Abyzon

Content creator | Know what you need | Lectures are the path to the future

[Abyzon @Abyzonn]

HARVARD FILMED THE LECTURE WHERE THEIR MOST CELEBRATED STATISTICS PROFESSOR DESTROYS THE WAY EVERY STUDENT THINKS ABOUT AVERAGES - AND SHOWS WHY THE SMARTEST SHORTCUT IN ALL OF PROBABILITY HAS BEEN HIDING IN PLAIN SIGHT SINCE THE FIRST DAY OF CLASS

This is Joe Blitzstein, Harvard, Statistics 110, lecture 9. He has won Harvard's Excellence in Teaching award multiple times and his course has been taken by over 2 million people across 190 countries. He opens with one claim - the expected value of a sum always equals the sum of the expected values. Always. Even when the variables are dependent.

He starts with a weighted average. Five ones, two threes, one five. You can add all eight numbers and divide by eight. Or you can group them, weight each group by its frequency, and average that way. Same answer. This is the entire idea behind expected value - weight each possible outcome by its probability and sum.

Then the fundamental bridge. Define an indicator random variable - one if an event occurs, zero otherwise. Its expected value equals the probability of the event. One equation. It connects every probability question to an expected value question and back. You can solve problems either way.

Then linearity in action. The expected value of a binomial takes one page of algebra using the definition - factorial manipulation, index shifts, the binomial theorem applied twice. Using linearity it takes one sentence. A binomial is a sum of n independent Bernoullis. Each Bernoulli has expected value p. The answer is np.

Then the hypergeometric. Drawing five cards from a deck, counting aces. The PMF involves products of binomial coefficients - a genuine mess to compute directly. With indicator random variables and linearity the answer takes three lines. One indicator per card, each has probability 4/52 of being an ace, sum them. Five times four over fifty-two. The cards are dependent - if the first four are aces the fifth cannot be - but linearity does not care about dependence.

Watch the moment he solves the geometric distribution expected value two ways. First with calculus - differentiate a geometric series to pull a factor of k out of the exponent. Then with a story proof - write down what the expected value must satisfy, use the memoryless property of the coin, solve a one-line equation. No calculus. No summation. Just the structure of the problem.

A data scientist I know rewatched this lecture before a technical interview on probability. Said it was the first time linearity felt like a superpower rather than a property to memorize.

Free on YouTube, Harvard, over 2 million views.

bookmark this and watch later - after this lecture every complicated probability calculation you face will feel like a sum of simple indicators waiting to be separated

[Abyzon @Abyzonn]

https://t.co/0ZZ9ecKpbk

[Abyzon @Abyzonn]

A MATHEMATICIAN WHO SPENT DECADES TEACHING AT MIT WALKED INTO A LECTURE HALL AND PROVED THAT HURRICANES AND TORNADOES ARE JUST PLACES WHERE ONE NUMBER BECOMES VERY LARGE - AND HOW THAT SAME NUMBER TELLS YOU WHETHER A FORCE FIELD CAN DO FREE WORK

This is Denis Auroux, MIT, 18.02 Multivariable Calculus, lecture 21. The same course that has been free on OpenCourseWare since 2007 and taken by engineers and physicists worldwide for nearly two decades. He opens with one claim - if a vector field is a gradient field, the work it does depends only on where you start and where you end. The path in between is irrelevant.

He starts with the test. If a vector field has components M and N, take the partial of M with respect to y and the partial of N with respect to x. If those two numbers are equal everywhere the field is defined, the field is a gradient. If they differ anywhere, it is not. One comparison. That is the entire test.

Then the two methods for finding the potential. The first is to pick a path from the origin to any point, break it into two legs - first along the x axis, then straight up - and integrate the field along each leg. The calculation on each leg loses one term because either dx or dy vanishes. What remains is two simple integrals that add to the potential function. The second method avoids integrals entirely. Integrate the first component with respect to x, allow the constant of integration to be a function of y, differentiate the result with respect to y, and match against the second component to find that function.

