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Incredible work by ア Mathematics sorcery! 🤯 From iterated composition of basic functions, a life form is born 🫡

Mathelirium

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38,918 次观看 • 8 个月前 •via X (Twitter)

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In Mathematics, a graph is defined as G = (V, E)... a collection of vertices V joined by edges E. From this deceptively simple idea emerges a living neural world, where signals race through a cortical graph and converge upon a morphing hypergraph core, revealing how abstract Mathematics can be transformed into something that appears almost alive.

In Mathematics, a graph is defined as G = (V, E)... a collection of vertices V joined by edges E. From this deceptively simple idea emerges a living neural world, where signals race through a cortical graph and converge upon a morphing hypergraph core, revealing how abstract Mathematics can be transformed into something that appears almost alive.

Mathelirium

20,959 次观看 • 1 个月前

From one of Mathematics’ most abstract ideas, a graph of nodes and edges, emerges something that feels almost alive.

From one of Mathematics’ most abstract ideas, a graph of nodes and edges, emerges something that feels almost alive.

Mathelirium

24,422 次观看 • 1 个月前

Mathematics is beautiful🤩❤️ My favourite from 2025. Merry Christmas guys! 🎄 Zeros and poles of a Blaschke-Quotient spinning under SU(1,1) Möbius symmetries on the Poincaré disk with the phase shaded by the Fubini-Study metric.

Mathematics is beautiful🤩❤️ My favourite from 2025. Merry Christmas guys! 🎄 Zeros and poles of a Blaschke-Quotient spinning under SU(1,1) Möbius symmetries on the Poincaré disk with the phase shaded by the Fubini-Study metric.

Mathelirium

20,051 次观看 • 8 个月前

A Mysterious New Life Form is born #GENs 👾

A Mysterious New Life Form is born #GENs 👾

Wilder World

138,111 次观看 • 3 年前

Mathematics art from Collatz Conjecture sequences.

Mathematics art from Collatz Conjecture sequences.

Mathelirium

21,618 次观看 • 1 年前

Much better visually. We now visualize the 3D version of our stunning Blaschke-Quotient Flow from our previous post.🤗🤩 What follows is a mesmerizing break of dawn in the some realm of complex space with zeros and poles still spinning under SU(1,1) Möbius symmetries on the Poincaré disk…but phase is now shaded by the Fubini-Study metric. 🤯🤯🤯

Much better visually. We now visualize the 3D version of our stunning Blaschke-Quotient Flow from our previous post.🤗🤩 What follows is a mesmerizing break of dawn in the some realm of complex space with zeros and poles still spinning under SU(1,1) Möbius symmetries on the Poincaré disk…but phase is now shaded by the Fubini-Study metric. 🤯🤯🤯

Mathelirium

15,826 次观看 • 11 个月前

The Trap in Every Mathematics Lecture If you’ve taken a lot of math courses, you start to recognize a pattern. There’s a moment where the lecturer is warming up with the obvious stuff...add matrices entrywise, scale by α, do the row-column product...and you’re thinking, alright… where is this going? Then you relax. You stop resisting. And right there, they slip in one line that changes how you see the whole subject. When Benedict Gross says "matrices represent linear operators,"he’s telling you to stop treating a matrix as a rectangle of numbers and start treating it as an action. A linear operator is a function T: Rⁿ → Rⁿ that respects two rules: T(u+v)=T(u)+T(v) and T(αu)=αT(u). Once you pick a basis, T is completely determined by where it sends the basis vectors e₁,…,eₙ. Put T(e₁),…,T(eₙ) into columns and you get a matrix A. That is what "A represents T" means...A is the coordinate portrait of the transformation. Now the punchline that makes matrix multiplication feel inevitable. If B represents S and A represents T, then doing S first and then T is the composition T∘S. In coordinates that becomes A(Bx)=(AB)x. So multiplying matrices is really composing transformations. That’s why multiplication is usually not commutative: T∘S is generally not the same transformation as S∘T, and the matrices inherit that noncommutativity. This explains half of Linear Algebra because it tells you what the course is really about...functions that move vectors around, not grids of numbers. A matrix is just the written form of that function once you choose coordinates. Then the rules stop feeling random Multiplying matrices means doing one move and then another, an inverse means you can undo the move, eigenvectors are directions that don’t get turned, and changing basis is just describing the same move in a different language. That one idea makes a lot of linear algebra click. #LinearAlgebra #Matrices #GroupTheory #GLn #MathLectures #Mathematics

