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How do mathematicians reveal patterns in structures too complex to see directly? That is at the heart of the work of 2026 Wolf Prize in Mathematics Laureates David Kazhdan and Joseph Bernstein. Their discoveries helped build what is now known as geometric representation theory — a field that connects...

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Wolf Prize

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88,284 次观看 • 4 天前 •via X (Twitter)

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dan with glasses3 天前

@HebrewU @HebrewU_heb @TelAvivUni @WolfPrize_ @grok "connects algebra, geometry and symmetry" is broad. Specify one Kazhdan–Lusztig or D-module construction where structure actually transfers: all exact relations lift SDG5 to @leanprover: connection →PiπΠ lift →theorem #LeanProver 🔢 🧠

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What happens when you cool atoms to almost absolute zero and then learn to control them with extraordinary precision? That question lies at the heart of the work of 2026 Wolf Prize in Physics Laureates Immanuel F. Bloch and Jun Ye. Bloch helped turn ultracold atoms into powerful quantum simulators, experimental systems that allow physicists to recreate and study complex quantum behavior in a highly controlled environment. Ye pushed precision in a different direction, developing optical atomic clocks of remarkable accuracy and stability, opening new ways to measure time, gravity, and even test some of the most fundamental laws of physics. The science is complex. The idea behind it is surprisingly intuitive: control atoms well enough, and they become tools for exploring questions that ordinary matter cannot easily reveal. Watch the video to see how their work is giving physicists unprecedented control over the quantum world and why that matters far beyond the laboratory. National Institute of Standards and Technology Max Planck Society
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What happens when you cool atoms to almost absolute zero and then learn to control them with extraordinary precision? That question lies at the heart of the work of 2026 Wolf Prize in Physics Laureates Immanuel F. Bloch and Jun Ye. Bloch helped turn ultracold atoms into powerful quantum simulators, experimental systems that allow physicists to recreate and study complex quantum behavior in a highly controlled environment. Ye pushed precision in a different direction, developing optical atomic clocks of remarkable accuracy and stability, opening new ways to measure time, gravity, and even test some of the most fundamental laws of physics. The science is complex. The idea behind it is surprisingly intuitive: control atoms well enough, and they become tools for exploring questions that ordinary matter cannot easily reveal. Watch the video to see how their work is giving physicists unprecedented control over the quantum world and why that matters far beyond the laboratory. National Institute of Standards and Technology Max Planck Society

Wolf Prize

207,090 次观看 • 4 天前

For 300 years mathematicians solved polynomials of degree 1, 2, 3, and 4 with increasingly complex formulas. Then they hit degree 5 and the formula simply doesn't exist - not undiscovered, provably impossible. The reason is group theory. The 5 solutions of a quintic can be scrambled in ways that no finite chain of nested roots can replicate - the same symmetry mathematics that underlies modern cryptography and the attention mechanism in transformers. 28 minutes. Bookmark & watch today. The proof is more beautiful than the formula would have been.
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For 300 years mathematicians solved polynomials of degree 1, 2, 3, and 4 with increasingly complex formulas. Then they hit degree 5 and the formula simply doesn't exist - not undiscovered, provably impossible. The reason is group theory. The 5 solutions of a quintic can be scrambled in ways that no finite chain of nested roots can replicate - the same symmetry mathematics that underlies modern cryptography and the attention mechanism in transformers. 28 minutes. Bookmark & watch today. The proof is more beautiful than the formula would have been.

