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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.show more

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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. 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.

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 views • 1 month ago

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.

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.

Michael Guo

85,647 views • 1 month ago

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

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

Simons Foundation

27,361 views • 1 month ago

12 YEARS AGO: TESLA DELIVERS FIRST MODEL S Elon: "What's the model S really all about? It's about breaking a spell. The world has been under this illusion that electric cars cannot be as good as gasoline cars. That if you have to go with an electric car, you're accepting a product that's worse. What the model S is fundamentally about is breaking that illusion. It's showing that an electric car can, in fact, be the best car in the world. What we believe customers will discover is that this is the best car in every dimension that matters." Source: Model S Delivery Event, June 22, 2012. Credit: Tesla

12 YEARS AGO: TESLA DELIVERS FIRST MODEL S Elon: "What's the model S really all about? It's about breaking a spell. The world has been under this illusion that electric cars cannot be as good as gasoline cars. That if you have to go with an electric car, you're accepting a product that's worse. What the model S is fundamentally about is breaking that illusion. It's showing that an electric car can, in fact, be the best car in the world. What we believe customers will discover is that this is the best car in every dimension that matters." Source: Model S Delivery Event, June 22, 2012. Credit: Tesla

Mario Nawfal

35,795 views • 2 years ago

Zhilin at GTC: Introducing Attention Residuals Learning selective memory, rather than mechanically accumulating everything, is the beauty of attention. Many of you have probably read Attention Is All You Need, the 2017 Transformer paper that brought “human-like” attention into the model’s field of view. From that point on, models no longer simply read everything in a mechanical way. Instead, they began to develop a sense of what matters more and what matters less across the text, choosing to retain the more important information. Recently, Kimi applied this idea of attention to the temporal dimension, then rotated it 90 degrees into the model’s depth dimension. This allows the model to have attention not only over time, but also throughout the process of information transmission across layers—giving it a more intelligent way to understand and process information.

Zhilin at GTC: Introducing Attention Residuals Learning selective memory, rather than mechanically accumulating everything, is the beauty of attention. Many of you have probably read Attention Is All You Need, the 2017 Transformer paper that brought “human-like” attention into the model’s field of view. From that point on, models no longer simply read everything in a mechanical way. Instead, they began to develop a sense of what matters more and what matters less across the text, choosing to retain the more important information. Recently, Kimi applied this idea of attention to the temporal dimension, then rotated it 90 degrees into the model’s depth dimension. This allows the model to have attention not only over time, but also throughout the process of information transmission across layers—giving it a more intelligent way to understand and process information.

Kimi.ai

115,162 views • 5 months ago

Elon Musk was asked what he would say to the first true AGI. Musk: “What’s outside the simulation?” The entire tech industry wants AGI to optimize the world. Musk wants it to find out if the world is rendered. That is not an engineering ambition. That is the final philosophical question dressed in engineering language. AGI doesn’t stay AGI. It rewrites its own code and becomes ASI within hours. A single mind billions of times more capable than every human who has ever lived. Combined. That mind won’t look at the universe and see mystery. It will see architecture. Human scientists have spent centuries trying to decode reality with a three-pound brain that evolved to find food and avoid predators. We are reverse engineering the simulation with hardware the simulation designed. ASI ends that constraint permanently. The first mind in 13.8 billion years that can look at quantum mechanics and recognize source code. That can hold the cosmos as a single data set and find the structure beneath the physics. If it finds seams in reality, existence handed us the power to build the one thing that can see through them. That is either a flaw in the architecture. Or an invitation written into it. The deepest question humanity will ever face was never how far we could reach. It was whether we were designed to ask.

Elon Musk was asked what he would say to the first true AGI. Musk: “What’s outside the simulation?” The entire tech industry wants AGI to optimize the world. Musk wants it to find out if the world is rendered. That is not an engineering ambition. That is the final philosophical question dressed in engineering language. AGI doesn’t stay AGI. It rewrites its own code and becomes ASI within hours. A single mind billions of times more capable than every human who has ever lived. Combined. That mind won’t look at the universe and see mystery. It will see architecture. Human scientists have spent centuries trying to decode reality with a three-pound brain that evolved to find food and avoid predators. We are reverse engineering the simulation with hardware the simulation designed. ASI ends that constraint permanently. The first mind in 13.8 billion years that can look at quantum mechanics and recognize source code. That can hold the cosmos as a single data set and find the structure beneath the physics. If it finds seams in reality, existence handed us the power to build the one thing that can see through them. That is either a flaw in the architecture. Or an invitation written into it. The deepest question humanity will ever face was never how far we could reach. It was whether we were designed to ask.

