. he is not a trading guru. his 18.06 lectures are the most watched math class on the planet. Skip to where he turns a wall of numbers into one vector. a single object carrying a thousand odds at once, in notation a beginner can follow. No slides. no jargon. one piece of chalk. a quant I know rewatches lecture one every year before he sizes a single position. You do not have a strategy problem. you have a math problem. the fix has been free for two decades, and you are still guessing.

Loran

47,557 views • 1 month ago

We had the housewarming party a couple of weeks back. It was tons of fun and should hopefully give you a better idea of where we're spending some of our time improving model architectures and systems 00:00: Introduction 00:40: Jerry Tworek (), Building the world’s most automated AI lab 12:10: James Demmel (UC Berkeley), Dense Numerical Linear Algebra: A brief history and current trends 42:11: Christoph Klein (NVIDIA), Dense Linear Algebra at NVIDIA 47:54: Mark Saroufim (), Linear Algebra Kernels for the Age of Research 51:43: Ben (Tilde), One Layer Deeper…

We had the housewarming party a couple of weeks back. It was tons of fun and should hopefully give you a better idea of where we're spending some of our time improving model architectures and systems 00:00: Introduction 00:40: Jerry Tworek (), Building the world’s most automated AI lab 12:10: James Demmel (UC Berkeley), Dense Numerical Linear Algebra: A brief history and current trends 42:11: Christoph Klein (NVIDIA), Dense Linear Algebra at NVIDIA 47:54: Mark Saroufim (), Linear Algebra Kernels for the Age of Research 51:43: Ben (Tilde), One Layer Deeper…

Mark Saroufim

58,427 views • 1 month ago

🚨FLASHBACK Trump at the CDC in 2020: “You know my Uncle was a great -- he was at MIT. He taught at MIT for a record number of years. He was a great super genius, Dr. John Trump. I like this stuff. I really get it. People are surprised that I understand it...Maybe I have a natural ability. Maybe I should've done that instead of running for president.” #TrumpMentalHealth

🚨FLASHBACK Trump at the CDC in 2020: “You know my Uncle was a great -- he was at MIT. He taught at MIT for a record number of years. He was a great super genius, Dr. John Trump. I like this stuff. I really get it. People are surprised that I understand it...Maybe I have a natural ability. Maybe I should've done that instead of running for president.” #TrumpMentalHealth

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3,115,510 views • 2 years ago

"Boy is angry at teacher now." 🔥 He got outraged as the teacher was giving old books to his friend. Now he is determined to file a complaint against the teacher. What a cute friendship among these kids.

"Boy is angry at teacher now." 🔥 He got outraged as the teacher was giving old books to his friend. Now he is determined to file a complaint against the teacher. What a cute friendship among these kids.

Suraj Kumar Bauddh

16,356 views • 5 months ago

emulating swing in a program meant for linear notation is really hard.. should i make the whole song

emulating swing in a program meant for linear notation is really hard.. should i make the whole song

chayre5792

29,314 views • 1 year ago

Fox News: How do you deal with people who might be disappointed because they voted for you on the assumption of no wars? Trump: Well, I have to do something in terms of making America great and keeping America great. My uncle was a great professor at MIT. He really got it. He was a highly respected man. He was there for 41 years at MIT.

Fox News: How do you deal with people who might be disappointed because they voted for you on the assumption of no wars? Trump: Well, I have to do something in terms of making America great and keeping America great. My uncle was a great professor at MIT. He really got it. He was a highly respected man. He was there for 41 years at MIT.

FactPost

281,620 views • 5 months ago

“I really like him. I just saw he was on ‘SNL’ a couple of weeks ago. He’s not only a great musician, but he’s really funny. I think he’s a good actor. Like, legitimately funny. I think he’s great. I’m thumbs up. I’m a fan.” - Actor Steve Carell talking about Harry Styles!

“I really like him. I just saw he was on ‘SNL’ a couple of weeks ago. He’s not only a great musician, but he’s really funny. I think he’s a good actor. Like, legitimately funny. I think he’s great. I’m thumbs up. I’m a fan.” - Actor Steve Carell talking about Harry Styles!

Best Of Harry Styles

80,677 views • 4 months ago

He was such a great teacher ❤️

He was such a great teacher ❤️

Funkeeee

557,872 views • 1 year ago

He was just a janitor at MIT. One day, while mopping the floor, he glanced at a math problem on the blackboard. He had no idea it was one of the most advanced, difficult equations in the world, yet he solved it effortlessly,this gained him a lot of attention.

He was just a janitor at MIT. One day, while mopping the floor, he glanced at a math problem on the blackboard. He had no idea it was one of the most advanced, difficult equations in the world, yet he solved it effortlessly,this gained him a lot of attention.

Ola

63,466 views • 5 months ago