Then the curl. Define curl F as the partial of N with respect to x minus the partial of M with respect to y. If this number is zero the field is conservative. If it is nonzero the field has rotation. A constant field moving everything in one direction has curl zero. A radial field pushing everything outward from a center has curl zero. The rotation field that spins everything counterclockwise has curl two - exactly twice the angular speed of the rotation.

Watch the moment he explains what curl means for a velocity field. Drop something that floats into a fluid. The curl at that point tells you exactly how fast the object will spin. In weather prediction the regions of high curl are hurricanes and tornadoes. The sign of the curl tells you which direction they rotate. One number. All of that.

A fluid dynamics engineer I know rewatched this lecture before building a vortex detection algorithm for a simulation pipeline. Said it was the first time curl felt like a physical measurement rather than a formula involving partial derivatives.

Free on YouTube, MIT OpenCourseWare, Creative Commons license.

bookmark this and watch later - after this lecture every swirling pattern you see will feel like a region where one number refused to be zero

[Abyzon @Abyzonn]

https://t.co/0ZZ9ecKpbk

[Abyzon @Abyzonn]

MIT FILMED THE LECTURE WHERE THEIR MOST DECORATED COMPUTER SCIENCE PROFESSOR EXPLAINS THE MATHEMATICS THAT PROTECTS EVERY BANK TRANSFER AND PRIVATE MESSAGE ON EARTH - AND SHOWS WHY ALAN TURING SOLVED IT 40 YEARS BEFORE ANYONE PUBLISHED IT

This is Marten van Dijk, MIT, 6.042J Mathematics for Computer Science, lecture 5. He taught this course alongside Tom Leighton - the professor who co-founded Akamai Technologies, whose content delivery network now moves a third of all internet traffic on earth. He opens with one claim - number theory is not abstract mathematics. It is the engine running inside every encrypted message ever sent.

He starts with Turing's first code. Take a message, translate it into a prime number, multiply by a secret prime key. To decrypt, divide by the key. The math is four lines. Then he shows how to break it in two. If you intercept two encrypted messages, compute their greatest common divisor. Since both are products of primes sharing the same key, the GCD is the key itself. The entire scheme collapses in one calculation.

Then Turing's second attempt. Instead of multiplying by the key, multiply and take the remainder after dividing by a public prime. Now division no longer works. You cannot simply divide a remainder. This is where modular arithmetic enters - and with it the concept of a multiplicative inverse. A number that when multiplied by k gives a remainder of 1. Not division. Something stranger and more powerful.

Then the known plaintext attack. If an attacker intercepts one message and knows what it said before encryption, they can compute the multiplicative inverse of the plain message, multiply it by the encrypted version, and recover the secret key. One leaked message breaks the entire system for every future message. Turing's second scheme falls the same way the first did.

Then Euler's totient function. Count how many integers below n share no common factor with n. Call that number phi of n. Euler's theorem says that if k shares no factor with n, then k raised to the power phi of n leaves a remainder of 1 when divided by n. The proof takes twenty minutes and three lemmas. The conclusion fits in one line.

Then RSA. Invented at MIT in 1977 by Rivest, Shamir and Adleman, who received the Turing Award for it. Generate two large primes. Multiply them to get n. Choose an encryption exponent e. Publish e and n as the public key. Keep the secret exponent d. Anyone can encrypt using the public key. Only the holder of d can decrypt. Breaking the scheme requires factoring n back into its two primes. Nobody has found an efficient way to do that in 47 years.

Watch the moment he proves that decryption actually recovers the original message. He applies Fermat's little theorem twice - once for each prime factor of n - and lands back at m. The proof uses every tool built in the lecture. Each one placed there for exactly this moment.

A security engineer I know rewatched this lecture the week before designing an authentication system. Said it was the first time RSA felt like a mathematical proof rather than a black box someone told him to trust.

