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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.show more

Michael Guo

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85,647 просмотров • 26 дней назад •via X (Twitter)

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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

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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27,057 просмотров • 6 дней назад

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.

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13,485 просмотров • 20 дней назад

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.

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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In 2014, a woman won the Fields Medal for the first time since it was established. Her story is fascinating because she was representing ordinary girls from all over the world. Her name was Maryam Mirzakhani, and she was from Iran. When Maryam was studying in Iran, there were separate schools for boys and girls. This did not make it easy for her to pursue science. Still, she did not give up. She worked hard and became one of the first Iranian girls to take part in the International Mathematical Olympiad, where she won a gold medal. The following year, she won another gold medal. She completed her early studies in Iran and later went to the United States, where she earned her PhD from Harvard University in 2004. Ten years later, she was awarded the Fields Medal for her important work in the geometry of Riemann surfaces and their moduli spaces. Stories like hers help inspire more women to be included in the world of mathematics.

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Blair Williams revealed that she genuinely enjoys what she does, recalling an experience involving an NFL player and his father that made her realize how much she enjoys the attention and excitement that comes with her lifestyle. She explained that she likes the feeling of being desired because it makes her feel confident in what she does, and that at this point, it’s no longer mainly about the money but more about the thrill and passion behind it. “The money is great, but I want to be fvvking like the gods, the god fvvkers.”

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ANATOMY OF A SCENE: And this ladies and gentle is why I say Icala is one of the best shows we've produced in Mzansi. Look at the quiet brilliance of this SCENE. This is how I read it... 1. Mashandu's wardrobe and how it serves the story without anyone saying it, it is brilliant! 2. The beats in the conversation between her and the chief... It starts with her being flirty, he takes the bait, when he tries to assert his dominance in the dynamic, she reels him back to her having the upper hand by playing vulnerable. This whole scene is about her being in control even though the overarching visual says she is submitting to the men around her. Big up to the director for the shoes thing... She shows up in heels which are inappropriate practically but asserts her feminity. Taking them off lures us the audience into false sense of her relinquishing that feminine power. But from there the director frames her mostly in mid-shots when she speaks thus framing her as filling a space rather than being a subordinate in that space.

Kgopolo

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