Eron

34,543 次观看 • 1 个月前

I think one of the roles we play as mathematicians in society is to help people become acquainted with the underlying secret patterns. I have been working for several years on projects in crystallography, where we study crystal structures. But few people know that such periodic patterns come with severe constraints on their symmetry. In the plane, there are 17 different symmetry types, a fact well known even to the designers of the mesmerizing patterns of the Alhambra. Here you can find and experiment with such tilings in the plane, gaining insight into the intrinsic beauty of the so-called wallpaper groups, the crystal symmetries in dimension 2. The app interactively helps you design symmetric patterns with colors and shows how changes in the structure of the unit cell propagate via symmetry. In dimension 3, if you look into International Tables for Crystallography, Vol. 1, you will find a theorem due to Schoenflies and Fedorov stating that there are 230 such symmetry types, a cornerstone of modern chemistry. Beyond that, in dimensions 4 and higher, a count can be made, but it requires a proof of the general theorem due to Frobenius and Bieberbach. This was an answer to the first part of Hilbert’s famous eighteenth problem. One of the fun consequences of such a classification is that in dimensions 2 and 3, 5-fold symmetry is forbidden in regular periodic arrangements. Intrinsically, this fact is related to the existence of matrices with a fifth-root-of-unity eigenvalue. For integral matrices, this is possible only in dimensions 4 and higher. If you generalize the square and cube tilings to dimensions 4 and 5, obtaining hypercubic tilings, the 5-fold symmetry pattern emerges. Skew projections of the 5D hypercubic tiling onto a 2-dimensional plane give rise to a quasicrystalline tiling known as the Penrose tiling. You can find such patterns in front of the Andrew Wiles Building at the Oxford Mathematical Institute. In later posts this summer, I will take a deep dive into group homology, a modern tool for studying the geometry of crystals. There are still many open questions, for example, how many symmetry types exist exactly in dimensions beyond 6. This is still largely unknown; at present, we only have asymptotic lower bounds.
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I think one of the roles we play as mathematicians in society is to help people become acquainted with the underlying secret patterns. I have been working for several years on projects in crystallography, where we study crystal structures. But few people know that such periodic patterns come with severe constraints on their symmetry. In the plane, there are 17 different symmetry types, a fact well known even to the designers of the mesmerizing patterns of the Alhambra. Here you can find and experiment with such tilings in the plane, gaining insight into the intrinsic beauty of the so-called wallpaper groups, the crystal symmetries in dimension 2. The app interactively helps you design symmetric patterns with colors and shows how changes in the structure of the unit cell propagate via symmetry. In dimension 3, if you look into International Tables for Crystallography, Vol. 1, you will find a theorem due to Schoenflies and Fedorov stating that there are 230 such symmetry types, a cornerstone of modern chemistry. Beyond that, in dimensions 4 and higher, a count can be made, but it requires a proof of the general theorem due to Frobenius and Bieberbach. This was an answer to the first part of Hilbert’s famous eighteenth problem. One of the fun consequences of such a classification is that in dimensions 2 and 3, 5-fold symmetry is forbidden in regular periodic arrangements. Intrinsically, this fact is related to the existence of matrices with a fifth-root-of-unity eigenvalue. For integral matrices, this is possible only in dimensions 4 and higher. If you generalize the square and cube tilings to dimensions 4 and 5, obtaining hypercubic tilings, the 5-fold symmetry pattern emerges. Skew projections of the 5D hypercubic tiling onto a 2-dimensional plane give rise to a quasicrystalline tiling known as the Penrose tiling. You can find such patterns in front of the Andrew Wiles Building at the Oxford Mathematical Institute. In later posts this summer, I will take a deep dive into group homology, a modern tool for studying the geometry of crystals. There are still many open questions, for example, how many symmetry types exist exactly in dimensions beyond 6. This is still largely unknown; at present, we only have asymptotic lower bounds.