Free on YouTube, MIT OpenCourseWare, Creative Commons license.

bookmark this and watch later - after this lecture every padlock icon in your browser will feel like a 300 year old theorem standing between your data and everyone else

[Abyzon @Abyzonn]

https://t.co/0ZZ9ecKpbk

[Abyzon @Abyzonn]

THE PROFESSOR WHOSE TEXTBOOKS SIT IN OVER 3000 UNIVERSITIES SHOWS IN 30 MINUTES WHY NEWTON'S METHOD HAS SURVIVED 400 YEARS UNCHANGED - AND WHY FOLLOWING A STRAIGHT LINE IS ALMOST ALWAYS GOOD ENOUGH

This is Gilbert Strang, MIT, a lecture on linear approximation and Newton's method. He opens with one sentence - both ideas come from the same place. Delta f over delta x. In one case you know x and want f. In the other case you know f and want x. The formula is the same. The insight is the same. Follow the tangent line instead of the curve.

First example - the square root of 9.06. You cannot compute it exactly in your head. But you know the square root of 9 is exactly 3, and you know the slope of the square root function at 9 is 1/6. Go across 0.06 on the tangent line, go up 0.01, and the answer is 3.01. The error is in the fourth decimal place.

Then Newton's method for the same problem. Set up the equation x squared minus 9.06 equals zero. Start at x equals 3. The function value there is minus 0.06. The slope is 6. Newton's formula gives a correction of 0.01. New guess: 3.01. Square it: 9.0601. The error is 0.0001 - way out in the fourth decimal place.

Then the second iteration of Newton's method. Start at 3.01. The error is 0.0001. The slope is 6.02. The correction is tiny beyond what you can compute in your head. Square the new x and the error has moved to somewhere around the eighth decimal place. Each step of Newton's method roughly doubles the number of correct decimal digits.

Watch the moment he connects linear approximation to Taylor series. The linear approximation of e to the x around zero is 1 plus x. The full Taylor series is 1 plus x plus x squared over 2 plus x cubed over 6 and so on. Linear approximation is just Taylor series stopped after the first two terms. Everything after that is the error of following the straight line instead of the curve.

A numerical methods engineer I know shows this lecture to every new hire before they implement any root-finding algorithm. Said it was the first time Newton's method felt like something you would naturally invent rather than something you memorize.

Free on YouTube, MIT OpenCourseWare, Gilbert Strang at a chalkboard.

bookmark this and watch later - after this lecture every equation you cannot solve exactly will feel like an invitation to follow a tangent line

[Abyzon @Abyzonn]

https://t.co/0ZZ9ecKpbk

[Abyzon @Abyzonn]

MIT FILMED THE PROFESSOR WHOSE TEACHING STYLE HAS BEEN CALLED THE CLEAREST EXPLANATION OF LINEAR ALGEBRA EVER RECORDED - AND IN ONE LECTURE HE EXPLAINS WHAT GILBERT STRANG BUILT HIS ENTIRE CAREER ON: WHY ROW REDUCTION IS NOT JUST AN ALGORITHM BUT A PROOF THAT THE SPACE NEVER CHANGES

This is Herb Gross, MIT, Calculus Revisited Part III, lecture 3. The same professor whose calculus course has been credited by engineers and mathematicians worldwide for finally making the subject click. He opens with one observation that changes everything - if you replace any vector in a spanning set by itself plus a multiple of another vector, the space spanned does not change. That single fact is why row reduction works.

He takes four vectors in a 4-dimensional space and asks what space they span. Instead of guessing, he encodes them as rows of a matrix and row reduces. Every row operation is a legitimate replacement of a spanning vector by a modified version of itself. The space never changes throughout the entire process.

Then a zero row appears. One vector has become the zero vector - which spans nothing. This immediately proves the original four vectors are linearly dependent and the space they span has dimension at most 3. He finds exactly which vector was redundant - alpha 3 is a linear combination of alpha 1 and alpha 2 - and writes it out explicitly.

The three remaining non-zero rows form a special basis called the betas. Their structure is almost an identity matrix in the first three coordinates. This means that once you know the first three components of any vector in the space, the fourth is completely determined. A vector either belongs to the space or it doesn't - and you can check in one arithmetic step.

Watch the moment he shows that the same vector written relative to two different bases gives completely different 3-tuples - 2,5,3 versus minus 2, 4, minus 1 - yet they name the same point in space. Most confusion in linear algebra comes from forgetting which basis you are using.

