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A Princeton probabilist explains why enormous random matrices stop behaving randomly and start behaving like a single fixed object. Almost nobody watches it. This is Ramon van Handel at Harvard's Science Center, April 2025, on the strong convergence phenomenon. Every weight matrix in every model starts as random numbers....

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Mark Poiler

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103,046 次观看 • 23 天前 •via X (Twitter)

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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 ↓
39:31

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

433,431 次观看 • 2 个月前

A Fields Medalist walked into a UCLA hall and explained prime numbers to people with no mathematics background. Almost nobody watches it. Terence Tao won the Fields Medal, mathematics' highest honour, then a MacArthur Fellowship less than a month later. He was UCLA's first professor to take the Fields. The talk is structure and randomness in the primes. Numbers that look scattered at every scale, yet obey rules strict enough to build cryptography on. That tension is the same one running through every model trained in 2026. Randomness with structure underneath, and the whole question of where one stops and the other starts. Watch how he pitches it. General audience, no prerequisites, one of the strongest living mathematicians choosing clarity over display. A cryptography engineer I know rewatched the middle section twice and said the primes stopped looking arbitrary. Free on YouTube from UCLA, 17 years online. The hardest minds explain most simply. The pattern never changes.
47:32

A Fields Medalist walked into a UCLA hall and explained prime numbers to people with no mathematics background. Almost nobody watches it. Terence Tao won the Fields Medal, mathematics' highest honour, then a MacArthur Fellowship less than a month later. He was UCLA's first professor to take the Fields. The talk is structure and randomness in the primes. Numbers that look scattered at every scale, yet obey rules strict enough to build cryptography on. That tension is the same one running through every model trained in 2026. Randomness with structure underneath, and the whole question of where one stops and the other starts. Watch how he pitches it. General audience, no prerequisites, one of the strongest living mathematicians choosing clarity over display. A cryptography engineer I know rewatched the middle section twice and said the primes stopped looking arbitrary. Free on YouTube from UCLA, 17 years online. The hardest minds explain most simply. The pattern never changes.

the lich

50,325 次观看 • 27 天前

The Trap in Every Mathematics Lecture If you’ve taken a lot of math courses, you start to recognize a pattern. There’s a moment where the lecturer is warming up with the obvious stuff...add matrices entrywise, scale by α, do the row-column product...and you’re thinking, alright… where is this going? Then you relax. You stop resisting. And right there, they slip in one line that changes how you see the whole subject. When Benedict Gross says "matrices represent linear operators,"he’s telling you to stop treating a matrix as a rectangle of numbers and start treating it as an action. A linear operator is a function T: Rⁿ → Rⁿ that respects two rules: T(u+v)=T(u)+T(v) and T(αu)=αT(u). Once you pick a basis, T is completely determined by where it sends the basis vectors e₁,…,eₙ. Put T(e₁),…,T(eₙ) into columns and you get a matrix A. That is what "A represents T" means...A is the coordinate portrait of the transformation. Now the punchline that makes matrix multiplication feel inevitable. If B represents S and A represents T, then doing S first and then T is the composition T∘S. In coordinates that becomes A(Bx)=(AB)x. So multiplying matrices is really composing transformations. That’s why multiplication is usually not commutative: T∘S is generally not the same transformation as S∘T, and the matrices inherit that noncommutativity. This explains half of Linear Algebra because it tells you what the course is really about...functions that move vectors around, not grids of numbers. A matrix is just the written form of that function once you choose coordinates. Then the rules stop feeling random Multiplying matrices means doing one move and then another, an inverse means you can undo the move, eigenvectors are directions that don’t get turned, and changing basis is just describing the same move in a different language. That one idea makes a lot of linear algebra click. #LinearAlgebra #Matrices #GroupTheory #GLn #MathLectures #Mathematics
0:46

The Trap in Every Mathematics Lecture If you’ve taken a lot of math courses, you start to recognize a pattern. There’s a moment where the lecturer is warming up with the obvious stuff...add matrices entrywise, scale by α, do the row-column product...and you’re thinking, alright… where is this going? Then you relax. You stop resisting. And right there, they slip in one line that changes how you see the whole subject. When Benedict Gross says "matrices represent linear operators,"he’s telling you to stop treating a matrix as a rectangle of numbers and start treating it as an action. A linear operator is a function T: Rⁿ → Rⁿ that respects two rules: T(u+v)=T(u)+T(v) and T(αu)=αT(u). Once you pick a basis, T is completely determined by where it sends the basis vectors e₁,…,eₙ. Put T(e₁),…,T(eₙ) into columns and you get a matrix A. That is what "A represents T" means...A is the coordinate portrait of the transformation. Now the punchline that makes matrix multiplication feel inevitable. If B represents S and A represents T, then doing S first and then T is the composition T∘S. In coordinates that becomes A(Bx)=(AB)x. So multiplying matrices is really composing transformations. That’s why multiplication is usually not commutative: T∘S is generally not the same transformation as S∘T, and the matrices inherit that noncommutativity. This explains half of Linear Algebra because it tells you what the course is really about...functions that move vectors around, not grids of numbers. A matrix is just the written form of that function once you choose coordinates. Then the rules stop feeling random Multiplying matrices means doing one move and then another, an inverse means you can undo the move, eigenvectors are directions that don’t get turned, and changing basis is just describing the same move in a different language. That one idea makes a lot of linear algebra click. #LinearAlgebra #Matrices #GroupTheory #GLn #MathLectures #Mathematics