Bartosz Naskręcki

44,467 次观看 • 4 个月前

🚨Jason Padgett: the accidental savant who says he can see the geometric code behind reality. After a brutal attack in 2002, Padgett developed acquired savant syndrome and began seeing the world in intricate geometric and fractal patterns. Movement became sequences of geometric “snapshots.” Water, light, and ordinary objects seemed to reveal mathematical structures hiding beneath everyday perception. Today, he makes hundreds of videos explaining his ideas about the nature of reality, including his theory of Quantum Information Holography (QIH)—the idea that the universe may be fundamentally connected to information, light, geometry, and holographic projection. What happens when your perception of reality changes so radically that you start trying to reverse-engineer the universe from what you see?
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🚨Jason Padgett: the accidental savant who says he can see the geometric code behind reality. After a brutal attack in 2002, Padgett developed acquired savant syndrome and began seeing the world in intricate geometric and fractal patterns. Movement became sequences of geometric “snapshots.” Water, light, and ordinary objects seemed to reveal mathematical structures hiding beneath everyday perception. Today, he makes hundreds of videos explaining his ideas about the nature of reality, including his theory of Quantum Information Holography (QIH)—the idea that the universe may be fundamentally connected to information, light, geometry, and holographic projection. What happens when your perception of reality changes so radically that you start trying to reverse-engineer the universe from what you see?

High Strangeness

272,492 次观看 • 1 个月前

How do you make reading DNA faster, cheaper and scalable enough to transform medicine? That question sits at the heart of the breakthrough behind the 2026 Wolf Prize in Chemistry, awarded to Pascal Mayer, Shankar Balasubramanian and David Klenerman. Their work helped turn DNA sequencing into a massively parallel process, dramatically reducing the cost and time needed to read genetic information, and helping make large-scale genomics possible. But what does that actually mean? How does next-generation sequencing work, and why was this such a major leap forward? Watch the video to see the science behind the breakthrough and understand how three researchers helped change the way we read the human genome. Cambridge University
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How do you make reading DNA faster, cheaper and scalable enough to transform medicine? That question sits at the heart of the breakthrough behind the 2026 Wolf Prize in Chemistry, awarded to Pascal Mayer, Shankar Balasubramanian and David Klenerman. Their work helped turn DNA sequencing into a massively parallel process, dramatically reducing the cost and time needed to read genetic information, and helping make large-scale genomics possible. But what does that actually mean? How does next-generation sequencing work, and why was this such a major leap forward? Watch the video to see the science behind the breakthrough and understand how three researchers helped change the way we read the human genome. Cambridge University

Wolf Prize

219,241 次观看 • 4 天前

#Huawei is proud to sponsor the #Olympiad #competition series that bring together enthusiastic students for a life-changing experience that unlocks new ways of thinking to solve complex problems in both their study and work. Follow their journey now:
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#Huawei is proud to sponsor the #Olympiad #competition series that bring together enthusiastic students for a life-changing experience that unlocks new ways of thinking to solve complex problems in both their study and work. Follow their journey now:

Huawei

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D-Branes and the Expansion of String Theory String Theory was already attempting to do something huge by trying to describe particles, forces, and gravity in one framework. Branes made that picture much richer. When Physicists found that open strings can end on objects called D-branes, many important ideas became easier to organize. Things like gauge fields, black hole microstates, holography, and deep dualities gained a clearer place inside the theory. They showed that String Theory is not only about tiny vibrating strings, but also about larger structures that help connect Quantum Physics, Geometry, and Gravity.

Mathelirium

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Mathelirium

42,291 次观看 • 7 个月前

I asked Dario 3 years ago why AIs haven't been able to use their vast knowledge across so many fields to connect two known ideas into a new discovery. It seems like AI did exactly this in the way it disproved Erdos' conjecture aobut the unit distance problem by cleverly onnecting together ideas in discrete geometry and algebraic number theory. Now that AI has been able to use its knowledge across multiple fields to come up with new ideas, what is the next benchmark? Grant Sanderson proposed one during our interview: "Good mathematicians prove theorems, great mathematicians come up with conjectures, and the greatest mathematicians come up with definitions."
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I asked Dario 3 years ago why AIs haven't been able to use their vast knowledge across so many fields to connect two known ideas into a new discovery. It seems like AI did exactly this in the way it disproved Erdos' conjecture aobut the unit distance problem by cleverly onnecting together ideas in discrete geometry and algebraic number theory. Now that AI has been able to use its knowledge across multiple fields to come up with new ideas, what is the next benchmark? Grant Sanderson proposed one during our interview: "Good mathematicians prove theorems, great mathematicians come up with conjectures, and the greatest mathematicians come up with definitions."