The Trap in Every Mathematics Lecture If you’ve taken a lot of math courses, you start to recognize a pattern. There’s a moment where the lecturer is warming up with the obvious stuff...add matrices entrywise, scale by α, do the row-column product...and you’re thinking, alright… where is this going? Then you relax. You stop resisting. And right there, they slip in one line that changes how you see the whole subject. When Benedict Gross says "matrices represent linear operators,"he’s telling you to stop treating a matrix as a rectangle of numbers and start treating it as an action. A linear operator is a function T: Rⁿ → Rⁿ that respects two rules: T(u+v)=T(u)+T(v) and T(αu)=αT(u). Once you pick a basis, T is completely determined by where it sends the basis vectors e₁,…,eₙ. Put T(e₁),…,T(eₙ) into columns and you get a matrix A. That is what "A represents T" means...A is the coordinate portrait of the transformation. Now the punchline that makes matrix multiplication feel inevitable. If B represents S and A represents T, then doing S first and then T is the composition T∘S. In coordinates that becomes A(Bx)=(AB)x. So multiplying matrices is really composing transformations. That’s why multiplication is usually not commutative: T∘S is generally not the same transformation as S∘T, and the matrices inherit that noncommutativity. This explains half of Linear Algebra because it tells you what the course is really about...functions that move vectors around, not grids of numbers. A matrix is just the written form of that function once you choose coordinates. Then the rules stop feeling random Multiplying matrices means doing one move and then another, an inverse means you can undo the move, eigenvectors are directions that don’t get turned, and changing basis is just describing the same move in a different language. That one idea makes a lot of linear algebra click. #LinearAlgebra #Matrices #GroupTheory #GLn #MathLectures #Mathematics

Mathelirium

66,892 次观看 • 8 个月前

If you’re an engineer, physicist, or CS person and you’ve been telling yourself that Pure Mathematics is optional, and you’re anywhere between an ambitious undergrad and a beginning PhD, gravity is usually where that story ends. Not because mathematicians are trying to show off, but because the basic object in the theory is Spacetime, and Spacetime is already a pure mathematical structure. It’s a Manifold with Topology built in. Sure you can get pretty far by memorising formulas, but at some point you realise you’re no longer reading the theory, you’re just reciting it. In 2015, during the 100th anniversary of general relativity and the International Year of Light, the Scientific Organizing Committee released a central set of 24 lectures by Frederic P. Schuller. The series is titled: A thorough introduction to the theory of general relativity. It builds the subject carefully from first principles, step by step, across 24 self-contained lectures. #GeneralRelativity #Spacetime #MathematicalPhysics #DifferentialGeometry #PhysicsEducation #Relativity

If you’re an engineer, physicist, or CS person and you’ve been telling yourself that Pure Mathematics is optional, and you’re anywhere between an ambitious undergrad and a beginning PhD, gravity is usually where that story ends. Not because mathematicians are trying to show off, but because the basic object in the theory is Spacetime, and Spacetime is already a pure mathematical structure. It’s a Manifold with Topology built in. Sure you can get pretty far by memorising formulas, but at some point you realise you’re no longer reading the theory, you’re just reciting it. In 2015, during the 100th anniversary of general relativity and the International Year of Light, the Scientific Organizing Committee released a central set of 24 lectures by Frederic P. Schuller. The series is titled: A thorough introduction to the theory of general relativity. It builds the subject carefully from first principles, step by step, across 24 self-contained lectures. #GeneralRelativity #Spacetime #MathematicalPhysics #DifferentialGeometry #PhysicsEducation #Relativity

Mathelirium

198,712 次观看 • 7 个月前

No woman should be turned away from emergency care if her life is on the line. We need an HHS secretary that understands the basic functions of our life-saving policies. I didn't see that from Mr. Kennedy today.