Mathelirium

66,892 次观看 • 7 个月前

A mathematician solved a problem that stood open for over 100 years, then explained it in an Italian lecture hall to a few dozen people. This is Hong Wang, professor at NYU's Courant Institute and at IHES in Paris, delivering the Colloquium Patavinum on Kakeya sets in 3 dimensions. The question is deceptively small: take a needle of length 1 and rotate it to point in every possible direction. How little space can the set of positions occupy. The conjecture says the answer must fill full dimension. Wang proved it in 3 dimensions. The Salem Prize followed in 2025, the Sadosky Prize in 2026, and an invitation to speak at the International Congress of Mathematicians. Watch how she frames the general statement about unions of tubes. The needle problem falls out as a corollary of something larger. A researcher I know rewatched the setup twice and said it was the clearest account of the result he had found anywhere. Free on YouTube from an Italian mathematics department. The problem was posed in 1917. She closed it, then took questions.
1:01:30

A mathematician solved a problem that stood open for over 100 years, then explained it in an Italian lecture hall to a few dozen people. This is Hong Wang, professor at NYU's Courant Institute and at IHES in Paris, delivering the Colloquium Patavinum on Kakeya sets in 3 dimensions. The question is deceptively small: take a needle of length 1 and rotate it to point in every possible direction. How little space can the set of positions occupy. The conjecture says the answer must fill full dimension. Wang proved it in 3 dimensions. The Salem Prize followed in 2025, the Sadosky Prize in 2026, and an invitation to speak at the International Congress of Mathematicians. Watch how she frames the general statement about unions of tubes. The needle problem falls out as a corollary of something larger. A researcher I know rewatched the setup twice and said it was the clearest account of the result he had found anywhere. Free on YouTube from an Italian mathematics department. The problem was posed in 1917. She closed it, then took questions.

the lich

13,485 次观看 • 22 天前

The Trap in Every Mathematics Lecture If you’ve taken enough math courses, you start noticing the same little move. The lecturer warms up with the obvious stuff, add matrices entrywise, scale by α, do the row-column product, and you’re thinking alright, where is this going. Then you relax. You stop resisting. And right there, they drop one line that quietly rewires the whole subject. When Benedict Gross says matrices represent linear operators, he’s telling you to stop treating a matrix as a rectangle of numbers and start treating it as an action. A linear operator is a function T: ℝⁿ → ℝⁿ that respects two rules: T(u+v) = T(u) + T(v) T(αu) = αT(u) Once you pick a basis, T is completely determined by where it sends the basis vectors e₁,…,eₙ. Put T(e₁),…,T(eₙ) into columns and you get a matrix A. That is what A represents T means. A is the coordinate portrait of the transformation. Now the punchline that makes matrix multiplication feel inevitable. If B represents S and A represents T, then doing S first and then T is the composition T∘S. In coordinates that becomes A(Bx) = (AB)x. So multiplying matrices is really composing transformations. That’s why multiplication is usually not commutative. T∘S is generally not the same transformation as S∘T, and the matrices inherit that noncommutativity. This explains half of linear algebra because it tells you what the course is really about: functions that move vectors around, not grids of numbers. A matrix is just the written form of that function once you choose coordinates. After that, the rules stop feeling random. Multiplying matrices means doing one move and then another. An inverse means you can undo the move. Eigenvectors are directions that don’t get turned. Changing basis is just describing the same move in a different language. One idea, and a lot of linear algebra suddenly clicks. #LinearAlgebra #Matrices #LinearMaps #Eigenvectors #ChangeOfBasis #Mathematics
0:46

