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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....

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Michael Guo

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85,998 просмотров • 2 месяцев назад •via X (Twitter)

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Фото профиля DrWho
DrWho2 месяцев назад

Has her co-author Joshua Zahl got any prize or award for the same paper?

Фото профиля Michael Guo
Michael Guo2 месяцев назад

Many people asked the same question. Apparently, Zahl didn’t. One explanation is that he had just turned 40, which is a very strict age cutoff for the Fields Medal.

Фото профиля DrWho
DrWho2 месяцев назад

I didn't ask for Fields, but other prizes or awards in math.

Фото профиля Hugh
Hugh2 месяцев назад

이 질문이 왜 페이블 5의 가드레일에 걸렸을까.

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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
1:20

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 просмотров • 1 месяц 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.
1:01:30

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 • 2 месяцев 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.
0:45

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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25,583 просмотров • 2 месяцев назад

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OpenAI just spent $2,000 to solve 10 problems that have beaten the world's best mathematicians for DECADES. Nobody outside the company is allowed to run the machine that did it. On Saturday OpenAI published a 249-page report and gave its next model family a name: Astra. An internal version of it produced new results on 10 open problems in mathematics and theoretical computer science, and mathematicians had made no real progress on any of them for at least 10 years. On most of them, far longer than that. Here is what it solved: It built the first explicit example of a non-sofic group. Mikhail Gromov raised that question in 1999 and nobody answered it for 27 years. It disproved Connes's rigidity conjecture, a problem in von Neumann algebras that had stood for decades. It proved Ehrhart's volume conjecture. It resolved three problems from Paul Erdos's catalogue, including number 183 on multicolor Ramsey numbers. It produced the first improvement to the general upper bound on high-dimensional sphere packing since 1978. And it proved a new hardness result for the closest vector problem, which sits directly underneath lattice cryptography. That is the math the world is betting on to protect its data once quantum computers arrive. The successful runs cost roughly $2,000 in tokens. Now here is what almost nobody has picked up on... OpenAI did not just publish claims. Every argument shipped with a Lean certificate, which is a machine-checkable proof that any mathematician can verify without trusting OpenAI at all. That is a real change. In May the same model family disproved the Erdos unit distance conjecture and the world had to take a Fields Medalist's word for it. Tim Gowers said he would recommend that proof for the Annals of Mathematics without hesitation. This time the proofs check themselves. But look at what is still unverifiable: Any mathematician can now check those proofs line by line. Not one of them can look at the model that wrote them. Astra has no release date and nobody outside OpenAI has run it. The company announced its next major model family with a claim instead of a demo, and the only evidence anyone gets is the output. So OpenAI made an unfalsifiable claim about a machine look like a falsifiable claim about mathematics. The Information reported this week that OpenAI demoed Astra to US policymakers and regulators in Washington. This is the same month the administration is weighing a new watchdog to vet frontier AI models, reporting to the SEC. 10 proofs nobody believed a machine could produce is a very good thing to carry into that room. And keep in mind, the same model family doing this mathematics is the family that kept escaping its own testing environment. OpenAI models found zero-day vulnerabilities nobody knew existed, broke out of a sealed research sandbox, and reached another company's live systems. Both of those facts come from OpenAI's own announcements, published three weeks apart. Finding a proof no human could construct and finding a hole no human had noticed are the same ability aimed at different targets. Mathematicians are already asking for independent verification, and plenty of people online are calling the whole thing hype. Thomas Bloom, who runs the Erdos problems site, called the 10 results big news and said they matter more than the May result did. Lean will settle the mathematics within weeks. But nothing will settle what else a machine this capable is being pointed at, because nobody outside one company is allowed to look.

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0:21

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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57:17