A graduate student I know rewatched this lecture before their qualifying exam in abstract algebra. Said it was the first time basis change felt like something geometric rather than something algebraic.

Free on YouTube, MIT OpenCourseWare, Creative Commons license.

bookmark this and watch later - after this lecture every matrix you row reduce will feel like a proof rather than a calculation

[Abyzon @Abyzonn]

https://t.co/0ZZ9ecKpbk

[Abyzon @Abyzonn]

MIT FILMED A LECTURE PROVING THAT NO MATTER HOW CLEVER YOUR CASINO STRATEGY IS - IF THE GAME IS FAIR YOU CANNOT WIN IN EXPECTATION - AND THE PROOF USES THE SAME MATH THAT RUNS EVERY STOCK PRICING MODEL ON WALL STREET

This is an MIT probability lecture, course 6.041, on stochastic processes. The professor opens with the simplest possible random walk - flip a fair coin, go up $1 or down $1, repeat forever. By the central limit theorem after t steps you will be within roughly the square root of t of where you started. Not t steps away. Square root of t. The process stays surprisingly close to zero even after millions of steps.

Then the gambler's ruin problem. You play until you win $100 or lose $50. What is the probability you win? By symmetry alone you might guess 1/2. The actual answer is 1/3. The formula is exact - if the two boundaries are A and B, the probability of hitting B first is A divided by A plus B. Derived in 5 lines using only the memoryless property of the random walk.

Then Markov chains. A stochastic process where the entire effect of the past on the future is captured by the current state alone. The transition probability matrix contains everything - multiply it by itself n times and you get the n-step probabilities. By the Perron-Frobenius theorem, any Markov chain with all positive transition probabilities converges to a unique stationary distribution regardless of where it started.

Then martingales - stochastic processes where the expected future value always equals the present value. A fair game. The optional stopping theorem proves that no stopping strategy - no matter how clever - can give you positive expected profit from a martingale. If the game is truly fair, you cannot win in expectation. Full stop.

Watch the moment he applies the optional stopping theorem to the gambler's ruin problem and recovers the exact 1/3 probability in two lines of algebra - the same answer that required a full recursive argument before.

A quantitative trader I know used this lecture to explain to his team why a certain options strategy that looked profitable on paper had zero expected value. Said the optional stopping theorem ended the argument in 30 seconds.

Free on YouTube, MIT OpenCourseWare, Creative Commons license.

bookmark this and watch later - after this lecture every "guaranteed" trading strategy will feel like a stopping time waiting to be analyzed

[Abyzon @Abyzonn]

https://t.co/0ZZ9ecKpbk

[Abyzon @Abyzonn]

https://t.co/0ZZ9ecKpbk

[Abyzon @Abyzonn]

HARVARD FILMED THE FIRST LECTURE OF THEIR MOST POPULAR STATISTICS COURSE - TAUGHT BY A PROFESSOR WHOSE STUDENTS CALL HIM THE BEST TEACHER THEY HAVE EVER HAD - AND IT PROVES WHY EVEN ISAAC NEWTON GOT PROBABILITY WRONG

This is Joe Blitzstein, Harvard, Statistics 110, lecture 1. He has won Harvard's Excellence in Teaching award multiple times, his textbook Introduction to Probability is used in over 200 universities worldwide, and his online course has been taken by over 2 million people across 190 countries. He opens by saying that after a few weeks of this course you will easily solve calculations that 300 years ago required consulting Isaac Newton - and Newton's intuition was still wrong.

He traces probability to Fermat and Pascal writing letters back and forth in the 1650s analyzing gambling games. No one had mathematically derived the rules before. They invented the subject by betting on dice in correspondence. Then he shows why the naive definition - probability equals favorable outcomes divided by total outcomes - breaks immediately. Ask what the probability of life on Neptune is. Either there is or there isn't. By the naive definition the answer is 1/2. So is the probability of intelligent life on Neptune. Something is severely wrong.

Then the multiplication rule. Two types of ice cream cone and three flavors gives 6 combinations - not because you memorized it but because you can draw a tree and count branches. Every counting problem in the course is just a bigger version of that tree. Then binomial coefficients - n choose k counts the number of ways to select k objects from n when order doesn't matter. The full house in poker falls out in 4 lines of multiplication once you understand the tree.