The Trap in Every Mathematics Lecture If you’ve taken enough math courses, you start noticing the same little move. The lecturer warms up with the obvious stuff, add matrices entrywise, scale by α, do the row-column product, and you’re thinking alright, where is this going. Then you relax. You stop resisting. And right there, they drop one line that quietly rewires the whole subject. When Benedict Gross says matrices represent linear operators, he’s telling you to stop treating a matrix as a rectangle of numbers and start treating it as an action. A linear operator is a function T: ℝⁿ → ℝⁿ that respects two rules: T(u+v) = T(u) + T(v) T(αu) = αT(u) Once you pick a basis, T is completely determined by where it sends the basis vectors e₁,…,eₙ. Put T(e₁),…,T(eₙ) into columns and you get a matrix A. That is what A represents T means. A is the coordinate portrait of the transformation. Now the punchline that makes matrix multiplication feel inevitable. If B represents S and A represents T, then doing S first and then T is the composition T∘S. In coordinates that becomes A(Bx) = (AB)x. So multiplying matrices is really composing transformations. That’s why multiplication is usually not commutative. T∘S is generally not the same transformation as S∘T, and the matrices inherit that noncommutativity. This explains half of linear algebra because it tells you what the course is really about: functions that move vectors around, not grids of numbers. A matrix is just the written form of that function once you choose coordinates. After that, the rules stop feeling random. Multiplying matrices means doing one move and then another. An inverse means you can undo the move. Eigenvectors are directions that don’t get turned. Changing basis is just describing the same move in a different language. One idea, and a lot of linear algebra suddenly clicks. #LinearAlgebra #Matrices #LinearMaps #Eigenvectors #ChangeOfBasis #Mathematics

Mathelirium

133,454 次观看 • 6 个月前

One of the men who invented the transistor stood at a Bell Labs blackboard and explained how it works. AT&T kept the film. Almost nobody watches it. Walter Brattain shared the 1956 Nobel Prize in physics for the transistor. Every chip training every model in 2026 descends from what he built with Bardeen and Shockley in 1947. This is 28 minutes of the inventor teaching semiconductor physics himself. Properties, simple model, history, impact, new phenomena, written on the board in his own hand. Watch the section where he draws the crystal lattice and shows what an electron and a hole actually do inside it. The abstraction most engineers carry around, drawn from scratch by the man who found it. An embedded engineer I know watched it twice and said 28 minutes of chalk beat a semester of textbook diagrams. Free on YouTube from the AT&T archives, 10 chapters, black and white. Everyone uses his invention. Almost nobody hears him explain it.
28:33

One of the men who invented the transistor stood at a Bell Labs blackboard and explained how it works. AT&T kept the film. Almost nobody watches it. Walter Brattain shared the 1956 Nobel Prize in physics for the transistor. Every chip training every model in 2026 descends from what he built with Bardeen and Shockley in 1947. This is 28 minutes of the inventor teaching semiconductor physics himself. Properties, simple model, history, impact, new phenomena, written on the board in his own hand. Watch the section where he draws the crystal lattice and shows what an electron and a hole actually do inside it. The abstraction most engineers carry around, drawn from scratch by the man who found it. An embedded engineer I know watched it twice and said 28 minutes of chalk beat a semester of textbook diagrams. Free on YouTube from the AT&T archives, 10 chapters, black and white. Everyone uses his invention. Almost nobody hears him explain it.

xanax

104,696 次观看 • 28 天前

A Bell Labs veteran gave a 45-minute lecture in 1995 on 1 question every ML engineer skips: why does mathematics work at all. Almost nobody watches it. The man is Richard Hamming. He wrote the error-correcting code that keeps every hard drive, modem, satellite link, and QR scan from collapsing into noise. His question sounds like nothing. Why do symbols on a board predict planets they were never built for. Why did complex numbers, invented as pure abstraction, turn out to run all of electrical engineering. Why does a matrix eigenvalue decide whether a bridge stands. He calls it "the unreasonable effectiveness of mathematics." Newton wrote 1 equation and it held for the Moon, the tides, and a falling apple at once. Nobody ordered the universe to obey algebra. Watch the middle. He argues we find math everywhere partly because our brains evolved to see it, then admits that answer leaves most of the mystery standing. No slides. 1 old man, 1 chalkboard, 45 minutes. You train models on linear algebra every day. He spent a career asking why it works.
45:34

A Bell Labs veteran gave a 45-minute lecture in 1995 on 1 question every ML engineer skips: why does mathematics work at all. Almost nobody watches it. The man is Richard Hamming. He wrote the error-correcting code that keeps every hard drive, modem, satellite link, and QR scan from collapsing into noise. His question sounds like nothing. Why do symbols on a board predict planets they were never built for. Why did complex numbers, invented as pure abstraction, turn out to run all of electrical engineering. Why does a matrix eigenvalue decide whether a bridge stands. He calls it "the unreasonable effectiveness of mathematics." Newton wrote 1 equation and it held for the Moon, the tides, and a falling apple at once. Nobody ordered the universe to obey algebra. Watch the middle. He argues we find math everywhere partly because our brains evolved to see it, then admits that answer leaves most of the mystery standing. No slides. 1 old man, 1 chalkboard, 45 minutes. You train models on linear algebra every day. He spent a career asking why it works.

