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Over a decade ago, a math professor in Chennai opened his first lecture with the simplest idea in all of math, and it is the exact thing every prediction market runs on today. NPTEL filmed it. it has been free ever since. 759,000 people have watched it, almost none...

27,825 görüntüleme • 20 gün önce •via X (Twitter)

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Ten million people have watched an MIT professor teach a course whose first lecture is literally titled "What is a Derivative?" Almost none have written down the two-line answer. He filmed the lecture once in the fall of 2007 and it has been on YouTube ever since. Math tutors charge $200 an hour to teach a diluted version of what he covered in 50 minutes for free. His name is David Jerison. He is a professor of mathematics at MIT and the instructor of 18.01 Single Variable Calculus, one of the most-watched math courses in the history of the internet. The 50-minute clip in this video is Lecture 1, filmed at MIT in the fall of 2007. Jerison is deriving the definition of a derivative from a single tangent line. The whole framework fits on a napkin. A derivative is just how much y changes when x moves a tiny bit. Draw a tangent line to any curve at any point. The slope of that line is the derivative. Memorize one formula, the power rule, and you can differentiate every polynomial on earth in your head. Chain that with a handful of exceptions and you can differentiate almost every function humanity has ever written down. That single set of rules is what every neural network runs on gradient descent, what every rocket landing at SpaceX solves in real time, and what every options desk at Goldman Sachs is running behind every quote you see on the screen. "In mathematics you don't understand things. You just get used to them." That is John von Neumann, the mathematician who helped design the atomic bomb and invent the modern computer. Jerison returns to the same idea in every lecture. Almost no student giving up on calculus has heard von Neumann say it out loud. Every quant fund on Wall Street pays entry-level analysts $250,000 to know the same power rule Jerison derives on the board. Every AI bootcamp charges tens of thousands to teach a diluted version of the same equation on a laptop. The lecture is free on MIT OpenCourseWare. The textbook is under sixty dollars. Almost none of the millions who watched have ever taken the power rule and applied it to their own numbers on their own paper. The math is free. The willingness to actually take one derivative before your next model, trade, or engineering trade-off is the entire edge.

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24,218 görüntüleme • 14 gün önce

A Yale professor recorded 26 hours of undergraduate financial theory in 2009 that quietly runs every mortgage desk, credit hedge fund, bank stress test, and repo market on earth. Yale charges $86,000 a year to sit in that classroom. He posted the entire course to YouTube for nothing. Millions have opened lecture one. Almost no retail trader has finished all twenty-six. His name is John Geanakoplos. He is the James Tobin Professor of Economics at Yale and co-founder of Ellington Capital Management, one of the largest mortgage hedge funds on Wall Street. He called the 2008 crash in a public lecture eight years early. The 75-minute clip in this video is one lecture from ECON 251 Financial Theory, filmed in the fall of 2009 at the MacMillan Center at Yale. The diagram on the board behind him looks trivial. It is the exact math that decides whether a bank stays solvent, whether a housing market corrects gently, and whether a mortgage fund survives a bad quarter. Geanakoplos covers the entire mathematical foundation of collateral, leverage, and financial crises in one semester. The Leverage Cycle. His original equation. Asset prices rise faster than fundamentals in booms and collapse harder in busts. Ellington priced every mortgage bond through 2008 with it. Collateral equilibrium. The price of an asset depends on who is allowed to borrow against it and how much. Not on discounted cash flow. Every housing bubble in history is a story about collateral. CDS and tranching. The math that turned $200 billion of subprime mortgages into $1.2 trillion of AAA bonds. Geanakoplos drew the diagram at Yale in 2005 and told his students the pool would default. Merrill, Citi, UBS, and Bear Stearns held it until it did. The natural buyers theory of price. A small number of optimists sets the price of every risky asset on earth. Remove their leverage and the market crashes faster than any change in fundamentals. By December 2007 Merrill had written down $9 billion, Citi $10 billion, UBS $13.7 billion. Total announced bank losses hit $52 billion. Geanakoplos had drawn the exact math for that outcome on the board two years earlier. Every mortgage desk on Wall Street pays entry-level analysts $250,000 to know this material before they walk in. Every senior MBS trader is paid $500,000 to remember it under pressure. Every central banker learns half of it and pretends the other half does not exist. "The most important variable in any market is not the interest rate. It is the collateral rate." That is a sentence Geanakoplos has repeated in every public lecture for twenty-five years. Bernanke ignored it in 2007. Every retail trader ignores it today. The lectures are free on Yale Open Courses. The Leverage Cycle paper is under thirty pages. The textbook chapters are free. The math is free. The willingness to sit through 26 hours of financial theory before opening a leveraged position, buying a mortgage ETF, or holding a bank stock through the next credit tightening is a much rarer commodity than the confidence to walk in without it.

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16,139 görüntüleme • 28 gün önce