A mathematician taught 100 million people through his math lectures and earned over $500,000.
He has taught calculus to more people than any room on Earth, and the 2 lines he writes in lecture 9 are what Wall Street pays six figures for.
David Jerison, MIT 18.01, 2007. Chalk, 1 locked camera. The platform it lives on has reached over 300 million people. Almost none of them get past lecture 4.
The topic sounds like filler. Linear approximation. Throw the whole curve away and keep the straight line touching it at 1 point. Then add 1 more term and the line becomes a parabola.
2 terms. That is the lecture.
Now walk onto a bond desk. A bond's price against interest rates is a curve nobody computes in their head, so the market does not use the curve. It uses the first derivative and calls it duration. It adds the second and calls it convexity.
Options desks run the same 2 numbers under different names. Delta is the first derivative. Gamma is the second. A trader saying he is long gamma is quoting the curvature term from minute 30 of a freshman lecture.
Nobody on those desks is doing anything deeper than what is on that board. They do it faster, on the right instrument, with size behind it.
The hard part was never the 2 terms. It was noticing the whole building stands on them.
MIT lecture 5 teaches you to answer a question you are not allowed to solve.
David Jerison, 18.01, Fall 2007. Chalk, one locked camera. The board says x squared plus y squared equals 1. A circle. He asks for the slope at a point.
The school method is to solve for y first. You get plus or minus the square root of 1 minus x squared. Two separate branches, a sign you have to pick by hand, and a derivative that blows up at the edges. Most students get there eventually and hate every step.
Jerison never solves for y.
He differentiates the equation as it stands. 2x plus 2y times y prime equals 0. One line of algebra later, y prime equals negative x over y. Done.
Look at what just happened. He found the slope of a curve without ever writing that curve as a function. The answer came out of a relationship, not out of a formula for y. The thing he wanted was never isolated.
And the answer is better than the one you fight for. Negative x over y is the radius slope flipped and negated, which is exactly what perpendicular means. The geometry falls out of the algebra for free.
Then he turns the same move on inverse functions, and the whole memorized table collapses.
You were made to memorize that the derivative of arcsin x is 1 over the square root of 1 minus x squared. There was never anything to memorize. Write y equals arcsin x as sin y equals x. Differentiate. cos y times y prime equals 1. Solve, use the triangle, and the formula appears in 4 lines. Same for arctan. Same for every one of them.
Skip to the circle. That is the lecture.
Here is the part nobody tells the students in that room.
That move has a name outside the class. The implicit function theorem. And it is not a calculus curiosity, it is load bearing in modern machine learning.
When a model has to take a gradient through an optimizer, or through a solver, or through a layer defined as the fixed point of an equation, unrolling every step is impossible. Thousands of iterations, all of them stored in memory. Deep equilibrium models, differentiable optimization, implicit meta learning, all hit the same wall.
The fix is what Jerison wrote on the board in 2007. Do not unroll the process. Differentiate the equation at the answer. Constant memory, no matter how long the solver ran.
The trick for finding the slope of a circle without solving for y is the trick for backpropagating through a computation you cannot afford to replay.
Nobody in that room knew that. He was teaching a standard topic on a standard Tuesday.
Most people watching lecture 5 today are trying to pass something. They practice the technique, get the answer, move on, and never notice what they were handed. It is not a shortcut for circles. It is a way of getting derivatives out of constraints, and almost everything real arrives as a constraint rather than a formula.
The board is 19 years old. What is on it shipped in production this year.
MIT lecture 5 teaches you to answer a question you are not allowed to solve.
David Jerison, 18.01, Fall 2007. Chalk, one locked camera. The board says x squared plus y squared equals 1. A circle. He asks for the slope at a point.
The school method is to solve for y first. You get plus or minus the square root of 1 minus x squared. Two separate branches, a sign you have to pick by hand, and a derivative that blows up at the edges. Most students get there eventually and hate every step.
Jerison never solves for y.