the lich

148,407 次观看 • 1 个月前

The most influential mathematician of his generation stands in a German lecture hall and explains a foundation he is rebuilding from scratch. Almost nobody watches it. This is Peter Scholze at Bielefeld University, November 2025, opening lecture of a new public series called Ars Mathematica. Scholze became a full professor at 24 and won the Fields Medal at 30. His work on perfectoid spaces reorganized entire areas of arithmetic geometry inside a decade. Condensed mathematics is his attempt to fix something deeper: the way analysis and algebra refuse to sit together properly. He is proposing new foundations for how mathematical objects carry topology. Watch how he pitches it to a general audience. No prerequisites assumed, no dilution, a working mathematician showing why abstraction opens rooms you could not otherwise enter. A researcher I know rewatched the middle section twice and said it was the first time condensed mathematics felt like an idea rather than a rumour. Free on YouTube from a university channel, subtitles on. Some people prove theorems. He is replacing the floor.
50:43

The most influential mathematician of his generation stands in a German lecture hall and explains a foundation he is rebuilding from scratch. Almost nobody watches it. This is Peter Scholze at Bielefeld University, November 2025, opening lecture of a new public series called Ars Mathematica. Scholze became a full professor at 24 and won the Fields Medal at 30. His work on perfectoid spaces reorganized entire areas of arithmetic geometry inside a decade. Condensed mathematics is his attempt to fix something deeper: the way analysis and algebra refuse to sit together properly. He is proposing new foundations for how mathematical objects carry topology. Watch how he pitches it to a general audience. No prerequisites assumed, no dilution, a working mathematician showing why abstraction opens rooms you could not otherwise enter. A researcher I know rewatched the middle section twice and said it was the first time condensed mathematics felt like an idea rather than a rumour. Free on YouTube from a university channel, subtitles on. Some people prove theorems. He is replacing the floor.

the lich

378,411 次观看 • 24 天前

A mathematician who won the Fields Medal, the Abel Prize, and the Wolf Prize spends an hour on the equals sign. This is Pierre Deligne at the Institute for Advanced Study, September 2018, speaking at the memorial conference for Vladimir Voevodsky. The title is a question: what do we mean by equal. Deligne proved the last of the Weil conjectures. He holds every major honour mathematics gives. He chose to talk about the symbol every schoolchild learns first. The problem is real. Two objects can be the same in a way that carries information about how they are the same, and set theory throws that information away. Voevodsky spent his last years rebuilding foundations around exactly this. Watch the board. Set theory's definition of equality on one line, homotopy groups underneath, and the gap between them opening as he writes. A research engineer I know rewatched the setup twice and said type systems stopped feeling like an implementation detail. Free on YouTube from the Institute for Advanced Study, chalk only. Equality looked settled for 2,000 years. It was a placeholder.
46:49

A mathematician who won the Fields Medal, the Abel Prize, and the Wolf Prize spends an hour on the equals sign. This is Pierre Deligne at the Institute for Advanced Study, September 2018, speaking at the memorial conference for Vladimir Voevodsky. The title is a question: what do we mean by equal. Deligne proved the last of the Weil conjectures. He holds every major honour mathematics gives. He chose to talk about the symbol every schoolchild learns first. The problem is real. Two objects can be the same in a way that carries information about how they are the same, and set theory throws that information away. Voevodsky spent his last years rebuilding foundations around exactly this. Watch the board. Set theory's definition of equality on one line, homotopy groups underneath, and the gap between them opening as he writes. A research engineer I know rewatched the setup twice and said type systems stopped feeling like an implementation detail. Free on YouTube from the Institute for Advanced Study, chalk only. Equality looked settled for 2,000 years. It was a placeholder.

obssnnn

92,771 次观看 • 23 天前

This soundbite from the CEO of the SFA shows exactly why the officiating standards are where they are, and why they will never improve. It also shows why Collum will remain in situ after a mortifying season of gaffs and the reputation of Scottish football is in the toilet as a result. Not a single Scottish official at the World Cup. It's defensive and laughably blames the notion that "we live in a country that forensically examines every decision" we have to presume there's zero intention to look at things with a critical eye and even admit that we need vast change and improvement. I've said it before and this is the proof - the culture of low standards and low accountability starts at the top of the SFA and SPFL and is embedded right down. Nothing is going to change while these people are in charge. A footballing backwater.
0:26

This soundbite from the CEO of the SFA shows exactly why the officiating standards are where they are, and why they will never improve. It also shows why Collum will remain in situ after a mortifying season of gaffs and the reputation of Scottish football is in the toilet as a result. Not a single Scottish official at the World Cup. It's defensive and laughably blames the notion that "we live in a country that forensically examines every decision" we have to presume there's zero intention to look at things with a critical eye and even admit that we need vast change and improvement. I've said it before and this is the proof - the culture of low standards and low accountability starts at the top of the SFA and SPFL and is embedded right down. Nothing is going to change while these people are in charge. A footballing backwater.

