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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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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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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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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.

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In 1962, a helicopter flying over the vast forests of Guatemala and Honduras saw a series of temples in the middle of these forests. After that, research was done on it and it was found out that it is an ancient Hindu temple and the description of snake god or Hades in Hindu culture is the same. At a short distance from here in Honduras, a huge cave and many statues of Hanuman Ji and evidence of an entire city have been found and many Hindu temples have been found. Watch National Geographic report

Baba Banaras™

240,926 Aufrufe • vor 1 Jahr

His lighthouse stood for 123 years. And in the end it was not the tower that failed. It was the rock underneath it. 🇬🇧 Two lighthouses stood on the Eddystone Rocks before him, 14 miles south of Plymouth, and the sea destroyed them both. The first, built of wood, vanished without trace in the Great Storm of 1703, taking its builder and 5 other men with it. The second stood for 47 years, then burned one December night in 1755, down to the rock it stood on. 🔥 So Britain faced a question: how do you build on a rock the sea owns? The Royal Society's answer was not a lighthouse man. It was John Smeaton, an Englishman from Austhorpe near Leeds, a maker of scientific instruments who had turned his mind to engineering. He started with a question nobody had thought to ask. Why does an oak tree survive a storm? Wide at the root, narrow at the top. So he shaped his tower like the trunk of an oak. Wood had washed away and wood had burned, so he built in granite, every block dovetailed into its neighbours like a carpenter's joint in stone, pinned with dowels of marble. For the mortar he ran experiment after experiment until he proved which limestone sets hard even underwater, a lime the Romans had used whose science had been lost. He worked out why and brought it back. 3 years, 1756 to 1759, 14 miles out in the open sea. Then the lamp was lit, and the sea came to test it, winter after winter. It did not move. He went on to build bridges, harbours, canals and mills across Britain, and because the only engineers Britain named were soldiers, he called himself a civil engineer, the first man in Britain to do it. In 1771 he and 6 others met in a London tavern and founded the first engineering society anywhere in the world. It still exists. 🏛️ His light burned for 123 years. When engineers finally found a fault in 1877, it was in the reef, not the tower. The sea was wearing away the rock beneath it. His tower had outlasted the rock it stood on. In 1882 the lamp went out for the last time. But nobody scrapped his tower. The top came down stone by stone and went back up on Plymouth Hoe, where it stands today in its red and white bands. You can climb it. ━━━━━━━━━━━━━━ Look at any lighthouse standing on a British rock. That curve is his oak, still holding. We are the home of British heroes. There is a place for you in it. 👉 👈 Be part of us. ☝️🇬🇧 Be Proud Of Us. 🙏🇬🇧
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His lighthouse stood for 123 years. And in the end it was not the tower that failed. It was the rock underneath it. 🇬🇧 Two lighthouses stood on the Eddystone Rocks before him, 14 miles south of Plymouth, and the sea destroyed them both. The first, built of wood, vanished without trace in the Great Storm of 1703, taking its builder and 5 other men with it. The second stood for 47 years, then burned one December night in 1755, down to the rock it stood on. 🔥 So Britain faced a question: how do you build on a rock the sea owns? The Royal Society's answer was not a lighthouse man. It was John Smeaton, an Englishman from Austhorpe near Leeds, a maker of scientific instruments who had turned his mind to engineering. He started with a question nobody had thought to ask. Why does an oak tree survive a storm? Wide at the root, narrow at the top. So he shaped his tower like the trunk of an oak. Wood had washed away and wood had burned, so he built in granite, every block dovetailed into its neighbours like a carpenter's joint in stone, pinned with dowels of marble. For the mortar he ran experiment after experiment until he proved which limestone sets hard even underwater, a lime the Romans had used whose science had been lost. He worked out why and brought it back. 3 years, 1756 to 1759, 14 miles out in the open sea. Then the lamp was lit, and the sea came to test it, winter after winter. It did not move. He went on to build bridges, harbours, canals and mills across Britain, and because the only engineers Britain named were soldiers, he called himself a civil engineer, the first man in Britain to do it. In 1771 he and 6 others met in a London tavern and founded the first engineering society anywhere in the world. It still exists. 🏛️ His light burned for 123 years. When engineers finally found a fault in 1877, it was in the reef, not the tower. The sea was wearing away the rock beneath it. His tower had outlasted the rock it stood on. In 1882 the lamp went out for the last time. But nobody scrapped his tower. The top came down stone by stone and went back up on Plymouth Hoe, where it stands today in its red and white bands. You can climb it. ━━━━━━━━━━━━━━ Look at any lighthouse standing on a British rock. That curve is his oak, still holding. We are the home of British heroes. There is a place for you in it. 👉 👈 Be part of us. ☝️🇬🇧 Be Proud Of Us. 🙏🇬🇧

Proudofus.uk

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