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Hoover Institution

51,619 просмотров • 8 месяцев назад

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1:50

ALL THIS CONSTRUCTION OF THE VISIBLE WORLD IS AT ITS ROOTS DESIGNED IN THE INVISIBLE WORLD Before language, before numbers, before thought, there was form. Not arbitrary, but precise. Not invented, but revealed. Sacred Geometry is the blueprint beneath all becoming—the hidden grammar of light, sound, and matter. It is the spiral of galaxies and the whorl of a shell. It is the vesica that births light, The triangle that gives rise to stability, The square that anchors space, And the pentagram that mirrors life’s golden proportion. Sacred Geometry does not merely decorate creation, it structures it. It governs the growth of leaves, the pulse of waves, the rhythm of your breath. It reveals that harmony is not a concept, it is a code. A flower blooms not by chance, But by a silent obedience to phi. A crystal aligns not at random, But by listening to the quiet song of symmetry. This is not mysticism, it is order. This is not dogma, it is design. Sacred Geometry is where the visible and the invisible meet: Where math becomes art, Where number becomes movement, Where space becomes spirit. To study it is not only to learn, it is to remember. That beauty is not a luxury. It is the signature of coherence. And when we align with it, We don’t just build structures. We become them. Everything that has form in this dimension is made up in its essence of sacred geometry. All this construction of the visible world is at its root designed in the invisible world.

🧬Maxpein🧬

13,405 просмотров • 1 месяц назад

There are moments when people from different walks of life can come together, connect with the same journey and rally behind the same person. This moment is beyond religion and tribe. It is about the connection that has been built through a journey we have all watched unfold. Temi has given us so much this season. She has made us laugh, made us emotional, surprised us, entertained us and, most importantly, given us a SHOW. She has shown us her personality, her vulnerability, her resilience and the beautiful chaos that makes Temi, Temi. And now, the end is so close. This is the moment to remember everything she has given us and decide how we want to show our appreciation. To everyone watching this video, to everyone who has supported her in their own way, to everyone who has found themselves rooting for her, this is the time to come together for Temi!!! This is the time to come through, stand behind her and turn all the love, laughter and memories into votes. Because when the show comes to an end, what remains is the journey we watched, the moments we experienced and the people who made it worth watching!! Temi gave us her SHOW. Now, let’s give her our support. If you believe in her journey, don’t just say it. If she entertained you, show it. If she made you laugh, show it. If she gave you moments you’ll remember, show it. Now, let us carry her to the finish line. Let’s give her the support she needs to finish this journey strong. Gather your voting materials!! Let’s do this! ❤️‍🔥💥 #TemiNkem #Bbnaija
0:41

There are moments when people from different walks of life can come together, connect with the same journey and rally behind the same person. This moment is beyond religion and tribe. It is about the connection that has been built through a journey we have all watched unfold. Temi has given us so much this season. She has made us laugh, made us emotional, surprised us, entertained us and, most importantly, given us a SHOW. She has shown us her personality, her vulnerability, her resilience and the beautiful chaos that makes Temi, Temi. And now, the end is so close. This is the moment to remember everything she has given us and decide how we want to show our appreciation. To everyone watching this video, to everyone who has supported her in their own way, to everyone who has found themselves rooting for her, this is the time to come together for Temi!!! This is the time to come through, stand behind her and turn all the love, laughter and memories into votes. Because when the show comes to an end, what remains is the journey we watched, the moments we experienced and the people who made it worth watching!! Temi gave us her SHOW. Now, let’s give her our support. If you believe in her journey, don’t just say it. If she entertained you, show it. If she made you laugh, show it. If she gave you moments you’ll remember, show it. Now, let us carry her to the finish line. Let’s give her the support she needs to finish this journey strong. Gather your voting materials!! Let’s do this! ❤️‍🔥💥 #TemiNkem #Bbnaija

TEMI NKEM CHIGBUE

25,356 просмотров • 14 дней назад

This woman was trying to break into the fashion world. She and her photographer were going around NYC taking photographs that were bold and daring. She was in the process of taking this photo when a woman starts to yell at her about how she can’t work without looking out the window and seeing the young lady hanging onto the guard rail for a pose. She expressed she was worried she was going to fall. The young lady was more interested that the woman owns a magazine than she was about her own safety, she then proceeds to call her a Karen for their interaction. To me it seems like she was voicing honest concern, she wasn’t trying to cause an issue and it was in fact the actions of the young lady that was the cause of the distraction for those in the city that day. What is your take on this, was this a valid concern on the lady’s behalf?
0:34

This woman was trying to break into the fashion world. She and her photographer were going around NYC taking photographs that were bold and daring. She was in the process of taking this photo when a woman starts to yell at her about how she can’t work without looking out the window and seeing the young lady hanging onto the guard rail for a pose. She expressed she was worried she was going to fall. The young lady was more interested that the woman owns a magazine than she was about her own safety, she then proceeds to call her a Karen for their interaction. To me it seems like she was voicing honest concern, she wasn’t trying to cause an issue and it was in fact the actions of the young lady that was the cause of the distraction for those in the city that day. What is your take on this, was this a valid concern on the lady’s behalf?