No woman should be turned away from emergency care if her life is on the line. We need an HHS secretary that understands the basic functions of our life-saving policies. I didn't see that from Mr. Kennedy today.

Senator Lisa Blunt Rochester

17,750 次观看 • 1 年前

The Trap in Every Mathematics Lecture If you’ve taken enough math courses, you start noticing the same little move. The lecturer warms up with the obvious stuff, add matrices entrywise, scale by α, do the row-column product, and you’re thinking alright, where is this going. Then you relax. You stop resisting. And right there, they drop one line that quietly rewires the whole subject. When Benedict Gross says matrices represent linear operators, he’s telling you to stop treating a matrix as a rectangle of numbers and start treating it as an action. A linear operator is a function T: ℝⁿ → ℝⁿ that respects two rules: T(u+v) = T(u) + T(v) T(αu) = αT(u) Once you pick a basis, T is completely determined by where it sends the basis vectors e₁,…,eₙ. Put T(e₁),…,T(eₙ) into columns and you get a matrix A. That is what A represents T means. A is the coordinate portrait of the transformation. Now the punchline that makes matrix multiplication feel inevitable. If B represents S and A represents T, then doing S first and then T is the composition T∘S. In coordinates that becomes A(Bx) = (AB)x. So multiplying matrices is really composing transformations. That’s why multiplication is usually not commutative. T∘S is generally not the same transformation as S∘T, and the matrices inherit that noncommutativity. This explains half of linear algebra because it tells you what the course is really about: functions that move vectors around, not grids of numbers. A matrix is just the written form of that function once you choose coordinates. After that, the rules stop feeling random. Multiplying matrices means doing one move and then another. An inverse means you can undo the move. Eigenvectors are directions that don’t get turned. Changing basis is just describing the same move in a different language. One idea, and a lot of linear algebra suddenly clicks. #LinearAlgebra #Matrices #LinearMaps #Eigenvectors #ChangeOfBasis #Mathematics

The Trap in Every Mathematics Lecture If you’ve taken enough math courses, you start noticing the same little move. The lecturer warms up with the obvious stuff, add matrices entrywise, scale by α, do the row-column product, and you’re thinking alright, where is this going. Then you relax. You stop resisting. And right there, they drop one line that quietly rewires the whole subject. When Benedict Gross says matrices represent linear operators, he’s telling you to stop treating a matrix as a rectangle of numbers and start treating it as an action. A linear operator is a function T: ℝⁿ → ℝⁿ that respects two rules: T(u+v) = T(u) + T(v) T(αu) = αT(u) Once you pick a basis, T is completely determined by where it sends the basis vectors e₁,…,eₙ. Put T(e₁),…,T(eₙ) into columns and you get a matrix A. That is what A represents T means. A is the coordinate portrait of the transformation. Now the punchline that makes matrix multiplication feel inevitable. If B represents S and A represents T, then doing S first and then T is the composition T∘S. In coordinates that becomes A(Bx) = (AB)x. So multiplying matrices is really composing transformations. That’s why multiplication is usually not commutative. T∘S is generally not the same transformation as S∘T, and the matrices inherit that noncommutativity. This explains half of linear algebra because it tells you what the course is really about: functions that move vectors around, not grids of numbers. A matrix is just the written form of that function once you choose coordinates. After that, the rules stop feeling random. Multiplying matrices means doing one move and then another. An inverse means you can undo the move. Eigenvectors are directions that don’t get turned. Changing basis is just describing the same move in a different language. One idea, and a lot of linear algebra suddenly clicks. #LinearAlgebra #Matrices #LinearMaps #Eigenvectors #ChangeOfBasis #Mathematics

Mathelirium

133,454 次观看 • 7 个月前

Which is the most incredible shot played by a batsman in any form of cricket?

Which is the most incredible shot played by a batsman in any form of cricket?

