October 1998. Warren Buffett, 68, faces a room of MBA students. Before he says a word about stocks, he gives them a test.
Imagine you could buy 10% of one classmate's earnings for the rest of their life. Who do you pick?
Not the highest IQ. Not the best grades. Everyone in the room is smart and driven. You'd pick the one who's honest, generous, gives others credit, and people want to follow.
Then the twist: you also have to short one classmate. You wouldn't pick the least intelligent. You'd pick the one who's egotistical, greedy, and cuts corners.
His point: none of these qualities are talent. Every good one can be learned. Every bad one can be dropped. But habits harden with age, so the time to choose them is now.
He borrows a rule from an Omaha businessman who hired for integrity, intelligence and energy. Without the first, "you want them dumb and lazy."
The lesson: you already own 100% of yourself. Become the person you'd pay to own 10% of.
October 1998. Warren Buffett, 68, faces a room of MBA students. Before he says a word about stocks, he gives them a test.
Imagine you could buy 10% of one classmate's earnings for the rest of their life. Who do you pick?
Not the highest IQ. Not the best grades. Everyone in the room is smart and driven. You'd pick the one who's honest, generous, gives others credit, and people want to follow.
Then the twist: you also have to short one classmate. You wouldn't pick the least intelligent. You'd pick the one who's egotistical, greedy, and cuts corners.
His point: none of these qualities are talent. Every good one can be learned. Every bad one can be dropped. But habits harden with age, so the time to choose them is now.
He borrows a rule from an Omaha businessman who hired for integrity, intelligence and energy. Without the first, "you want them dumb and lazy."
The lesson: you already own 100% of yourself. Become the person you'd pay to own 10% of.
In 1983, Steve Jobs stood in a tent and described WiFi, the App Store, and the web, years before any of them existed. Apple stock was 10 cents that morning. It's above $200 now.
It's Bill Benter. He figured horse racing was just another counting problem. Same math, more moving parts.
He and a partner showed up with $180k and a computer. Benter spent years teaching that computer to guess one thing, the real chance each horse had to win. If his number was better than the odds the bookies gave, he bet. If not, he skipped it.
That's the whole trick. Expected value.
EV = p · b - (1 - p)
Only bet when your win chance p, at odds b, is worth more than your chance of losing.
This recording was never meant to be some hidden gem. Nobody expected Professor Tsitsiklis to hand the whole foundation away in 45 minutes, but that's exactly what happens on the board. Students in that room pay over $80,000 a year to sit through it. It's free right here. It's free right here.
Every quant, every professional bettor, every hedge fund analyst started with this exact hour. Benter just watched it and actually did the homework.
Almost nobody knows this lecture even exists. Watch it before it gets taken down.
Goldman Sachs uses this exact formula to decide if a company is worth $14,000,000.
Most of their analysts learned it from one free MIT lecture.
A Goldman recruiter once told a candidate: "If you can't derive an annuity price in under two minutes, we don't continue the interview." Starting offer for those who could: $250,000.
The formula fits on one line. MIT teaches it in 80 minutes. For free.
This is MIT 6.042J. Mathematics for Computer Science. The lecture Wall Street forgot to take down.
The professor opens with a simple question: $50,000 a year for 20 years, or $1,000,000 today?
Most people pick the million. Most people are right.
Then he shows you exactly why - with math you can verify yourself in 30 seconds.
Then the formula.
Every annuity - student loans, home mortgages, lottery payouts - is secretly just a geometric series. One formula prices all of them. He derives it live on the board using nothing but algebra.
Then Wall Street.
He explains how slight differences in interest rate assumptions - the p in the formula - let banks make money off the same instrument. Two banks, same contract, different p. One wins. He explains how that confusion caused the 2008 subprime collapse. The entire global recession. Traced back to one variable.
Then the company valuation.
A company adding $50,000 more in profit every year forever - what do you pay for it today? He plugs into the formula. Answer: $14,700,000. That is how acquisitions get priced on Wall Street.