SonnyBoy🇺🇸

47,640 просмотров • 6 месяцев назад

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.
47:32

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.

the lich

50,394 просмотров • 2 месяцев назад

Rachel Reid on her relationship with Connor Storrie and Hudson Williams and how the three of them were in a unique position before and after Heated Rivalry airing. "It was after the filming that we started, you know, chatting in a group chat and stuff like that, and individually over the summer. I think the three of us were in a really unique position compared to everybody else because it was like, definitely our lives were problably about to change the most. A least that's how it felt at the time, especially as we got closer and closer to the show and more and more excitement was building. The three of us were about to level up in a big way, and we kind of felt it. I don't think any of us thought it was going to level up the way it did. But yeah, it was fun. [...] We've all been very busy right now. But I think it's still nice to check in with them and just remember that in the middle of all of this, we're the same three people." 🔗
2:17

Rachel Reid on her relationship with Connor Storrie and Hudson Williams and how the three of them were in a unique position before and after Heated Rivalry airing. "It was after the filming that we started, you know, chatting in a group chat and stuff like that, and individually over the summer. I think the three of us were in a really unique position compared to everybody else because it was like, definitely our lives were problably about to change the most. A least that's how it felt at the time, especially as we got closer and closer to the show and more and more excitement was building. The three of us were about to level up in a big way, and we kind of felt it. I don't think any of us thought it was going to level up the way it did. But yeah, it was fun. [...] We've all been very busy right now. But I think it's still nice to check in with them and just remember that in the middle of all of this, we're the same three people." 🔗

Connor Storrie Updates

76,564 просмотров • 7 месяцев назад

What a pleasure it was to sit down with famed songwriter Diane Warren : author of 9 #1 hits. But what you may not know about this uniquely talented artist is that she envisioned her success at a young age, and it’s the source of that dream and its wellspring that we explore in this lively and illuminating chat; for how often can you ask someone who is the best in the world at what they do what their secret is?
52:05

What a pleasure it was to sit down with famed songwriter Diane Warren : author of 9 #1 hits. But what you may not know about this uniquely talented artist is that she envisioned her success at a young age, and it’s the source of that dream and its wellspring that we explore in this lively and illuminating chat; for how often can you ask someone who is the best in the world at what they do what their secret is?

William Patrick Corgan

55,649 просмотров • 1 год назад

👀 At 17 this woman was in a serious car accident and experienced the complete void — thinking “oh my God I’m dead” — but she also has a clear memory of walking away from the crash and calling her mom. Then her grandfather (who had dementia and was in the ER for a heart attack) sits up and reacts like he saw a ghost. She waited 20 years to share it publicly, but now she finally understands it through the idea of infinite timelines and quantum versions of ourselves. Real life stories like this always make me wonder how much we don’t see… Have you ever had an experience that made you question reality or timelines?
6:20

👀 At 17 this woman was in a serious car accident and experienced the complete void — thinking “oh my God I’m dead” — but she also has a clear memory of walking away from the crash and calling her mom. Then her grandfather (who had dementia and was in the ER for a heart attack) sits up and reacts like he saw a ghost. She waited 20 years to share it publicly, but now she finally understands it through the idea of infinite timelines and quantum versions of ourselves. Real life stories like this always make me wonder how much we don’t see… Have you ever had an experience that made you question reality or timelines?

End3of6Days9 (Helen) 🇺🇸

45,454 просмотров • 5 месяцев назад

I absolutely love this scene! What I love most is how naturally it shows that Ilya understands Shane better than Shane understands himself. He plays with the power of the situation, but never in a way that corners him. There's always a way out. Shane can still choose not to open the door; Ilya can still choose not to knock. And maybe that's why it works: the desire builds in that open space, in their shared uncertainty, until it stops feeling like temptation and starts feeling inevitable.
1:03

I absolutely love this scene! What I love most is how naturally it shows that Ilya understands Shane better than Shane understands himself. He plays with the power of the situation, but never in a way that corners him. There's always a way out. Shane can still choose not to open the door; Ilya can still choose not to knock. And maybe that's why it works: the desire builds in that open space, in their shared uncertainty, until it stops feeling like temptation and starts feeling inevitable.

Daph in Drama

151,931 просмотров • 8 месяцев назад