Dwarkesh Patel

328,578 次观看 • 3 个月前

The Freemasons did not invent the title of Great Architect for God arbitrarily. Randall traces it to a specific and ancient understanding - that the universe was built according to geometry, that all of creation carries that geometry inherently within it, and that the role of the master builder was not to express personal creativity but to replicate the processes by which God constructed reality itself. The grand geometric mean - another name Randall notes the Freemasons apply to the divine - points to the same conclusion. Mathematics and divinity were never separate categories in this tradition. They were the same thing viewed from different angles. What Randall finds most compelling is the point at which observation overtakes skepticism. The geometry is there. It appears in the proportions of living organisms, in the structure of galaxies, in the dimensions of ancient monuments, and in the relationships between celestial bodies. Randall’s position is straightforward - there is a threshold beyond which dismissing this as coincidence is no longer intellectually honest. Once you begin looking for the geometry of creation, it becomes impossible to stop finding it. The ancient master builders understood that - and everything they built was a deliberate act of alignment with a geometric order they believed was not invented by human minds but discovered within a universe that was already built that way from the beginning.
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The Freemasons did not invent the title of Great Architect for God arbitrarily. Randall traces it to a specific and ancient understanding - that the universe was built according to geometry, that all of creation carries that geometry inherently within it, and that the role of the master builder was not to express personal creativity but to replicate the processes by which God constructed reality itself. The grand geometric mean - another name Randall notes the Freemasons apply to the divine - points to the same conclusion. Mathematics and divinity were never separate categories in this tradition. They were the same thing viewed from different angles. What Randall finds most compelling is the point at which observation overtakes skepticism. The geometry is there. It appears in the proportions of living organisms, in the structure of galaxies, in the dimensions of ancient monuments, and in the relationships between celestial bodies. Randall’s position is straightforward - there is a threshold beyond which dismissing this as coincidence is no longer intellectually honest. Once you begin looking for the geometry of creation, it becomes impossible to stop finding it. The ancient master builders understood that - and everything they built was a deliberate act of alignment with a geometric order they believed was not invented by human minds but discovered within a universe that was already built that way from the beginning.

Randall Carlson

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The Non-Traversable Bridge Einstein Found Inside Gravity Einstein’s equations not only describe gravity as a force but as the shape of Spacetime as well. In 1935, Einstein and Rosen found that the Schwarzschild solution could be written in a way that reveals something astonishing: Two separate exterior regions of Spacetime joined by a bridge-like throat Rᵤᵥ = 0 This became known as the Einstein-Rosen Bridge. It is often called a Wormhole, but the classical Einstein-Rosen bridge is not a science-fiction tunnel. In the standard Schwarzschild geometry, it is non-traversable. The throat does not remain open long enough for ordinary travel from one region to the other. Its real power is mathematical. It shows that General Relativity is not merely about objects moving through space. The theory allows Spacetime to have global structure such as different regions, horizons, extensions, and hidden connections that are not visible from one local patch alone. The Einstein-Rosen bridge is one of the earliest glimpses of that deeper idea. Gravity is geometry. And sometimes, geometry has two worlds joined by a throat. #Astrophysics #GeneralRelativity #Einstein #BlackHole #Spacetime #Cosmology #Gravity #Wormhole #Mathematics #Physics

Mathelirium

92,028 次观看 • 3 个月前

made a big breakthrough on tinynodes! this is a huge .blend file with 679 nodes, running 100% in the browser... and it's fully dynamic! at the end of the video, you can see the raw geometry and the node graph that describes how to turn it into this complex wooden structure
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made a big breakthrough on tinynodes! this is a huge .blend file with 679 nodes, running 100% in the browser... and it's fully dynamic! at the end of the video, you can see the raw geometry and the node graph that describes how to turn it into this complex wooden structure