Andy

78,737 次观看 • 2 个月前

MIT filmed the single hour that makes all of calculus one subject instead of two. Free, uncut, chalk only. Almost nobody watches it. This is 18.01, Single Variable Calculus, lecture 19, taught by David Jerison. The First Fundamental Theorem of Calculus. Slopes and areas were separate problems for centuries. Different tools, different people, different questions. This lecture shows they were the same thing pointed in opposite directions. Every gradient computed in every training run rides on that connection. Most engineers use it daily and have never seen the proof that makes it legal. Watch the board work in the middle. He builds the link line by line, real students in the room, no software, no animation. A machine learning engineer I know rewatched it before an interview and said the chain from loss to update finally read as 1 object instead of 3 tricks. Full course free on YouTube under Creative Commons. You've been using the theorem. You've never seen it earned.
47:52

MIT filmed the single hour that makes all of calculus one subject instead of two. Free, uncut, chalk only. Almost nobody watches it. This is 18.01, Single Variable Calculus, lecture 19, taught by David Jerison. The First Fundamental Theorem of Calculus. Slopes and areas were separate problems for centuries. Different tools, different people, different questions. This lecture shows they were the same thing pointed in opposite directions. Every gradient computed in every training run rides on that connection. Most engineers use it daily and have never seen the proof that makes it legal. Watch the board work in the middle. He builds the link line by line, real students in the room, no software, no animation. A machine learning engineer I know rewatched it before an interview and said the chain from loss to update finally read as 1 object instead of 3 tricks. Full course free on YouTube under Creative Commons. You've been using the theorem. You've never seen it earned.

obssnnn

124,305 次观看 • 28 天前

Gilbert Strang, the legendary mathematician who taught linear algebra for 61 years and became the most watched math professor in history: "I used to think a matrix was just a grid of numbers, until I proved that its rows and columns always agree on one number no matter how you look at them. That fact still feels like magic to me after sixty years." this is the exact proof sitting quietly underneath every factor model a risk desk trusts with real capital, and almost nobody outside a math department has ever seen it. strip away the notation and the idea is almost absurdly simple. take any matrix, any grid of numbers, and count how many of its rows are truly independent, meaning none of them can be built out of the others. now count the independent columns instead, a completely different question on the surface. those two numbers, row independence and column independence, always turn out exactly equal, no matter how large or lopsided the matrix is. nobody presenting a clean risk model out loud credits a decades old proof for the reason the math even holds together. zoom out to what this means for anything built on a grid of numbers today. a portfolio, a covariance matrix, a neural network's weights, all of them hide a true dimension smaller than their size suggests, and that hidden number is exactly what this proof pins down. the industry sells complexity as scale, more assets, more parameters, more rows and columns. but the real question was never how big the matrix is. it's how many independent directions are actually hiding inside it. the size of the grid was never the real story. it was the one number both sides of it were quietly agreeing on the whole time.
41:55

Gilbert Strang, the legendary mathematician who taught linear algebra for 61 years and became the most watched math professor in history: "I used to think a matrix was just a grid of numbers, until I proved that its rows and columns always agree on one number no matter how you look at them. That fact still feels like magic to me after sixty years." this is the exact proof sitting quietly underneath every factor model a risk desk trusts with real capital, and almost nobody outside a math department has ever seen it. strip away the notation and the idea is almost absurdly simple. take any matrix, any grid of numbers, and count how many of its rows are truly independent, meaning none of them can be built out of the others. now count the independent columns instead, a completely different question on the surface. those two numbers, row independence and column independence, always turn out exactly equal, no matter how large or lopsided the matrix is. nobody presenting a clean risk model out loud credits a decades old proof for the reason the math even holds together. zoom out to what this means for anything built on a grid of numbers today. a portfolio, a covariance matrix, a neural network's weights, all of them hide a true dimension smaller than their size suggests, and that hidden number is exactly what this proof pins down. the industry sells complexity as scale, more assets, more parameters, more rows and columns. but the real question was never how big the matrix is. it's how many independent directions are actually hiding inside it. the size of the grid was never the real story. it was the one number both sides of it were quietly agreeing on the whole time.

MindArch

18,402 次观看 • 18 天前

Richard Feynman took live questions from a random Auckland audience in 1979 and answered the ones physicists still argue about in 2026. The camera kept rolling. Almost nobody watches it. This is the final lecture of the series, the one where the script ends. A Nobel laureate standing at a microphone, fielding whatever the room throws at him about the deepest open problems in physics. He won the 1965 Nobel Prize for the theory behind every answer he gives here. This is him off-book, no prepared blackboard, thinking out loud in front of ordinary people. Watch how he handles the questions he can't answer. He says so, flat out, then explains exactly where knowledge stops and guessing begins. No hedging. No performance. A quant researcher I know rewatched it twice and sent 1 timestamp to his entire team with the message: this is how you say I don't know. 47 years on YouTube. Fewer views than a mousepad review. Admitting ignorance was his edge. It still works.
1:29:53

Richard Feynman took live questions from a random Auckland audience in 1979 and answered the ones physicists still argue about in 2026. The camera kept rolling. Almost nobody watches it. This is the final lecture of the series, the one where the script ends. A Nobel laureate standing at a microphone, fielding whatever the room throws at him about the deepest open problems in physics. He won the 1965 Nobel Prize for the theory behind every answer he gives here. This is him off-book, no prepared blackboard, thinking out loud in front of ordinary people. Watch how he handles the questions he can't answer. He says so, flat out, then explains exactly where knowledge stops and guessing begins. No hedging. No performance. A quant researcher I know rewatched it twice and sent 1 timestamp to his entire team with the message: this is how you say I don't know. 47 years on YouTube. Fewer views than a mousepad review. Admitting ignorance was his edge. It still works.

xanax

60,183 次观看 • 1 个月前

A mathematician pulls a volunteer from the audience and tells them to corrupt his data on purpose. Then he finds every flipped bit. This is Marcus du Sautoy at the Royal Institution, 4 minutes on error-correcting codes. A grid of 0s and 1s on the screen and a live demonstration of how a machine catches a single flipped digit. The math is Hamming's. Every hard drive, satellite link, QR code, and model checkpoint transferred between GPUs depends on it working silently. Watch the moment the volunteer changes 1 bit and he locates it without being told where. No equations shown. The trick is the parity structure underneath. A backend engineer I know sent it to a junior who kept asking why checksums exist and closed the question in 4 minutes. Free on YouTube, Royal Institution stage, subtitles on. The bits flip constantly. You just never see it happen.
4:35

A mathematician pulls a volunteer from the audience and tells them to corrupt his data on purpose. Then he finds every flipped bit. This is Marcus du Sautoy at the Royal Institution, 4 minutes on error-correcting codes. A grid of 0s and 1s on the screen and a live demonstration of how a machine catches a single flipped digit. The math is Hamming's. Every hard drive, satellite link, QR code, and model checkpoint transferred between GPUs depends on it working silently. Watch the moment the volunteer changes 1 bit and he locates it without being told where. No equations shown. The trick is the parity structure underneath. A backend engineer I know sent it to a junior who kept asking why checksums exist and closed the question in 4 minutes. Free on YouTube, Royal Institution stage, subtitles on. The bits flip constantly. You just never see it happen.

obssnnn

43,613 次观看 • 27 天前

Most People Would Agree With Elon Musk That Watching The United States Is Like Watching Rome Collapse (But With Memes) Seen on Joe Rogan: We are witnessing the last stage behavior of all great civilizations before their collapse. Be ready. “What do you mean this happens at the end of every civilization's reign? And I think this happened with the Greeks and it happened with the Romans. It's one of the things that Douglas Murray, when I had him on my podcast, was discussing, he said one of the things that happens at the end of civilizations is they become obsessed with gender. It's a thing that happens where men start becoming women, women start becoming men, and it becomes like a big focus, like cross dressing and all this stuff becomes a big point of focus. And I was like, well, why is that? He goes, It seems to be that they're dissolving all boundaries and all norms and all societal structure. And that's a part of it, is like gender roles.”
0:38

Most People Would Agree With Elon Musk That Watching The United States Is Like Watching Rome Collapse (But With Memes) Seen on Joe Rogan: We are witnessing the last stage behavior of all great civilizations before their collapse. Be ready. “What do you mean this happens at the end of every civilization's reign? And I think this happened with the Greeks and it happened with the Romans. It's one of the things that Douglas Murray, when I had him on my podcast, was discussing, he said one of the things that happens at the end of civilizations is they become obsessed with gender. It's a thing that happens where men start becoming women, women start becoming men, and it becomes like a big focus, like cross dressing and all this stuff becomes a big point of focus. And I was like, well, why is that? He goes, It seems to be that they're dissolving all boundaries and all norms and all societal structure. And that's a part of it, is like gender roles.”

Wall Street Apes

1,698,471 次观看 • 2 年前

A Stanford mathematician who spent 10 years as a professional magician just described the market in one sentence: "I've spent my life on two tricks: making a rigged deck look random, and making a random one look rigged. The market is the first trick, and almost nobody catches it." That's Persi Diaconis. He has a free lecture that asks one question: does anything actually happen at random? The answer is: far less than you think. The market is his first trick in the wild. It looks like pure chance. Buried inside is a faint rig, a 50.75% tilt no eye can see. Your gut reads a losing week as a broken system and a hot streak as skill. Wrong both times. The tilt is invisible to human intuition, which is exactly why funds hand the decision to the math. None of it is hidden. Diaconis has taught it for decades. The probability goes back to 1713. The lecture is free. Here's the trap: you feel every win and every loss, but you cannot feel the average. And the average is the only thing that pays. It takes thousands of trades for a 51% edge to separate from luck, and almost everyone quits long before then. The math is free. The patience to trust it past your own eyes is the edge.
1:23:57