Watch the moment he fills in the sampling table - with or without replacement, order matters or doesn't. Three of the four boxes are immediate from the multiplication rule. The fourth requires a proof he saves for next lecture. That one box is harder than the other three combined.

A data scientist I know rewatched this lecture before switching careers into statistics. Said it was the first time probability felt like a system with rules rather than a collection of tricks.

Free on YouTube, Harvard, over 2 million views.

bookmark this and watch later - after this lecture you will never again confuse equally likely with obviously true

[the lich @thelichhh]

https://t.co/aqsY18NvVz

[Abyzon @Abyzonn]

A TEENAGE MATH OLYMPIAD CHAMPION WHO BECAME THE YOUNGEST FULL PROFESSOR IN UCLA HISTORY AND ONE OF THE MOST DECORATED MATHEMATICIANS ALIVE SPENT AN HOUR PROVING THAT ELLIPTIC CURVES ARE SECRETLY HIDING INSIDE THE SIMPLEST QUESTIONS ABOUT DRAWING LINES ON PAPER

This is Terence Tao, UCLA, Minerva Lectures at Princeton, 2013. He won 4 Math Olympiad medals before age 18, received the Fields Medal at 31, and publishes research across more areas of mathematics simultaneously than most mathematicians touch in a lifetime. He was introduced by Manjul Bhargava as someone whose writings are read by the Princeton math department pretty much every day.

He opens with a question that sounds like a puzzle for children. Draw n points on a plane, not all on one line. How few ordinary lines - lines passing through exactly 2 of your points - can you have? Sylvester asked this in 1893. The first published proof that at least one ordinary line must exist appeared in 1944.

The answer turns out to be at least n/2 for even n and 3n/4 for odd n - and the configurations that achieve these minimums are not random. They come from taking equally spaced points on a circle plus points at infinity, or from taking finite subgroups of elliptic curves. A question about counting lines has elliptic curves as its extremal examples.

The proof uses Euler's formula from topology - vertices minus edges plus faces equals 2 - applied to the dual configuration of points and lines. Every face must have at least 3 sides. Every edge touches 2 faces. These constraints force the dual picture to look like a triangular grid, which forces the original configuration to contain hexagonal patterns, which the Cayley-Bacharach theorem forces onto cubic curves.

Watch the moment he explains the Cayley-Bacharach theorem. If a cubic curve passes through 8 of 9 special points, it must pass through the 9th. No choice. This 19th-century result is what forces elliptic curves to appear in a problem about counting lines.

A combinatorialist I know showed this lecture to his research group before starting a new project on point-line incidences. Said it was the first time they understood why algebraic geometry keeps appearing in combinatorics.

Free on YouTube, recorded at Princeton University.

bookmark this and watch later - after this lecture the next time you draw points on paper you will wonder what curve is hiding inside them

[the lich @thelichhh]

https://t.co/aqsY18NvVz

[Abyzon @Abyzonn]

ONE OF THE MOST BRILLIANT PROFESSORS IN THE WORLD EXPLAINED IN UNDER 20 MINUTES THE IDEA THAT TOOK MATHEMATICIANS 200 YEARS TO MAKE RIGOROUS - AND ALMOST NOBODY WATCHES IT

This is Herb Gross, MIT, Calculus Revisited, the professor whose teaching style has been called the clearest explanation of calculus ever recorded. Oxford students, MIT graduates and self-taught engineers credit this exact course for passing exams they had no business passing.

He opens with continuity - the idea that a function is continuous at a point if the limit equals the value. One sentence. But then he shows what breaks when it fails. A function defined as x squared minus 1 over x minus 1 approaches 2 as x approaches 1 - but at exactly x equals 1, it produces 0 divided by 0 and collapses. The graph has a hole punched in it at precisely the point you need.

Then the intermediate value theorem. If a continuous function starts at one height and ends at another, it must pass through every height in between. He proves it with a car accelerating from 20 to 30 miles per hour - at some moment it had to be going exactly 27. The curve cannot jump over a value without crossing it.