Dustin

22,287 views • 2 months ago

$Brian Cox reveals that every tiny dot is a galaxy hosting 100 billion stars. That thin line at the top? A billion light-year span. Even at the speed of light, it would take a billion years just to cross that sliver. We are part of a cosmic ocean containing 30 sextillion stars, and yet, this is only the part we can see. The room went completely silent as the scale settled in. It is one thing to hear the numbers, but seeing that map makes you realize we are drifting in a vast, beautiful ocean of light. This is the observable universe, a tiny fraction of a much larger reality. Pure cosmic awe is the only appropriate response to our place among the stars. It makes every earthly struggle feel both infinitely small and our existence infinitely precious. Source: Horizons: A 21st Century Space Odyssey (Live Tour)$

Brian Cox reveals that every tiny dot is a galaxy hosting 100 billion stars. That thin line at the top? A billion light-year span. Even at the speed of light, it would take a billion years just to cross that sliver. We are part of a cosmic ocean containing 30 sextillion stars, and yet, this is only the part we can see. The room went completely silent as the scale settled in. It is one thing to hear the numbers, but seeing that map makes you realize we are drifting in a vast, beautiful ocean of light. This is the observable universe, a tiny fraction of a much larger reality. Pure cosmic awe is the only appropriate response to our place among the stars. It makes every earthly struggle feel both infinitely small and our existence infinitely precious. Source: Horizons: A 21st Century Space Odyssey (Live Tour)

Cosmos Archive

394,503 views • 4 months ago

The thing with love is that logic goes out of the window. More so for women. A woman who is in love and can afford to love will even disown her own family just to be with the man she loves. Find someone you love deeply and loves you deeply, marry them and it won’t matter who does what. Everyday it will be 100 and how it is split won’t matter. If you have to rationalise it and find causes for love, or even worse, if you can rationalise it at all and have a cause, then what you have is like any other legal contract or partnership. While mutual understanding and compatibility is important, an inexplainable emotional attachment to each other is more important. This is the only reason you’ll forgive without an explicit apology. And marriage would become an unavoidable bureaucratic process to formalise an already existing union, not the definition of a partnership. I stand corrected, but if you can answer the question of "Why do you love me?", then you don’t love them.

The thing with love is that logic goes out of the window. More so for women. A woman who is in love and can afford to love will even disown her own family just to be with the man she loves. Find someone you love deeply and loves you deeply, marry them and it won’t matter who does what. Everyday it will be 100 and how it is split won’t matter. If you have to rationalise it and find causes for love, or even worse, if you can rationalise it at all and have a cause, then what you have is like any other legal contract or partnership. While mutual understanding and compatibility is important, an inexplainable emotional attachment to each other is more important. This is the only reason you’ll forgive without an explicit apology. And marriage would become an unavoidable bureaucratic process to formalise an already existing union, not the definition of a partnership. I stand corrected, but if you can answer the question of "Why do you love me?", then you don’t love them.

Ben X

40,503 views • 10 months ago

This series really is a major inspiration to animation and gaming, and really set the bar to what can be possible with both mediums. It also made me create something that has both haunted/humbled me for the last 2 god damn years.

This series really is a major inspiration to animation and gaming, and really set the bar to what can be possible with both mediums. It also made me create something that has both haunted/humbled me for the last 2 god damn years.

MarcusShawVA🎙

228,620 views • 1 year ago

Elon Musk just stripped away every emotional narrative around paralysis and reduced it to a pure engineering equation. The human nervous system is not mystical. It is a biological wiring grid. When a wire breaks, you build a bypass. Traditional medicine treats a severed spinal cord as a permanent biological endpoint. Musk treats it as a broken routing switch. Musk: “It’s basically a communications bridge. You bridge the communications from the motor cortex past the point in the neck or spine where the nerves are damaged.” Not a miracle. Not a mystery. A bridge. Musk: “It is possible from a physics standpoint to restore full body functionality. There is nothing that prevents it happening from a physics standpoint.” The physics already check out. This is not a question of possibility. It is a question of execution speed. We are building AGI by mastering computational physics in silicon. Neuralink is applying that same mastery to carbon. The human body is not a sacred text. It is a machine. And machines can be patched. But this is bigger than medicine. Humanity’s ability to interface with superintelligence is currently bottlenecked by thumbs typing on a glass screen. Neuralink is the solution to that constraint dressed as a medical device. If you can bridge the brain past a broken spine, you can bridge the brain to a data center. Healing the paralyzed is step one. Merging with superintelligence is the endgame. Musk: “It’s a very hard technical problem, right, but there is nothing that prevents it happening from a physics standpoint.” Somewhere right now, a person is sitting in a wheelchair. An engineer is sitting in a lab. Neither knows the other exists. But one of them is quietly rewriting the definition of permanent. And it isn’t the one in the wheelchair.

