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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...

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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.
22:43

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

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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
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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

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Elon Musk says “Grok 4 is going to get to the point where it’s going to get every answer right in every exam. And where it doesn’t get an answer right, it’s going to tell you what’s wrong with the question or, if the question is ambiguous, disambiguate the question into answers A, B, and C, and tell you what answer A, B, and C would be with a disambiguated question. So then the only real test would be reality. Can it discover new science? That will be the only thing actually left.
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Elon Musk says “Grok 4 is going to get to the point where it’s going to get every answer right in every exam. And where it doesn’t get an answer right, it’s going to tell you what’s wrong with the question or, if the question is ambiguous, disambiguate the question into answers A, B, and C, and tell you what answer A, B, and C would be with a disambiguated question. So then the only real test would be reality. Can it discover new science? That will be the only thing actually left.

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Russian robotic complex "Stalker" demining liberated territory in Kursk border area The operator can control the machine at a distance of up to 1-3 km, receiving images from four cameras placed on the "Stalker". The machine was developed by Chelyabinsk "DST-Ural" and a year ago was tested near Avdeevka, and now, probably, is being serially supplied to engineering units. The "Stalker" has a mass of 27 tons and an engine with a capacity of 540 hp. It is designed to clear the area of ​​explosive objects and anti-personnel mines. In the event of an anti-tank mine detonation, the protective casing of the robot will be damaged, which can be replaced - it is a consumable.
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Russian robotic complex "Stalker" demining liberated territory in Kursk border area The operator can control the machine at a distance of up to 1-3 km, receiving images from four cameras placed on the "Stalker". The machine was developed by Chelyabinsk "DST-Ural" and a year ago was tested near Avdeevka, and now, probably, is being serially supplied to engineering units. The "Stalker" has a mass of 27 tons and an engine with a capacity of 540 hp. It is designed to clear the area of ​​explosive objects and anti-personnel mines. In the event of an anti-tank mine detonation, the protective casing of the robot will be damaged, which can be replaced - it is a consumable.

Zlatti71

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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.
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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

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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.
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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.

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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.
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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.

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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)
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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

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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.
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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🎙

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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.
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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

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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.
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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.

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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.
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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.

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🚨 NEW: Fox’s Brit Hume gives a reality check on peace with Iran: “Even if it does happen you have the fundamental question of whether any deal reached with some remnant of Iran’s regime can be trusted.” “The Iranians lie, cheat and every word that comes out of their mouths you have to regard with extreme scepticism.” “A lot of it is manifestly untrue and their recent description if their attack on Israel is a perfect example. So we still have the question of whether it is possible to get a verifiable deal with this regime.”
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🚨 NEW: Fox’s Brit Hume gives a reality check on peace with Iran: “Even if it does happen you have the fundamental question of whether any deal reached with some remnant of Iran’s regime can be trusted.” “The Iranians lie, cheat and every word that comes out of their mouths you have to regard with extreme scepticism.” “A lot of it is manifestly untrue and their recent description if their attack on Israel is a perfect example. So we still have the question of whether it is possible to get a verifiable deal with this regime.”

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Naval Ravikant: “Human creativity is non-linear” “The right idea can be worth almost infinitely more than the wrong idea. And so it’s only a small number of innovators that are needed to really drive any endeavor you can imagine…. Assembling a small number of the right people to interact with each other will drive everything.” Naval continues: “Every revolution - whether it’s scientific, political, technological, or physical - is driven by a small number of like-minded people who are at the cutting edge of thought, getting together and brainstorming with each other.” This is as true of the Founding Founders as it is of many of the great companies in Silicon Valley. Naval argues: “You just need to figure out how to get a small number of very innovative people in the same idea space together and cooperating with each other to create the next round of institutions… A few dozen, a few hundred, a few thousand people can come up with the right ideas that will completely change things for everybody.” Video source: Balaji Naval (2024)
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Naval Ravikant: “Human creativity is non-linear” “The right idea can be worth almost infinitely more than the wrong idea. And so it’s only a small number of innovators that are needed to really drive any endeavor you can imagine…. Assembling a small number of the right people to interact with each other will drive everything.” Naval continues: “Every revolution - whether it’s scientific, political, technological, or physical - is driven by a small number of like-minded people who are at the cutting edge of thought, getting together and brainstorming with each other.” This is as true of the Founding Founders as it is of many of the great companies in Silicon Valley. Naval argues: “You just need to figure out how to get a small number of very innovative people in the same idea space together and cooperating with each other to create the next round of institutions… A few dozen, a few hundred, a few thousand people can come up with the right ideas that will completely change things for everybody.” Video source: Balaji Naval (2024)

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Elon Musk: Leading an engineering department without being good at engineering is like being a cavalry captain who can't ride a horse. “If somebody is going to lead something in technology, they must themselves be good at technology. If they're going to lead something that involves complex engineering, they must themselves be good at engineering. They don't necessarily need to be the best engineer on the team, but they need to be very competent in their field. This is incredibly important. To me, if somebody's leading a given engineering field or engineering department, and they are not good at that, then that would be like a cavalry captain who can't ride a horse. Problem: great leader in every way, except he can't ride a horse. Then you've got to charge into battle, and the cavalry captain falls off the horse. It's not inspiring. So, the cavalry captain must be able to ride a horse. They don't need to be the best horse rider, but they must be competent in this regard. Otherwise, they cannot evaluate the talent of the team. And they don't understand the technology that's being developed. This may seem like a simple thing, but it is often the case that this is overlooked.” Interview at West Point, August 16, 2024
1:03

Elon Musk: Leading an engineering department without being good at engineering is like being a cavalry captain who can't ride a horse. “If somebody is going to lead something in technology, they must themselves be good at technology. If they're going to lead something that involves complex engineering, they must themselves be good at engineering. They don't necessarily need to be the best engineer on the team, but they need to be very competent in their field. This is incredibly important. To me, if somebody's leading a given engineering field or engineering department, and they are not good at that, then that would be like a cavalry captain who can't ride a horse. Problem: great leader in every way, except he can't ride a horse. Then you've got to charge into battle, and the cavalry captain falls off the horse. It's not inspiring. So, the cavalry captain must be able to ride a horse. They don't need to be the best horse rider, but they must be competent in this regard. Otherwise, they cannot evaluate the talent of the team. And they don't understand the technology that's being developed. This may seem like a simple thing, but it is often the case that this is overlooked.” Interview at West Point, August 16, 2024

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