He differentiates the equation as it stands. 2x plus 2y times y prime equals 0. One line of algebra later, y prime equals negative x over y. Done.
Look at what just happened. He found the slope of a curve without ever writing that curve as a function. The answer came out of a relationship, not out of a formula for y. The thing he wanted was never isolated.
And the answer is better than the one you fight for. Negative x over y is the radius slope flipped and negated, which is exactly what perpendicular means. The geometry falls out of the algebra for free.
Then he turns the same move on inverse functions, and the whole memorized table collapses.
You were made to memorize that the derivative of arcsin x is 1 over the square root of 1 minus x squared. There was never anything to memorize. Write y equals arcsin x as sin y equals x. Differentiate. cos y times y prime equals 1. Solve, use the triangle, and the formula appears in 4 lines. Same for arctan. Same for every one of them.
Skip to the circle. That is the lecture.
Here is the part nobody tells the students in that room.
That move has a name outside the class. The implicit function theorem. And it is not a calculus curiosity, it is load bearing in modern machine learning.
When a model has to take a gradient through an optimizer, or through a solver, or through a layer defined as the fixed point of an equation, unrolling every step is impossible. Thousands of iterations, all of them stored in memory. Deep equilibrium models, differentiable optimization, implicit meta learning, all hit the same wall.
The fix is what Jerison wrote on the board in 2007. Do not unroll the process. Differentiate the equation at the answer. Constant memory, no matter how long the solver ran.
The trick for finding the slope of a circle without solving for y is the trick for backpropagating through a computation you cannot afford to replay.
Nobody in that room knew that. He was teaching a standard topic on a standard Tuesday.
Most people watching lecture 5 today are trying to pass something. They practice the technique, get the answer, move on, and never notice what they were handed. It is not a shortcut for circles. It is a way of getting derivatives out of constraints, and almost everything real arrives as a constraint rather than a formula.
The board is 19 years old. What is on it shipped in production this year.
A guy I know cut his working week from 70 hours to 12 and tripled his income in a year. The whole thing started with three words from an Oxford maths lecture.
The words are: be lazy.
The clip is from an Oxford Mathematics lecture on Fourier series. Whiteboard full of integrals from minus pi to pi. He stops in the middle of a derivation, turns to the room, and says this is the one thing he tells all his students.
You can grind through the calculation. Or you can step back and ask whether there is a trick that gets you there without doing a lot of work. His answer to the room is that yes, there almost always is.
Look at what he points at. The integral on that board never gets computed. It gets dismissed, because the function is periodic and the interval is symmetric, and the moment you see that, the work was never necessary.
Noticing the symmetry is the skill. The computation is what you do after you failed to notice it.
The guy I mentioned wrote data pipelines. Hardest worker on his team, last one promoted, because effort was the only thing he was selling and effort is the cheapest thing on the market.
He changed one habit. Ten minutes before every ticket, asking whether the ticket needed to exist.
That quarter he deleted more code than he wrote. Two services went away. A report that cost a team three days a month became a query that ran in four seconds. He stopped being the person who closed tickets and became the person who made them stop appearing.
The offers started after that. Nobody has ever paid six figures for typing speed.
And it is not just careers. Every serious idea in computing is laziness with a formal name. Caching is refusing to compute twice. Memoization is refusing to recurse twice. Dynamic programming is refusing to solve a subproblem twice. The KV cache that makes running a language model affordable is one more refusal to redo work you already did.
School spends twelve years paying you for grinding. The market pays exclusively for skipping. Nobody tells you the rules changed.
He tells his first years, in three words, in the middle of a Fourier series.
A guy I know cut his working week from 70 hours to 12 and tripled his income in a year. The whole thing started with three words from an Oxford maths lecture.
The words are: be lazy.
The clip is from an Oxford Mathematics lecture on Fourier series. Whiteboard full of integrals from minus pi to pi. He stops in the middle of a derivation, turns to the room, and says this is the one thing he tells all his students.