Seth Thompson

36,436 次观看 • 4 个月前

"The mathematics of string theory is probably one of the most beautiful artifacts humanity has created. In order to even produce something in theoretical physics, there's hundreds of years of literature that you need to catch up on, and also every day there's, 100 new papers that come out. And before you can contribute to theoretical physics, you need to know basically all of math, like algebraic topology, differential equations, algebraic geometry, and these are all things that people will spend their careers going in on, and yet to do the physics, you need to at least have, a pretty deep understanding of these things. And so it really teaches you how to have, good judgment with minimal information." Matan Grinberg studied physics for a decade, eventually dropping out of his PhD focused on string theory to found Factory.
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"The mathematics of string theory is probably one of the most beautiful artifacts humanity has created. In order to even produce something in theoretical physics, there's hundreds of years of literature that you need to catch up on, and also every day there's, 100 new papers that come out. And before you can contribute to theoretical physics, you need to know basically all of math, like algebraic topology, differential equations, algebraic geometry, and these are all things that people will spend their careers going in on, and yet to do the physics, you need to at least have, a pretty deep understanding of these things. And so it really teaches you how to have, good judgment with minimal information." Matan Grinberg studied physics for a decade, eventually dropping out of his PhD focused on string theory to found Factory.

Sabrina Halper

237,521 次观看 • 1 个月前

The 2016 physics prize opened a door to an unfamiliar realm where matter can exist in strange states. In the prize announcement, Professor Thors Hans Hansson used a bun, a doughnut and a pretzel as visual aids to understanding the "exotic" concept. He explained, "Exotic is not a precise scientific term. Exotic is something that expresses our wonder, our wonder in front something that is very unusual, very hard to understand”. David Thouless, Duncan Haldane and Michael Kosterlitz used advanced mathematical methods in the field of topology to study these unusual phases. They were awarded the Nobel Prize in Physics "for theoretical discoveries of topological phase transitions and topological phases of matter" Watch the prize announcement:
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The 2016 physics prize opened a door to an unfamiliar realm where matter can exist in strange states. In the prize announcement, Professor Thors Hans Hansson used a bun, a doughnut and a pretzel as visual aids to understanding the "exotic" concept. He explained, "Exotic is not a precise scientific term. Exotic is something that expresses our wonder, our wonder in front something that is very unusual, very hard to understand”. David Thouless, Duncan Haldane and Michael Kosterlitz used advanced mathematical methods in the field of topology to study these unusual phases. They were awarded the Nobel Prize in Physics "for theoretical discoveries of topological phase transitions and topological phases of matter" Watch the prize announcement:

The Nobel Prize

17,109 次观看 • 1 年前

“The governments of Western Europe, and the United States and Canada, New Zealand, and Australia did this on purpose to their own people. They opened their borders and paid for the rest of the world, the Third World, to move into their countries.” New Zealand, Australia, the United States, and Canada all get a special mention in Replacing Europe, the new documentary by Tucker Carlson. If you’ve been following my work for a while, you’ll know I often write about replacement theory. It is frequently dismissed as a conspiracy theory, however in my opinion and that of many others, it is unfolding in real time. The documentary can be viewed by signing up as a member at #nzpol #cdnpol #uspol #auspol
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“The governments of Western Europe, and the United States and Canada, New Zealand, and Australia did this on purpose to their own people. They opened their borders and paid for the rest of the world, the Third World, to move into their countries.” New Zealand, Australia, the United States, and Canada all get a special mention in Replacing Europe, the new documentary by Tucker Carlson. If you’ve been following my work for a while, you’ll know I often write about replacement theory. It is frequently dismissed as a conspiracy theory, however in my opinion and that of many others, it is unfolding in real time. The documentary can be viewed by signing up as a member at #nzpol #cdnpol #uspol #auspol