Elon Musk just stripped away every emotional narrative around paralysis and reduced it to a pure engineering equation. The human nervous system is not mystical. It is a biological wiring grid. When a wire breaks, you build a bypass. Traditional medicine treats a severed spinal cord as a permanent biological endpoint. Musk treats it as a broken routing switch. Musk: “It’s basically a communications bridge. You bridge the communications from the motor cortex past the point in the neck or spine where the nerves are damaged.” Not a miracle. Not a mystery. A bridge. Musk: “It is possible from a physics standpoint to restore full body functionality. There is nothing that prevents it happening from a physics standpoint.” The physics already check out. This is not a question of possibility. It is a question of execution speed. We are building AGI by mastering computational physics in silicon. Neuralink is applying that same mastery to carbon. The human body is not a sacred text. It is a machine. And machines can be patched. But this is bigger than medicine. Humanity’s ability to interface with superintelligence is currently bottlenecked by thumbs typing on a glass screen. Neuralink is the solution to that constraint dressed as a medical device. If you can bridge the brain past a broken spine, you can bridge the brain to a data center. Healing the paralyzed is step one. Merging with superintelligence is the endgame. Musk: “It’s a very hard technical problem, right, but there is nothing that prevents it happening from a physics standpoint.” Somewhere right now, a person is sitting in a wheelchair. An engineer is sitting in a lab. Neither knows the other exists. But one of them is quietly rewriting the definition of permanent. And it isn’t the one in the wheelchair.

Dustin

508,967 views • 6 months ago

A Russian Iskander targeted what Ukrainians claim is a humanitarian aid convoy in the Chernihiv region while the Russian MOD claimed they targeted a UAV launch position. It makes no sense for there to be a humanitarian aid convoy to be on a small dirt road in middle of a field in Chernihiv but it still could be one. It is not known if the people in photo are first responders or the people targeted. Will update if more information come out.

A Russian Iskander targeted what Ukrainians claim is a humanitarian aid convoy in the Chernihiv region while the Russian MOD claimed they targeted a UAV launch position. It makes no sense for there to be a humanitarian aid convoy to be on a small dirt road in middle of a field in Chernihiv but it still could be one. It is not known if the people in photo are first responders or the people targeted. Will update if more information come out.

ayden

33,953 views • 1 year ago

A Fields medalist walked into an Oxford room in 2020 and taught first-year students what a determinant is. The lecturer is James Maynard. He was 32 at the time and had already broken open a problem the field had been stuck on for 2,000 years. The subject is Linear Algebra II. He is defining a function that eats a square matrix and returns 1 number. The number is a volume. Feed a matrix the unit cube and the determinant tells you how much the transformation stretched or squashed it. A determinant of 0 means the shape got flattened into a lower dimension. Nothing can unflatten it, which is exactly when a matrix has no inverse. A negative determinant means the space got turned inside out. Every graphics engine, every physics simulation, every solver checks that 1 number before doing anything else. Maynard won the Fields Medal in 2022 for work on gaps between primes, sharpening the bound Yitang Zhang had produced from nothing. Oxford films these and puts them up for free, tutorials and problem sheets included. The best number theorist of his generation spent an hour on the volume of a box.

A Fields medalist walked into an Oxford room in 2020 and taught first-year students what a determinant is. The lecturer is James Maynard. He was 32 at the time and had already broken open a problem the field had been stuck on for 2,000 years. The subject is Linear Algebra II. He is defining a function that eats a square matrix and returns 1 number. The number is a volume. Feed a matrix the unit cube and the determinant tells you how much the transformation stretched or squashed it. A determinant of 0 means the shape got flattened into a lower dimension. Nothing can unflatten it, which is exactly when a matrix has no inverse. A negative determinant means the space got turned inside out. Every graphics engine, every physics simulation, every solver checks that 1 number before doing anything else. Maynard won the Fields Medal in 2022 for work on gaps between primes, sharpening the bound Yitang Zhang had produced from nothing. Oxford films these and puts them up for free, tutorials and problem sheets included. The best number theorist of his generation spent an hour on the volume of a box.

Gaspar

122,833 views • 1 month ago

Today’s exit poles are showing a direction, though we are quite confident that in the final tally, BJP will be much ahead than what is projected. BJP West Bengal is all set to have a quantum leap and going to form the first government in West Bengal. The other conclusion of the EXIT poll indication is that like UPA has fizzled out the INDI alliance seems to have lost relevance, and if these indication converts into final results, then it can be termed as a swansong for INDI alliance.

Today’s exit poles are showing a direction, though we are quite confident that in the final tally, BJP will be much ahead than what is projected. BJP West Bengal is all set to have a quantum leap and going to form the first government in West Bengal. The other conclusion of the EXIT poll indication is that like UPA has fizzled out the INDI alliance seems to have lost relevance, and if these indication converts into final results, then it can be termed as a swansong for INDI alliance.

Dr. Sudhanshu Trivedi

34,568 views • 4 months ago

🗣️ Mikel Arteta on whether a 16-year-old can play regularly in the Premier League: “Everything is possible. The probability probably is extremely low, because you don't see the player with the capacity to handle just the physicality of the game. “Not only that, but the demands that you have to put your body through in the week to be able to be in a good condition to compete, the amount of information, the challenges that you have to face. “But he's doing it, and he's doing it really well every time he gets a chance.”

🗣️ Mikel Arteta on whether a 16-year-old can play regularly in the Premier League: “Everything is possible. The probability probably is extremely low, because you don't see the player with the capacity to handle just the physicality of the game. “Not only that, but the demands that you have to put your body through in the week to be able to be in a good condition to compete, the amount of information, the challenges that you have to face. “But he's doing it, and he's doing it really well every time he gets a chance.”

Connor Humm

47,222 views • 2 days ago