You can grind through the calculation. Or you can step back and ask whether there is a trick that gets you there without doing a lot of work. His answer to the room is that yes, there almost always is.
Look at what he points at. The integral on that board never gets computed. It gets dismissed, because the function is periodic and the interval is symmetric, and the moment you see that, the work was never necessary.
Noticing the symmetry is the skill. The computation is what you do after you failed to notice it.
The guy I mentioned wrote data pipelines. Hardest worker on his team, last one promoted, because effort was the only thing he was selling and effort is the cheapest thing on the market.
He changed one habit. Ten minutes before every ticket, asking whether the ticket needed to exist.
That quarter he deleted more code than he wrote. Two services went away. A report that cost a team three days a month became a query that ran in four seconds. He stopped being the person who closed tickets and became the person who made them stop appearing.
The offers started after that. Nobody has ever paid six figures for typing speed.
And it is not just careers. Every serious idea in computing is laziness with a formal name. Caching is refusing to compute twice. Memoization is refusing to recurse twice. Dynamic programming is refusing to solve a subproblem twice. The KV cache that makes running a language model affordable is one more refusal to redo work you already did.
School spends twelve years paying you for grinding. The market pays exclusively for skipping. Nobody tells you the rules changed.
He tells his first years, in three words, in the middle of a Fourier series.
A guy made 100,000 dollars in a single month selling a math course he did not create, did not own, and did not pay a cent for.
The course is MIT 18.01, Single Variable Calculus, Fall 2007. David Jerison, chalk, one locked camera. MIT put it online under Creative Commons and anyone on earth can watch it right now for free.
He was not the teacher. He was the guy who noticed something in the numbers.
Millions of people start Lecture 1. Almost nobody reaches Lecture 4, the chain rule, which is where the course stops being arithmetic and starts being the thing that actually pays. The lectures were never the bottleneck. Finishing them was.
So he did not record anything. He opened a room, put 40 people in it, and they watched Jerison together on a schedule. Same free video. Fixed time every week. A place where you had to say out loud that you did not understand the last step.
He charged for the schedule and the room, not for the math.
First cohort was 40 people. By the third he was turning people away, because completion rate was above 80 percent and people were posting screenshots of finishing a course they had abandoned twice before.
Month four he crossed six figures. The product cost him nothing but the calendar invite.
The lesson under it is uncomfortable. The best calculus teaching in the world has been free for twenty years and the market barely moved, because knowledge was never the scarce thing. Attention, structure and someone waiting for you on Thursday, that is the scarce thing.
Jerison gave away the hard part in 2007. The easy part is still worth 100,000 dollars a month.
Watch Lecture 4. It is free. It always was.
A guy made 100,000 dollars in a single month selling a math course he did not create, did not own, and did not pay a cent for.
The course is MIT 18.01, Single Variable Calculus, Fall 2007. David Jerison, chalk, one locked camera. MIT put it online under Creative Commons and anyone on earth can watch it right now for free.
He was not the teacher. He was the guy who noticed something in the numbers.
Millions of people start Lecture 1. Almost nobody reaches Lecture 4, the chain rule, which is where the course stops being arithmetic and starts being the thing that actually pays. The lectures were never the bottleneck. Finishing them was.
So he did not record anything. He opened a room, put 40 people in it, and they watched Jerison together on a schedule. Same free video. Fixed time every week. A place where you had to say out loud that you did not understand the last step.
He charged for the schedule and the room, not for the math.
First cohort was 40 people. By the third he was turning people away, because completion rate was above 80 percent and people were posting screenshots of finishing a course they had abandoned twice before.
Month four he crossed six figures. The product cost him nothing but the calendar invite.
The lesson under it is uncomfortable. The best calculus teaching in the world has been free for twenty years and the market barely moved, because knowledge was never the scarce thing. Attention, structure and someone waiting for you on Thursday, that is the scarce thing.
Jerison gave away the hard part in 2007. The easy part is still worth 100,000 dollars a month.
Watch Lecture 4. It is free. It always was.