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A Million-Dollar Storm Mathematics Still Cannot Tame. Turbulence matters because it is the default behavior of real fluids once motion becomes strong enough, e.g. air over wings, blood through vessels, weather in the atmosphere, water in oceans, fuel in engines, and flow in pipes and turbines. We can write down the Navier-Stokes equations for all of this, but in 3D one of the deepest open questions is still whether smooth solutions always stay smooth, or can break down in finite time. That is crucial because it asks whether the basic equations of fluid motion remain mathematically under control forever, or can form a true singularity where the theory itself breaks. Solve that and you got yourself a million dollars

A Million-Dollar Storm Mathematics Still Cannot Tame. Turbulence matters because it is the default behavior of real fluids once motion becomes strong enough, e.g. air over wings, blood through vessels, weather in the atmosphere, water in oceans, fuel in engines, and flow in pipes and turbines. We can write down the Navier-Stokes equations for all of this, but in 3D one of the deepest open questions is still whether smooth solutions always stay smooth, or can break down in finite time. That is crucial because it asks whether the basic equations of fluid motion remain mathematically under control forever, or can form a true singularity where the theory itself breaks. Solve that and you got yourself a million dollars

Mathelirium

30,056 次观看 • 5 个月前

This is one of my favourite experiments so far. An entire synthetic ecology built from Mathematics and Physics. The organisms move through coupled dynamical systems, chemotaxis, stochastic motion, spring networks, constrained mechanics and collision dynamics.

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Mathelirium

44,183 次观看 • 12 天前

What you're seeing here is the root dynamics of a smoothly time-modulated complex polynomial. A living membrane breathes while four satellites orbit, dock, fuse with the core, then split again. From the simplest task in algebra...finding roots...emerges natural-feeling, sophisticated motion. #ComplexPolynomials #ComplexAnalysis #MathArt #Mathematics

What you're seeing here is the root dynamics of a smoothly time-modulated complex polynomial. A living membrane breathes while four satellites orbit, dock, fuse with the core, then split again. From the simplest task in algebra...finding roots...emerges natural-feeling, sophisticated motion. #ComplexPolynomials #ComplexAnalysis #MathArt #Mathematics

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63,283 次观看 • 10 个月前

Submarine moving beneath sea ice sends pressure through the water and bends the frozen ceiling above it. The Mathematics of fluid-flow, elasticity and flexural-gravity bring this scene to life.

Submarine moving beneath sea ice sends pressure through the water and bends the frozen ceiling above it. The Mathematics of fluid-flow, elasticity and flexural-gravity bring this scene to life.

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VFX breakdown of this incredible shot of Daredevil from ‘DAREDEVIL: BORN AGAIN’ S2E2 by Effetti Digitali Italiani.

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How can something as abstract as a graph, consisting of nodes, edges, and a few dynamical rules, end up looking so alive? It's one of the strangest strengths of Mathematics.

How can something as abstract as a graph, consisting of nodes, edges, and a few dynamical rules, end up looking so alive? It's one of the strangest strengths of Mathematics.

Mathelirium

11,052 次观看 • 16 天前

When Light Becomes Heavy Enough to Trap Itself Can light collapse into a black hole? In General Relativity, light is not weightless in the geometric sense. It has energy, it carries momentum, and energy curves Spacetime. A Vaidya-type collapse describes a mass that grows because radiation is falling inward. The mathematics is the same brutal idea behind Einstein’s equation Gᵤᵥ = 8πTᵤᵥ If the stress-energy Tᵤᵥ is made from radiation, then light itself becomes a source of curvature. As more radiation falls inward, the mass aspect grows, the Spacetime fabric tightens, and a clean black horizon appears where escaping paths begin to fail. #GeneralRelativity #EinsteinEquations #BlackHole #Spacetime #Astrophysics #TheoreticalPhysics #Light #Mathematics #Science

When Light Becomes Heavy Enough to Trap Itself Can light collapse into a black hole? In General Relativity, light is not weightless in the geometric sense. It has energy, it carries momentum, and energy curves Spacetime. A Vaidya-type collapse describes a mass that grows because radiation is falling inward. The mathematics is the same brutal idea behind Einstein’s equation Gