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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....

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13,485 просмотров • 1 месяц назад •via X (Twitter)

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Fields Medalist Wang Hong explains the century-old Kakeya problem: More than 100 years ago, Sōichi Kakeya asked: If an infinitely thin needle is rotated 180 degrees, how small can the area it sweeps out be? A. S. Besicovitch later showed that, with a carefully designed motion, the area can be made arbitrarily small. The question then evolved: What is the smallest possible dimension of a set containing a unit line segment in every direction? Mathematicians believe such a set must still have the largest possible dimension. The Kakeya conjecture is deeply connected to Fourier analysis, a field with important applications in medicine, engineering, communications and information science.
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Fields Medalist Wang Hong explains the century-old Kakeya problem: More than 100 years ago, Sōichi Kakeya asked: If an infinitely thin needle is rotated 180 degrees, how small can the area it sweeps out be? A. S. Besicovitch later showed that, with a carefully designed motion, the area can be made arbitrarily small. The question then evolved: What is the smallest possible dimension of a set containing a unit line segment in every direction? Mathematicians believe such a set must still have the largest possible dimension. The Kakeya conjecture is deeply connected to Fourier analysis, a field with important applications in medicine, engineering, communications and information science.

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25,106 просмотров • 1 месяц назад

When Hong Wang won the Fields Medal, everyone talked about the honor: her age, her journey, the history she had made. But the most interesting question was barely discussed: What did she actually solve? It begins with a needle. Turn it until it has pointed in every possible direction. How little space can that movement occupy? Almost none, strangely. And yet, that tiny set may still carry the full complexity of three-dimensional space. This is the Kakeya conjecture. It sounds like a puzzle, but it resisted mathematicians for more than a century and sits at the heart of how mathematics understands waves and their concentration—the same world of ideas behind MRI reconstruction, image compression, sound and quantum physics. In 2025, Hong Wang and Joshua Zahl finally solved the three-dimensional case. This video starts with that simple needle and slowly reveals the mathematics behind the medal. We celebrated the person. This is a chance to understand the work.
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When Hong Wang won the Fields Medal, everyone talked about the honor: her age, her journey, the history she had made. But the most interesting question was barely discussed: What did she actually solve? It begins with a needle. Turn it until it has pointed in every possible direction. How little space can that movement occupy? Almost none, strangely. And yet, that tiny set may still carry the full complexity of three-dimensional space. This is the Kakeya conjecture. It sounds like a puzzle, but it resisted mathematicians for more than a century and sits at the heart of how mathematics understands waves and their concentration—the same world of ideas behind MRI reconstruction, image compression, sound and quantum physics. In 2025, Hong Wang and Joshua Zahl finally solved the three-dimensional case. This video starts with that simple needle and slowly reveals the mathematics behind the medal. We celebrated the person. This is a chance to understand the work.

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85,998 просмотров • 1 месяц назад

2026 Fields medalist Hong Wang proved the three-dimensional version of a century-old problem that’s simple to explain, yet difficult to solve: How much space does it take to turn a needle so it points in every direction? Watch the full video about her work and learn more about this year's Field Medals: #math #FieldsMedals #ICM2026
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2026 Fields medalist Hong Wang proved the three-dimensional version of a century-old problem that’s simple to explain, yet difficult to solve: How much space does it take to turn a needle so it points in every direction? Watch the full video about her work and learn more about this year's Field Medals: #math #FieldsMedals #ICM2026

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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.
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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.

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Richard Feynman stood at a Cornell blackboard in 1964 and explained the problem every AI lab is fighting in 2026. The BBC filmed it. Almost nobody watches it. The lecture is about why nature only answers in mathematics. Every team forcing language models to reason is hitting the wall he mapped 62 years ago. He was 46. The Nobel Prize came 11 months later. The footage survived on film reels and now sits free on YouTube with fewer views than a keyboard unboxing. Watch the blackboard section near the middle. He takes 1 of Kepler's laws and rebuilds it from nothing, with notation a 12-year-old can follow. No slides. No jargon. 1 piece of chalk. An ML engineer I know paused it 4 times and made his whole team watch it before standup. You're 62 years late. The lecture is still free.
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Richard Feynman stood at a Cornell blackboard in 1964 and explained the problem every AI lab is fighting in 2026. The BBC filmed it. Almost nobody watches it. The lecture is about why nature only answers in mathematics. Every team forcing language models to reason is hitting the wall he mapped 62 years ago. He was 46. The Nobel Prize came 11 months later. The footage survived on film reels and now sits free on YouTube with fewer views than a keyboard unboxing. Watch the blackboard section near the middle. He takes 1 of Kepler's laws and rebuilds it from nothing, with notation a 12-year-old can follow. No slides. No jargon. 1 piece of chalk. An ML engineer I know paused it 4 times and made his whole team watch it before standup. You're 62 years late. The lecture is still free.

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The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US $1 million prize for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the Millennium Meeting held on May 24, 2000. Thus, on the official website of the Clay Mathematics Institute, these seven problems are officially called the Millennium Problems. To date, the only Millennium Prize problem to have been solved is the Poincaré conjecture. The Clay Institute awarded the monetary prize to Russian mathematician Grigori Perelman in 2010. However, he declined the award as it was not also offered to Richard S. Hamilton, upon whose work Perelman built.

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Andrew Wiles worked on Fermat's Last Theorem alone in his attic for 7 years and told nobody except his wife. The problem was 358 years old. Fermat scribbled in a margin in 1637 that he had a proof and no room to write it, and every mathematician since had failed. Wiles saw the statement in a library book at 10 years old. He never let it go. He was a Princeton professor when he started in 1986. He stopped publishing new work and released old results in pieces to hide the silence. He announced it in Cambridge in June 1993, over 3 lectures, revealing the target only at the end. Newspapers ran it worldwide. Then a referee found a gap. One step in the proof did not hold, and the error was fundamental. He spent 14 months trying to close it in public view, with the whole field watching. He was ready to quit. The fix arrived in September 1994. He has said he stared at it in disbelief for 20 minutes. The BBC filmed him describing that moment. He gets a few words out, then turns away from the camera in tears. He kept the greatest result of the century secret so nobody could take it.
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Andrew Wiles worked on Fermat's Last Theorem alone in his attic for 7 years and told nobody except his wife. The problem was 358 years old. Fermat scribbled in a margin in 1637 that he had a proof and no room to write it, and every mathematician since had failed. Wiles saw the statement in a library book at 10 years old. He never let it go. He was a Princeton professor when he started in 1986. He stopped publishing new work and released old results in pieces to hide the silence. He announced it in Cambridge in June 1993, over 3 lectures, revealing the target only at the end. Newspapers ran it worldwide. Then a referee found a gap. One step in the proof did not hold, and the error was fundamental. He spent 14 months trying to close it in public view, with the whole field watching. He was ready to quit. The fix arrived in September 1994. He has said he stared at it in disbelief for 20 minutes. The BBC filmed him describing that moment. He gets a few words out, then turns away from the camera in tears. He kept the greatest result of the century secret so nobody could take it.

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French President Emmanuel Macron posted a video on social media on July 23, in which he called Chinese mathematician Wang Hong to congratulate her on winning the Fields Medal. Chinese mathematicians Deng Yu and Wang Hong were awarded the Fields Medals, marking the first time mathematicians of Chinese nationality have won the prestigious honor. Wang Hong is currently a professor at IHES in France.
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French President Emmanuel Macron posted a video on social media on July 23, in which he called Chinese mathematician Wang Hong to congratulate her on winning the Fields Medal. Chinese mathematicians Deng Yu and Wang Hong were awarded the Fields Medals, marking the first time mathematicians of Chinese nationality have won the prestigious honor. Wang Hong is currently a professor at IHES in France.

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An MIT mathematician spent the last decade building one equation that assigns every chart pattern on Wall Street a precise probability of having been drawn by pure random noise. She filmed the entire framework in a 110-minute lecture and put it on YouTube for nothing. Millions of traders draw trendlines every day. Almost none have watched it. Her name is Yilin Wang. She is a mathematician at MIT, previously at ETH Zurich, and winner of the 2023 Salem Prize, the highest recognition for a young mathematician working in analysis. The 110-minute video in this post is one of her seminars on Schramm-Loewner Evolution and Loewner energy, filmed at a chalkboard in a small university lecture hall. MIT charges $85,000 a year to sit in a room like that. She posted the entire talk to YouTube for free. Wang covers the mathematical foundation of "how random is this pattern" in one afternoon. Schramm-Loewner Evolution. A family of random curves that turned out to be the scaling limit of almost every 2D random system physicists ever studied: percolation, the Ising model, self-avoiding walks. Driving function. Every SLE curve is encoded by one 1D signal, a Brownian motion that steers it. Extract that signal from a price chart and you can measure exactly how far the chart is from pure noise. Loewner energy. The number Wang built her career on. It assigns to every smooth curve on the plane a single real value between zero and infinity. A perfect circle gets zero. Every other shape costs energy. Large deviation principle. The probability that a random SLE curve looks approximately like a given shape decays like exp of minus its Loewner energy divided by kappa. Low energy shapes are almost indistinguishable from noise. High energy shapes noise would essentially never draw. Every quant fund on Wall Street pays PhD statisticians $500,000 a year to formalize exactly this question: is the pattern on the screen a signal, or is it something pure randomness would have drawn anyway. Wang wrote the closed-form answer at a chalkboard, in one lecture, for nothing. "The most surprising fact about a random curve is not how random it looks. It is how much of what humans call a pattern is exactly what pure randomness would have drawn." That is a paraphrase of the framing she returns to across the seminar. The lecture is free on YouTube. The paper introducing Loewner energy is free on arXiv. The full framework fits in under forty pages. The formula is free. The willingness to measure the energy of a chart before betting a mortgage on the pattern is a much rarer commodity than the confidence to draw the trendline without it.
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An MIT mathematician spent the last decade building one equation that assigns every chart pattern on Wall Street a precise probability of having been drawn by pure random noise. She filmed the entire framework in a 110-minute lecture and put it on YouTube for nothing. Millions of traders draw trendlines every day. Almost none have watched it. Her name is Yilin Wang. She is a mathematician at MIT, previously at ETH Zurich, and winner of the 2023 Salem Prize, the highest recognition for a young mathematician working in analysis. The 110-minute video in this post is one of her seminars on Schramm-Loewner Evolution and Loewner energy, filmed at a chalkboard in a small university lecture hall. MIT charges $85,000 a year to sit in a room like that. She posted the entire talk to YouTube for free. Wang covers the mathematical foundation of "how random is this pattern" in one afternoon. Schramm-Loewner Evolution. A family of random curves that turned out to be the scaling limit of almost every 2D random system physicists ever studied: percolation, the Ising model, self-avoiding walks. Driving function. Every SLE curve is encoded by one 1D signal, a Brownian motion that steers it. Extract that signal from a price chart and you can measure exactly how far the chart is from pure noise. Loewner energy. The number Wang built her career on. It assigns to every smooth curve on the plane a single real value between zero and infinity. A perfect circle gets zero. Every other shape costs energy. Large deviation principle. The probability that a random SLE curve looks approximately like a given shape decays like exp of minus its Loewner energy divided by kappa. Low energy shapes are almost indistinguishable from noise. High energy shapes noise would essentially never draw. Every quant fund on Wall Street pays PhD statisticians $500,000 a year to formalize exactly this question: is the pattern on the screen a signal, or is it something pure randomness would have drawn anyway. Wang wrote the closed-form answer at a chalkboard, in one lecture, for nothing. "The most surprising fact about a random curve is not how random it looks. It is how much of what humans call a pattern is exactly what pure randomness would have drawn." That is a paraphrase of the framing she returns to across the seminar. The lecture is free on YouTube. The paper introducing Loewner energy is free on arXiv. The full framework fits in under forty pages. The formula is free. The willingness to measure the energy of a chart before betting a mortgage on the pattern is a much rarer commodity than the confidence to draw the trendline without it.

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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.
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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.

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50,394 просмотров • 1 месяц назад

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.
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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.

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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.
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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.

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#WATCH | Delhi: On media reports that the central government is likely to bring a bill to curb the powers of the Waqf Board over assets, Former Vice Chairman Of National Commission For Minorities Atif Rasheed says, "The Waqf Act was formed in 1954. The then government in 1995 changed it completely. In 2013, a lot of amendments were made to the act. So, now if an amendment is taking place, it does not need to be taken negatively. We should trust the government, it is dedicated to 'Sabka Sath, Sabka Vikas'... As per the reports, it seems that there are going to be around 32 amendments in the act. If it is about registration with the Collector or a judicial inquiry, then why should one have a problem with it? In 2013, it was amended that the government should map it every 10 years... This is not an interference in the Shariat and it does not decrease the power of the Waqf..."
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ANI