Then the connection most students miss entirely. Every differentiable function is automatically continuous - but not the other way around. The absolute value of x is continuous everywhere but has a sharp corner at 0. Continuous means unbroken. Differentiable means smooth. A smooth curve must be unbroken. An unbroken curve does not have to be smooth.

Watch the moment he writes out the proof that differentiability implies continuity in 4 lines. The whole thing hinges on multiplying by x minus a divided by x minus a - a trick so simple it looks like cheating.

A mathematics teacher I know uses this lecture before touching derivatives. Says it is the only explanation where continuity feels like something physical rather than a definition.

Free on YouTube under MIT Creative Commons license.

bookmark this and watch later - after this lecture the word "continuous" will feel less like a technicality and more like the reason calculus works at all

[the lich @thelichhh]

https://t.co/aqsY18NvVz

[Abyzon @Abyzonn]

THE MATHEMATICIAN WHOSE TEXTBOOKS HAVE TORTURED GRADUATE STUDENTS AT EVERY TOP UNIVERSITY FOR 60 YEARS GAVE ONE PUBLIC LECTURE EXPLAINING HOW A SINGLE VIBRATING STRING ACCIDENTALLY INVENTED AN ENTIRELY NEW BRANCH OF MATHEMATICS

This is Walter Rudin, University of Wisconsin, 1987. His textbook Principles of Mathematical Analysis has been the standard torture device for first-year PhD students at MIT, Harvard, Princeton and Oxford for 6 decades. The joke in mathematics departments is that you haven't suffered until you've done Rudin.

The story starts in 1750 with a vibrating string. Euler, Bernoulli and d'Alembert spent 20 years arguing about which functions could describe its motion. The argument was never resolved - but it forced mathematicians to ask a question nobody had properly asked before: what is a function?

Fourier said any function can be written as an infinite sum of sines and cosines. No proof. No conditions. Just examples that worked. His coefficients - computed by a single integral - became the foundation of signal processing, heat transfer and every compression algorithm running today.

Then Cantor tried to prove a uniqueness theorem for these series and stumbled into something nobody expected. He defined limit points to handle exceptions at finitely many points. Then countably many. Then he needed to count infinities - and discovered that the infinity of real numbers is strictly larger than the infinity of integers. Not metaphorically larger. Provably, permanently, mathematically larger.

Watch the moment Rudin explains that Cantor's diagonal argument - one of the most beautiful proofs in mathematics - wasn't even in the original paper. The uncountability of the real line came first through a completely different method.

A logician I know assigns this lecture before teaching set theory. Says students who watch it first never ask why any of it matters.

Free on YouTube, recorded at the University of Wisconsin, one fixed camera.

bookmark this and watch later - after this lecture infinity will never feel like one thing again

[the lich @thelichhh]

https://t.co/aqsY18NvVz

[Abyzon @Abyzonn]

THE PROFESSOR WHOSE STUDENTS LEAVE MIT AND LAND ROLES PAYING OVER $3.5M - JUST EXPLAINED IN 50 MINUTES WHY MOST PEOPLE LEARN LINEAR ALGEBRA COMPLETELY WRONG

This is Gilbert Strang, the most legendary mathematics professor in MIT history. Over 50 years of teaching, 3,000 universities using his textbook, and a generation of engineers who credit this exact course for everything they built after.

He opens with 4 different ways to multiply two matrices - by numbers, by columns, by rows, by blocks. All four give the same answer. Each reveals something the others hide. Most courses teach one and call it done.

Then he shows why some matrices have no inverse - not through determinants but through columns. If two columns point in the same direction, no combination escapes that line. The matrix is trapped.

The proof that kills any inverse - if a non-zero vector X gives zero when multiplied by A, then A inverse cannot exist. Because if it did, multiplying back would force X to be zero. But X is not zero. Contradiction.

Watch the Gauss-Jordan moment. Stick the identity next to A, eliminate until the left becomes the identity - whatever appeared on the right is the inverse. It just showed up automatically.

A machine learning engineer I know rewatched this before implementing backpropagation from scratch. Said it was the first time matrices felt like geometry rather than arithmetic.