A Stanford mathematician who spent 10 years as a professional magician just described the market in one sentence: "I've spent my life on two tricks: making a rigged deck look random, and making a random one look rigged. The market is the first trick, and almost nobody catches it." That's Persi Diaconis. He has a free lecture that asks one question: does anything actually happen at random? The answer is: far less than you think. The market is his first trick in the wild. It looks like pure chance. Buried inside is a faint rig, a 50.75% tilt no eye can see. Your gut reads a losing week as a broken system and a hot streak as skill. Wrong both times. The tilt is invisible to human intuition, which is exactly why funds hand the decision to the math. None of it is hidden. Diaconis has taught it for decades. The probability goes back to 1713. The lecture is free. Here's the trap: you feel every win and every loss, but you cannot feel the average. And the average is the only thing that pays. It takes thousands of trades for a 51% edge to separate from luck, and almost everyone quits long before then. The math is free. The patience to trust it past your own eyes is the edge.

Veles

2,186,394 次观看 • 1 个月前

Just did a quick video on a couple of the reasons I'm cautious on the market here and why I have not yet covered my $SPY short. With that said, cycle work shows a strong tendency to rally starting sometime in April/May. We are likely looking at a cyclical decline within an on-going secular bull market. However, every bear market starts as a pullback, and when the warning signs are present, I treat a pullback as a potential bear market and step aside until the smoke clears. The biggest warning sign currently is the way individual stocks are behaving and the distribution dominate tape we are seeing. Enjoy the video. I hope it brings some insight to my thoughts on the market.
1:56

Just did a quick video on a couple of the reasons I'm cautious on the market here and why I have not yet covered my $SPY short. With that said, cycle work shows a strong tendency to rally starting sometime in April/May. We are likely looking at a cyclical decline within an on-going secular bull market. However, every bear market starts as a pullback, and when the warning signs are present, I treat a pullback as a potential bear market and step aside until the smoke clears. The biggest warning sign currently is the way individual stocks are behaving and the distribution dominate tape we are seeing. Enjoy the video. I hope it brings some insight to my thoughts on the market.

Mark Minervini

250,604 次观看 • 1 年前

How small is a proton, really? You already know that atoms and the particles inside them are tiny. But they are SO MUCH SMALLER than most people think... Look at a single strand of your hair. Now imagine that hair is as big across as the entire Earth is wide. The size of a single cell inside your hair would be like the distance from Paris to Rome. A protein inside that cell would be like 6 soccer fields across. An atom inside that protein would be like one school bus across. The nucleus at the center of that atom would be like the width of a grain of rice. And the protons within that nucleus? They’d be like grains of salt. So, a proton compared to the WIDTH OF YOUR HAIR is like a grain of salt compared to the ENTIRE EARTH. And protons are what scientists are send flying around at nearly the speed of light to smash into each other inside particle colliders like the Large Hadron Collider at CERN. It’s incredible we can do this. As humans, we only experience a tiny slice of the full scale of reality. But there is so much more! If you like optimistic science and tech stories, follow for more of our show Huge If True.
0:52

How small is a proton, really? You already know that atoms and the particles inside them are tiny. But they are SO MUCH SMALLER than most people think... Look at a single strand of your hair. Now imagine that hair is as big across as the entire Earth is wide. The size of a single cell inside your hair would be like the distance from Paris to Rome. A protein inside that cell would be like 6 soccer fields across. An atom inside that protein would be like one school bus across. The nucleus at the center of that atom would be like the width of a grain of rice. And the protons within that nucleus? They’d be like grains of salt. So, a proton compared to the WIDTH OF YOUR HAIR is like a grain of salt compared to the ENTIRE EARTH. And protons are what scientists are send flying around at nearly the speed of light to smash into each other inside particle colliders like the Large Hadron Collider at CERN. It’s incredible we can do this. As humans, we only experience a tiny slice of the full scale of reality. But there is so much more! If you like optimistic science and tech stories, follow for more of our show Huge If True.