Watch the moment he describes how people made hundreds of billions during the financial crisis while everyone else lost - "money went from one place to another." He says it casually. The room goes quiet.
A quant analyst at Bridgewater told me this was the first lecture that made financial modeling feel like arithmetic. Starting salary: $350,000. Bonus year: $900,000.
MIT 6.042J Lecture 12 | Mathematics for Computer Science | Fall 2010
an insurer isn't just pricing how likely you'll need a payout, it's pricing how differently you'll act once covered.
jonathan gruber, mit, 14.01, social insurance.
adverse selection: insurers can't see true risk the way you can, higher risk people buy more coverage, raising the average premium.
then the impossible part: moral hazard compounds it, fire cover reduces upkeep on extinguishers, health cover reduces spending on prevention.
then the collapse: the rand experiment found free care spending 20 to 30% higher than cost sharing care, same health, different bill.
then the transfer: any quote prices two things, the risk he carries and the risk he picks up once covered, the second is often bigger.
watch the moment he draws fire insurance and the fire extinguisher on the same board.
a premium was never just a bet on bad luck, it was also a bet on what coverage would change.
a trade that ends at the price it started can still cost you money, calculus explains why in three lines.
denis auroux taught this at mit, course 18.02
a field is conservative when its cross partials match, one test decides everything that follows.
then the impossible part: once that holds, a closed round trip, any path back to its start, integrates to exactly zero, however convoluted.
then the collapse: the long way is a full path integral, the shortcut is one potential function evaluated twice, same answer, less work.
then the transfer: real trading cost is not that field, a round trip to his starting price still bills every leg, fees do not cancel just because price did.
watch the moment he tests the cross partials, then swaps the path integral for one function at two points.
price can return to where it started, the bill for getting it there almost never does.
THE MIT PROFESSOR WHOSE CALCULUS STUDENTS SAY NO ONE HAS EVER MADE THEM FEEL MORE CAPABLE INTRODUCES LINE INTEGRALS BY PROVING THAT SOMETIMES THE GEOMETRIC INSIGHT SOLVES IN THREE LINES WHAT THE CALCULATION TAKES HALF A BLACKBOARD TO FINISH
This is Denis Auroux, MIT, 18.02 Multivariable Calculus, Fall 2007. His students consistently rank him among the most beloved teachers in the mathematics department. He opens with one claim - vector fields and line integrals are completely different from double integrals and it actually helps to forget everything from last week.
He starts with vector fields. At every point in the plane you have a vector. Wind maps are vector fields. Gravitational fields are vector fields. The field xi plus yj points radially outward from the origin and grows with distance. The field minus yi plus xj rotates everything counterclockwise at unit angular velocity. A particle of fluid in that field traces a perfect circle and returns to its starting point in exactly two pi units of time.
Then work. When a force pushes a particle along a trajectory the work done is the force dotted with the displacement. For a straight line and constant force this is simple multiplication. For a curved trajectory where the force changes at every point you cut the path into infinitely many tiny pieces, dot the force with each tiny displacement, and sum. That sum is the line integral.
Then computation. Parameterize the curve with a single variable. Express x and y in terms of that variable. Replace dx and dy with their derivatives times dt. The two-dimensional integral collapses into a single ordinary integral you already know how to solve.
Then the geometric shortcut. The line integral equals the integral of the tangential component of the force along the curve. If the force is always perpendicular to the curve the work is zero with no calculation needed. The field xi plus yj on a circle of radius a gives zero immediately because the radial force is always perpendicular to the circular path. The field minus yi plus xj on the same circle gives two pi a squared immediately because the force always points exactly along the path with magnitude a.
Watch the moment he computes the same integral two ways side by side. The geometric method takes three lines. The parametric method takes half a blackboard. Same answer. The insight about perpendicularity or parallelism does in seconds what algebra does in minutes.