14,687 просмотров • 2 лет назад

David Simon on the barriers "The Wire" (2002-2008) faced: "Interviewer: Do you think the fact you're telling stories in different ways than is traditional, and it has this darkness to it, was that the big barrier to the show becoming more popular than it was? Would you say it was the racial makeup of the cast? Simon: There were a lot of barriers. The racial makeup of the cast was problematic and we knew that going in. The complexity of the serial itself -- the fact that you couldn't miss a couple of episodes and feel comfortable watching it. Though I think that HBO was a wonderful vehicle for that with the multiple viewings, the DVDs and ultimately with On Demand. It was less of a problem as the show went on. It was also less of a problem as people who watched the show got used to its rhythms. The first season was on some level training the audience to watch television a little bit differently, and reducing the expectations in terms of pacing, in terms of cliffhangers, in terms of the requirement to absorb detail or even to look for symbolism. Those were problems. The other problem is, no easy gratifications, other than some real effort at careful characterization and humor. That was it. Without the humor, it would have been unbearable. Without an acknowledgement of the humanity of the characters, despite all their flaws, their vanities, their absurdities -- if on some level, you can't make people care about the characters, you've got a problem no matter what you're doing. We had some obligations to people if they wanted to watch, but a happy ending was not among the list of obligations." (David Simon's interview with Alan Sepinwall, 2008) P.S: On this day, 24 years ago, the first episode of "The Wire" was aired worldwide.
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David Simon on the barriers "The Wire" (2002-2008) faced: "Interviewer: Do you think the fact you're telling stories in different ways than is traditional, and it has this darkness to it, was that the big barrier to the show becoming more popular than it was? Would you say it was the racial makeup of the cast? Simon: There were a lot of barriers. The racial makeup of the cast was problematic and we knew that going in. The complexity of the serial itself -- the fact that you couldn't miss a couple of episodes and feel comfortable watching it. Though I think that HBO was a wonderful vehicle for that with the multiple viewings, the DVDs and ultimately with On Demand. It was less of a problem as the show went on. It was also less of a problem as people who watched the show got used to its rhythms. The first season was on some level training the audience to watch television a little bit differently, and reducing the expectations in terms of pacing, in terms of cliffhangers, in terms of the requirement to absorb detail or even to look for symbolism. Those were problems. The other problem is, no easy gratifications, other than some real effort at careful characterization and humor. That was it. Without the humor, it would have been unbearable. Without an acknowledgement of the humanity of the characters, despite all their flaws, their vanities, their absurdities -- if on some level, you can't make people care about the characters, you've got a problem no matter what you're doing. We had some obligations to people if they wanted to watch, but a happy ending was not among the list of obligations." (David Simon's interview with Alan Sepinwall, 2008) P.S: On this day, 24 years ago, the first episode of "The Wire" was aired worldwide.

DepressedBergman

33,114 просмотров • 3 месяцев назад

The only physicist ever to win the Fields Medal taught a full Princeton course in 2022. The recordings have almost no views. Edward Witten works at the Institute for Advanced Study. He reshaped string theory and large parts of pure geometry, and mathematicians gave him their highest prize for it. This is Physics 539, Topics in High Energy Physics, autumn 2022. Full semester, lecture by lecture, chalk on a board, graduate students in the room. No lecture notes released. No production. No description on the videos. Someone sat in the back row and hit record. Watch how little he writes. A few symbols, 1 small diagram, and the whole argument carried in speech while the board stays nearly empty. A theoretical physicist I know worked through the playlist over a summer and said it read like watching someone think in real time. Free on YouTube, uploaded by an attendee, no institution behind it. Universities publish the public talks. Somebody filmed the real course.
1:26:47

The only physicist ever to win the Fields Medal taught a full Princeton course in 2022. The recordings have almost no views. Edward Witten works at the Institute for Advanced Study. He reshaped string theory and large parts of pure geometry, and mathematicians gave him their highest prize for it. This is Physics 539, Topics in High Energy Physics, autumn 2022. Full semester, lecture by lecture, chalk on a board, graduate students in the room. No lecture notes released. No production. No description on the videos. Someone sat in the back row and hit record. Watch how little he writes. A few symbols, 1 small diagram, and the whole argument carried in speech while the board stays nearly empty. A theoretical physicist I know worked through the playlist over a summer and said it read like watching someone think in real time. Free on YouTube, uploaded by an attendee, no institution behind it. Universities publish the public talks. Somebody filmed the real course.

Gaspar

22,934 просмотров • 1 месяц назад

A student named Chitra at #DelhiUniversity was allegedly harassed by a professor over a certain issue. She created a reel about the incident and posted it on Instagram. When the head of the department found out about the reel, they pressured her to delete it. However, Chitra stood her ground and refused to take it down. The DU administration must ensure justice for the student and take appropriate action against the professor involved in the harassment.
1:31

A student named Chitra at #DelhiUniversity was allegedly harassed by a professor over a certain issue. She created a reel about the incident and posted it on Instagram. When the head of the department found out about the reel, they pressured her to delete it. However, Chitra stood her ground and refused to take it down. The DU administration must ensure justice for the student and take appropriate action against the professor involved in the harassment.

Hate Detector 🔍

571,583 просмотров • 9 месяцев назад