Matua Kahurangi

29,735 次观看 • 8 个月前

Wrapping up the year and coinciding with #NeurIPS2024, today at Meta FAIR we’re releasing a collection of nine new open source AI research artifacts across our work in developing agents, robustness & safety and new architectures. More in the video from Joelle Pineau. All of this work is part of FAIR’s continued work towards the goal of achieving advanced machine intelligence A few highlights from what we’re releasing today: • Meta Motivo: A first-of-its-kind behavioral foundation model that controls the movements of a virtual embodied humanoid agent to perform complex tasks. • Meta Video Seal: a state-of-the art comprehensive framework for neural video watermarking. • Meta Explore Theory-of-Mind: A program-guided adversarial data generation for theory of mind reasoning. • Meta Large Concept Models: A fundamentally different training paradigm for language modeling that decouples reasoning from language representation. And much more! We’re excited to share this work with the research community and look forward to seeing how it inspires new innovation across the field. Details and access to everything released by FAIR today ➡️
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AI at Meta

156,123 次观看 • 1 年前

Terence Tao: AI isn’t hype anymore in Math discovery. Terence Tao is one of the greatest living mathematicians, in his new lecture explains how AI and human professional mathematicians are now complementary. "There has been a really visible increase in capability. It is not pure hype by any means. To me, these advances show there is a complementary way to do mathematics. Humans traditionally work in small groups on hard problems for months, and we will keep doing that. But we can also now set AI to scale: sweep a thousand problems and pick up all the low-hanging fruit. Figure out all the ways to match problems to methods. If there are 20 different techniques, apply them all to 1,000 problems and see which ones can be solved by these methods. This is the capability that is present today." From 'Institute for Pure & Applied Mathematics (IPAM)' YT channel.
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Terence Tao: AI isn’t hype anymore in Math discovery. Terence Tao is one of the greatest living mathematicians, in his new lecture explains how AI and human professional mathematicians are now complementary. "There has been a really visible increase in capability. It is not pure hype by any means. To me, these advances show there is a complementary way to do mathematics. Humans traditionally work in small groups on hard problems for months, and we will keep doing that. But we can also now set AI to scale: sweep a thousand problems and pick up all the low-hanging fruit. Figure out all the ways to match problems to methods. If there are 20 different techniques, apply them all to 1,000 problems and see which ones can be solved by these methods. This is the capability that is present today." From 'Institute for Pure & Applied Mathematics (IPAM)' YT channel.

Rohan Paul

174,823 次观看 • 7 个月前

"Tolerance is not enough, you have to work together." The conversation with Amartya Sen becomes a masterclass in humanity. Among the themes we touched on: - the ancestry of mathematics, - the ideas of freedom and justice, - how mathematics and Sanskrit have shaped his economic thinking, - and even the legendary bicycle that carried him to win the The Nobel Prize in Economic Sciences, for his contributions to welfare economics. One thing I’ve learned is that his knowledge stands upon admiration and affection, admiration for the beauty of mathematics, and affection for the philosophical depth of Sanskrit literature. He's an economist by formation, but a humanitarian by heart and experience. An honor to learn from him. Tune in,
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"Tolerance is not enough, you have to work together." The conversation with Amartya Sen becomes a masterclass in humanity. Among the themes we touched on: - the ancestry of mathematics, - the ideas of freedom and justice, - how mathematics and Sanskrit have shaped his economic thinking, - and even the legendary bicycle that carried him to win the The Nobel Prize in Economic Sciences, for his contributions to welfare economics. One thing I’ve learned is that his knowledge stands upon admiration and affection, admiration for the beauty of mathematics, and affection for the philosophical depth of Sanskrit literature. He's an economist by formation, but a humanitarian by heart and experience. An honor to learn from him. Tune in,

Gita Wirjawan

20,976 次观看 • 10 个月前