A mechanical engineering student I know rewatched this lecture before a problem set on conservative force fields. Said it was the first time the dot product felt like it was measuring something physical rather than producing a number.
Paul Samuelson was the first American to win the Nobel Prize in Economics. He spent his career proving that ordinary people should not try to beat the market. He also quietly beat the market himself for 60 years. His last full-length interview explains how. Almost nobody has watched it.
Samuelson taught at MIT for 65 years, from 1940 until he died in 2009. His textbook "Economics" sold roughly four million copies. He rewrote the field. Every finance professional working today learned economics from a book he wrote or a book written by his students.
He also ran his own money quietly. His returns reportedly outpaced most active managers of his era, and he was an early investor in Warren Buffett's Berkshire Hathaway. He never advertised the numbers. He said the opposite in public. His most famous line about investing:
"Investing should be more like watching paint dry or watching grass grow. If you want excitement, take $800 and go to Las Vegas."
He was one of the earliest advocates for index funds. He believed almost nobody could beat the market and almost nobody should try. His nephew Larry Summers became Treasury Secretary. His students founded half the modern economics profession. He was invited into every important economic policy debate of his lifetime.
His view on personal finance was unusually blunt for a Nobel laureate. In one of his final interviews, near the end of his life, he explained his framework in three sentences. Personal finance is not a science. It is a set of common-sense decisions repeated for decades. Save more than you spend. Diversify. Do not chase excitement. Do not trust anyone who promises certainty. He said these things thousands of times over 70 years and the industry ignored him every year.
The full interview covers his childhood, his years at Chicago and Harvard, his rise at MIT, his Nobel, and his philosophy on money. He was 94 years old at the time. His voice is thin and his answers are direct. He does not soften anything. He treats the interviewer like a graduate student who happens to be holding a camera.
The more sophisticated a market becomes, the more valuable the boring advice becomes. Every investor who ignored Samuelson's rules is a receipt for how right he was. Every quant who read his mathematics and skipped his common sense missed the point.
Samuelson died December 2009. He was 94. His textbook is still in print. The interview is free.
you have been pricing your options with math that assumes the chart underneath has a slope, and it never does.
choongbum lee teaches this at mit, course 18.s096
model a stock as brownian motion, squaring its wiggle over a tiny instant gives back the instant itself, not its square, calculus is wrong here.
then the impossible part: the price path never jumps, continuous everywhere, yet has no slope anywhere, drawn with no lifted pen, never a tangent.
then the collapse: itō's lemma exists because of that rule, it adds a second term classical calculus never carries, itō calculus needs both.
then the transfer: any option price you estimate with ordinary growth math is missing that term, the gap moves one direction, always.
watch the moment he writes the second term on the board and says calculus stops there.
after this, a smooth chart stops meaning a predictable one.
You can hand a stranger your money with no contract and no way to make him pay it back, and the math says people do it anyway.
frank schilbach teaches this at mit, course 14.13, free on mit ocw.
player one gets $10, sends any share to player two, it triples in transit, player two decides how much, if any, to return, no obligation.
then the impossible part: the rational move is send $0, player two has no reason to return it, yet real players sent $5.16 on average.
then the collapse: the average return was $4.66, the sender ended with $9.50, less than the $10 he started with, trust didn't pay for itself and people sent it.
then the transfer: any deal with no contract runs on this reciprocity, and what's worth risking tracks how visible it is.
watch the moment he tallies how much came back, and it isn't zero.
after this, deals trusted on a handshake stop looking irrational.
In 1999 a baseball player saved $3,000 a year starting at age 22 and never saved another dollar after age 37.
He retired at 70 with $703,000.
His coworker saved nothing for the first 15 years. Then saved $3,000 every single year until retirement. Same amount per year. Twice as many years. Disciplined. Patient.
He retired with $356,000.
Half as much. For saving more than twice as long.