Free on YouTube, MIT OpenCourseWare, 50 years of the same room and the same ideas.

bookmark this and watch later - after this lecture every matrix will feel like it either has an escape route or doesn't

[the lich @thelichhh]

https://t.co/aqsY18NvVz

[Abyzon @Abyzonn]

MIT RECORDED THIS LECTURE ON THE DIFFERENCE BETWEEN A PROOF AND "CHECKED 40 TIMES AND SEEMS TRUE" - AND IT'S THE ONLY REASON MATHEMATICS WORKS AT ALL

This is the first lecture of MIT's discrete mathematics course. The professor teaching it co-founded a company that at its peak carried a third of all internet traffic on the planet.

There's a formula that gives the right answer forty times in a row. Looks like a law of nature. On the forty-first - it breaks completely. Euler built a similar conjecture for 218 years until one mathematician disproved it with a single six-digit example.

There's a statement whose smallest counterexample has over a thousand digits. No computer on earth finds it by brute force even in a million years. And statements exactly like this one protect every bank transaction on the planet.

Then at the end - Gödel. He proved that any mathematical system either has contradictions or has questions that can never be answered. Russell and Whitehead spent 40 years of their lives trying to build the perfect system. Gödel showed up and proved it cannot exist.

Watch the moment he explains the difference between "checked a million examples" and "proved." That gap is the entire game.

A mathematician I know shows this lecture to every new student on day one. Says after it people think differently - not just about math.

Free on YouTube under MIT's Creative Commons license.

bookmark this and watch later - after this lecture the word "proven" will never sound the same.

[the lich @thelichhh]

https://t.co/aqsY18NvVz

[Abyzon @Abyzonn]

JP MORGAN ENGINEER WHO PROCESSES $10B IN PAYMENTS DAILY SHOWED HOW THEY DETECT PROBLEMS BEFORE CUSTOMERS NOTICE

most companies find out something broke when customers complain - JP Morgan finds it before the request finishes processing

every payment is a graph - authentication to notification is a node - when one node slows down the system knows exactly where to look instead of checking everything

the difference between anomaly and drift - one day your commute takes 20 extra minutes that is anomaly - one year later every commute takes 20 extra minutes and nobody noticed - most systems never catch drift

tested on millions of traces over 7 days - injected real problems - trained to recognize the difference before anything went live

fix rolls out to 5% of machines first, monitor, verify, then 100% - automating the wrong solution at scale in payments is worse than the problem itself

mean time to discovery dropped from multiple time windows to one - in real time payments every millisecond costs money

JP Morgan now runs Opus 5 and Fable 5 agents that replaced entire departments - 200 analysts replaced by 3 agents monitoring $10B in transactions 24/7

save this - this is how the people moving your money actually think

[Noryx @0xNoryxx]

https://t.co/zTZ8iP7Awo

[Abyzon @Abyzonn]

HE WAS THE 5TH EMPLOYEE AT GOOGLE - AND IN 1 HOUR AT STANFORD EXPLAINED HOW AI WILL CHANGE YOUR LIFE IN 2026

in 1990 he thought 32 processors would solve the problem - turned out you need a million times more - not 32

in 2012 they showed a network 10 million YouTube videos with zero labels - it found cats on its own - nobody told it what a cat was

100 million people talking to their phones for 3 minutes a day - Google had to double all its servers just for one feature

they built their own chip - TPU was 30x faster than CPU - new Ironwood is 3,600x more powerful than the first one

in 2022 the model solved problems about rabbits - in 2025 it won a gold medal at the international math olympiad

for $7 in Opus 5 you can run the same power that won the olympiad - and build a business on top of it

save this and watch today - 1 hour from the person who built what all modern AI stands on

[Noryx @0xNoryxx]

https://t.co/zTZ8iP7Awo

[Abyzon @Abyzonn]

He has studied AI for 10 years, built OpenAI - and shared everything he knows in a lecture in Silicon Valley

90% of models train incorrectly - not because the architecture is bad but because someone defined how the model understands its mistakes wrong

loss function is not a technical detail - it is how AI understands reality - one mistake here and the model confidently moves in the wrong direction