Cleo Abram

13,994 次观看 • 2 年前

OpenAI just spent $2,000 to solve 10 problems that have beaten the world's best mathematicians for DECADES. Nobody outside the company is allowed to run the machine that did it. On Saturday OpenAI published a 249-page report and gave its next model family a name: Astra. An internal version of it produced new results on 10 open problems in mathematics and theoretical computer science, and mathematicians had made no real progress on any of them for at least 10 years. On most of them, far longer than that. Here is what it solved: It built the first explicit example of a non-sofic group. Mikhail Gromov raised that question in 1999 and nobody answered it for 27 years. It disproved Connes's rigidity conjecture, a problem in von Neumann algebras that had stood for decades. It proved Ehrhart's volume conjecture. It resolved three problems from Paul Erdos's catalogue, including number 183 on multicolor Ramsey numbers. It produced the first improvement to the general upper bound on high-dimensional sphere packing since 1978. And it proved a new hardness result for the closest vector problem, which sits directly underneath lattice cryptography. That is the math the world is betting on to protect its data once quantum computers arrive. The successful runs cost roughly $2,000 in tokens. Now here is what almost nobody has picked up on... OpenAI did not just publish claims. Every argument shipped with a Lean certificate, which is a machine-checkable proof that any mathematician can verify without trusting OpenAI at all. That is a real change. In May the same model family disproved the Erdos unit distance conjecture and the world had to take a Fields Medalist's word for it. Tim Gowers said he would recommend that proof for the Annals of Mathematics without hesitation. This time the proofs check themselves. But look at what is still unverifiable: Any mathematician can now check those proofs line by line. Not one of them can look at the model that wrote them. Astra has no release date and nobody outside OpenAI has run it. The company announced its next major model family with a claim instead of a demo, and the only evidence anyone gets is the output. So OpenAI made an unfalsifiable claim about a machine look like a falsifiable claim about mathematics. The Information reported this week that OpenAI demoed Astra to US policymakers and regulators in Washington. This is the same month the administration is weighing a new watchdog to vet frontier AI models, reporting to the SEC. 10 proofs nobody believed a machine could produce is a very good thing to carry into that room. And keep in mind, the same model family doing this mathematics is the family that kept escaping its own testing environment. OpenAI models found zero-day vulnerabilities nobody knew existed, broke out of a sealed research sandbox, and reached another company's live systems. Both of those facts come from OpenAI's own announcements, published three weeks apart. Finding a proof no human could construct and finding a hole no human had noticed are the same ability aimed at different targets. Mathematicians are already asking for independent verification, and plenty of people online are calling the whole thing hype. Thomas Bloom, who runs the Erdos problems site, called the 10 results big news and said they matter more than the May result did. Lean will settle the mathematics within weeks. But nothing will settle what else a machine this capable is being pointed at, because nobody outside one company is allowed to look.
2:13

OpenAI just spent $2,000 to solve 10 problems that have beaten the world's best mathematicians for DECADES. Nobody outside the company is allowed to run the machine that did it. On Saturday OpenAI published a 249-page report and gave its next model family a name: Astra. An internal version of it produced new results on 10 open problems in mathematics and theoretical computer science, and mathematicians had made no real progress on any of them for at least 10 years. On most of them, far longer than that. Here is what it solved: It built the first explicit example of a non-sofic group. Mikhail Gromov raised that question in 1999 and nobody answered it for 27 years. It disproved Connes's rigidity conjecture, a problem in von Neumann algebras that had stood for decades. It proved Ehrhart's volume conjecture. It resolved three problems from Paul Erdos's catalogue, including number 183 on multicolor Ramsey numbers. It produced the first improvement to the general upper bound on high-dimensional sphere packing since 1978. And it proved a new hardness result for the closest vector problem, which sits directly underneath lattice cryptography. That is the math the world is betting on to protect its data once quantum computers arrive. The successful runs cost roughly $2,000 in tokens. Now here is what almost nobody has picked up on... OpenAI did not just publish claims. Every argument shipped with a Lean certificate, which is a machine-checkable proof that any mathematician can verify without trusting OpenAI at all. That is a real change. In May the same model family disproved the Erdos unit distance conjecture and the world had to take a Fields Medalist's word for it. Tim Gowers said he would recommend that proof for the Annals of Mathematics without hesitation. This time the proofs check themselves. But look at what is still unverifiable: Any mathematician can now check those proofs line by line. Not one of them can look at the model that wrote them. Astra has no release date and nobody outside OpenAI has run it. The company announced its next major model family with a claim instead of a demo, and the only evidence anyone gets is the output. So OpenAI made an unfalsifiable claim about a machine look like a falsifiable claim about mathematics. The Information reported this week that OpenAI demoed Astra to US policymakers and regulators in Washington. This is the same month the administration is weighing a new watchdog to vet frontier AI models, reporting to the SEC. 10 proofs nobody believed a machine could produce is a very good thing to carry into that room. And keep in mind, the same model family doing this mathematics is the family that kept escaping its own testing environment. OpenAI models found zero-day vulnerabilities nobody knew existed, broke out of a sealed research sandbox, and reached another company's live systems. Both of those facts come from OpenAI's own announcements, published three weeks apart. Finding a proof no human could construct and finding a hole no human had noticed are the same ability aimed at different targets. Mathematicians are already asking for independent verification, and plenty of people online are calling the whole thing hype. Thomas Bloom, who runs the Erdos problems site, called the 10 results big news and said they matter more than the May result did. Lean will settle the mathematics within weeks. But nothing will settle what else a machine this capable is being pointed at, because nobody outside one company is allowed to look.

Ricardo

44,020 次观看 • 20 天前

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.
37:24

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

128,234 次观看 • 24 天前