Jonathan Gruber spends an entire lecture on the reason in MIT's introductory economics course. A dollar saved today compounds on itself. It earns interest on the interest. The earlier money goes in, the more time it has to multiply before you touch it.
That gap between $703,000 and $356,000 is not about discipline. It is not about sacrifice. It is about arithmetic and a calendar.
Which means every savings account has two numbers. The amount. And the when.
Max Scherzer signed a $210 million baseball contract. That was not $210 million. It was $15 million a year for 14 years, spread past his playing career. In present value terms at 4.7% interest, it was worth $166 million. Still a lot of money. But it dropped him from the second most valuable pitcher contract in history to the fourth.
He negotiated the number. Nobody negotiated the date.
A $290 million lottery jackpot paid over 20 years at 7% interest is worth $164 million today. The advertised number is not the real number. The real number is always smaller. How much smaller depends entirely on when you receive it and what you could have earned in between.
The people who understand this do not earn more money. They earn the same money at better times.
Four ways to make money. Wages arrive now and stop when the work stops. Capital arrives later and multiplies while it waits. The difference between them is not effort. It is which side of the interest rate you are sitting on.
Jonathan Gruber taught this at MIT for 25 years. His students helped design legislation covering 330 million people. The ones who went to finance started at $250,000.
They all learned it in the same lecture.
bookmark this and watch later - after this lecture every salary offer you receive will feel like a number waiting to be placed on a timeline
A 2 dollar lottery ticket with a 1 in 300 million chance of a 500 million dollar payout has an expected value of negative 33 cents. A 30 thousand dollar car insured against theft in a neighborhood where 1 in 200 cars is stolen a year is worth positive 150 dollars in expected value.
The math to compute either one takes 4 seconds. Almost no one runs it.
Andrew Lo has been teaching Session 1 of MIT 15.401 since 2003. The Fall 2008 recording sits free on MIT OpenCourseWare. Every decision his students will ever make, from a stock trade to a job offer to which route to drive home, reduces to the same 4-second calculation. Expected value equals probability times payoff.
Institutional desks run it before every trade. Retail investors run it before none. The gap between them has a name and it is not luck.
The math is free. The willingness to run it before you sign is the entire fortune.
The hedge fund manager who taught Michael Burry to pick stocks accidentally destroyed the mutual fund industry in a free Talks at Google lecture on the two-line formula that turned $10,000 into $8.3 million.
His fund charged 2 and 20. He gave the strategy away in a $12 book.
Almost no one paying a financial advisor 1 percent of their retirement has finished the lecture.
His name is Joel Greenblatt. He founded Gotham Capital in 1985 and compounded roughly 40 percent a year for twenty consecutive years. He returned all outside capital in 1994 because his edge was too crowded to scale.
He has been teaching value investing at Columbia Business School every year since 1996. Michael Burry - the doctor who shorted the housing bubble in "The Big Short" - learned to pick stocks from Greenblatt's 1997 book.
The 55-minute clip in this video is Greenblatt at Google in 2017 walking a room of engineers through his Magic Formula.
The whole framework fits on one napkin. Rank every stock in the S&P 500 by return on invested capital, highest first. Then rank every stock by earnings yield, highest first. Sum the two rankings. Buy the top twenty. Hold for one year. Sell. Repeat.
That single formula would have beaten the S&P 500 by roughly 14 percent a year over the last three decades if any retail investor had actually followed it.
"Cheap and good beats expensive and average. Every time."
That is Joel Greenblatt at Google in 2017. He has repeated the sentence in every public talk since. Almost no retail investor buying Nvidia at $140 has heard it.
Every hedge fund on Wall Street pays $500,000-a-year analysts to backtest more sophisticated versions of the same equation. Every financial advisor in America charges you 1 percent of your account per year to underperform it.
The Talks at Google video is free on YouTube. "The Little Book That Beats the Market" is twelve dollars on Amazon.
Almost none of the millions who watched have ever run the two-line formula on their own portfolio.