SVM says wrong or not wrong - Softmax is never satisfied and always wants to be more confident - that is why GPT and Claude use Softmax not SVM

an agent that can always improve is 40% more reliable than an agent that thinks it is already good enough

learning rate is the only parameter that can destroy everything - too large and the model jumps chaotically, too small and it does not move at all

save this and watch today - 60 minutes that replace a $5,000 course on the same topic

[Raytar @Raytar]

https://t.co/eAsr7cajuP

[Abyzon @Abyzonn]

THEY SPENT 3 YEARS AND BURNED $300K ON TOKENS TO FIND AN AGENT THAT IS 47% BETTER

95% of teams spend $500K on the model and $0 on memory - and wonder why the agent keeps answering wrong

vector database returns similar not relevant - like asking for a pharmacy and getting a list of every hospital in the city

Graph RAG: break documents into a graph → extract entities → enrich with PageRank

LinkedIn deployed a knowledge graph - ticket resolution time dropped 28.6% without changing the model

same model, different data structure - LLM accuracy 3x higher on graphs than SQL

an agent without a graph guesses from 100 options - an agent with a graph knows the right 3 in under a second

[Sprytix @Sprytixl]

https://t.co/YgrHCOwDs0

[Abyzon @Abyzonn]

THE MAN WHO INVENTED ARTIFICIAL INTELLIGENCE CAME TO MIT AND SHARED EVERYTHING HE LEARNED IN 60 YEARS - IN 2 HOURS

Marvin Minsky - father of AI - and he said what most AI companies don't want to hear

a four-year-old learns more in one year than GPT-4 learned in all its training - and without billions of parameters

pleasure is a mechanism that shuts down all other thoughts so the brain can record what worked - without this there is no learning - and no LLM has this

pain is not a bug - it is a signal that interrupts everything until the problem is solved - that is exactly how an AI agent should work

the problem is not model size - we are teaching machines to memorize answers instead of understanding how to think

he said this in 2007 - most people building AI today still haven't understood it

save this and watch today - 2 hours that replace 60 years of learning

[Noryx @0xNoryxx]

https://t.co/Daecl2TU5B

[Abyzon @Abyzonn]

THIS 2007 ELON MUSK INTERVIEW WAS LOST FOR 18 YEARS - AND EVERY SINGLE THING HE PREDICTED CAME TRUE

he sold Zip2 for $37 million - eBay bought PayPal - and instead of retiring he took that money and started building rockets when nobody believed it was possible

someone asked why he doesn't relax - he said sitting still is torture - a startup is like eating glass and staring into the abyss - and he chose that over a beach

in 2007 he laid out the exact Tesla roadmap - sports car first - then $49,000 sedan - then $30,000 mass market - it happened exactly that way

they asked who his competition was - he said no one serious - Branson needs 9 units of energy to go suborbital - we need 625 to reach orbit - it's not the same sport

he had a cubicle at SpaceX surrounded by engineers - woke up at 7:30 - spent 80% of his time on rockets - 2 days a month on Tesla

18 years ago he described exactly what he was going to build - then went and built it

[Sprytix @Sprytixl]

https://t.co/YgrHCOwDs0

[Abyzon @Abyzonn]

Stanford professors explained what AI actually is in 1984 - and predicted everything that's happening right now in 28 minutes better than $3000 AI history courses.

put expert knowledge into systems -> spread world-class expertise to anyone -> accept that common sense is the hardest problem to solve.

That's why 40 years later we're still working on the same core challenges.

expert systems + symbolic reasoning + knowledge engineering + natural language - that's the stack.

Watch and save it, then notice how little the fundamental problems have changed

[Abyzon @Abyzonn]

Jeff Bezos built Amazon in a garage and turned it into a trillion dollar company. Here's how he thinks about innovation - in 50 minutes better than $3000 business courses.

obsess over what customers will never stop wanting -> lower the cost of experiments -> reject either-or thinking -> ignore the media and build.

That's the difference between a company that reacts and a company that invents.

customer obsession + low-cost experimentation + self-service + rejecting either-or thinking - that's the stack.

Watch and save it, then run one small experiment in your business this week.