The framework is free. The willingness to actually run it before your next stock pick, retirement rebalance, or brokerage transfer is the entire edge.
A lawyer walks into a casino, buys $3.35 million in chips, and walks out without playing a single hand.
Why?
Atlantic City, December 1990. The casino is Trump Castle. The money belongs to Fred Trump, and the man who needs it is his son. Donald has an $18.4 million interest payment due, and analysts doubted he could make it. The chips are a secret loan. Regulators later ruled it illegal.
Eight months earlier, Donald Trump sat down with Larry King, two weeks after opening the biggest casino in the world.
"The Taj Mahal is a tremendous success. The things that I do are trophies."
Now do the math. The Taj was built on $675 million of junk bonds at 14% interest. That is $94.5 million a year, or about $259,000 every day, on the bonds alone. In its first 16 days, the state's own records show the Taj's bank account went below zero on four of them. In total, Trump owed $3.4 billion, and he had personally guaranteed $832.5 million of it.
By August, contractors had sued for as much as $80 million. Regulators warned that a complete financial collapse of the Trump Organization "was not out of the question." The banks capped his personal spending at $450,000 a month.
A year later, he was walking down Fifth Avenue with Marla Maples when he saw a man with a tin cup outside Tiffany. He told Esquire what he said to her: "that man is worth $900 million more than I am."
In public, he called it a trophy. In private, he knew he was worth less than a man with a tin cup.
So why didn't the banks finish him? The lawyer who represented them as a group said it was no longer about a bank and a piece of real estate. It was "a bank and Trump's actual survival."
Sit with that for a second. Three casinos went through bankruptcy and he gave up half of the Taj. Yet between 1990 and 1996, the Wall Street Journal found he still pulled more than $160 million out of Atlantic City. You read that right.
In 1995, he reported a $916 million loss on one tax return. In 2004, he was hosting The Apprentice. In 2016, he won the presidency.
Owe the bank a little and it owns you. Owe it enough and it needs you to survive. Almost nobody learns this, because people who test it at your size get liquidated, not restructured.
Before you size your next trade, ask one thing: if it goes wrong, whose problem is it?
This man teaches at a community college in California.
His salary: around $800,000 a year.
The engineers who passed calculus because of him: $1,800,000 to start.
He has more calculus students than Harvard, MIT, and Stanford combined.
This is Professor Leonard's Calculus 2, Lecture 6.2. Free on YouTube.
Professor Leonard has taught calculus on YouTube for over a decade. His channel has millions of subscribers across 150 countries. Every major university has students who watch him the night before their exam.
Then the concept.
An inverse function is a machine that undoes another machine. If a function takes 2 and gives you 8, the inverse takes 8 and gives you back 2. Finding an inverse means switching every x and y in the equation and solving for y again. The graph flips across the line y = x like a mirror.
Then the problem.
Sometimes it is easy to find the inverse. Sometimes it is impossible to write it explicitly. A function like 3π sin x + sin x cannot be solved for x with algebra. You have to think. What angle makes the whole thing equal to 1? You work backwards through the unit circle until the answer appears.
Then the shortcut.
If you want the derivative of an inverse at a point, you do not need the inverse itself. You only need the derivative of the original function. The formula: the derivative of the inverse at a point equals 1 divided by the derivative of the original function evaluated at the switched point. The inverse flips the coordinates, so you flip where you plug in.
Watch the moment he shows why G prime of 8 equals 1/12 without ever writing the inverse function.
Every engineering student memorizes the derivative rules. Professor Leonard's lecture is the one that shows why the inverse derivative formula is just those same rules run backwards.
A software engineer at a semiconductor company in Austin said Professor Leonard's channel is the reason she passed Calculus 2 on her second attempt. She graduated, joined the company, and now makes $165,000 a year.
Bookmark this and watch later - after this lecture every inverse problem on your exam will feel like a question you already answered.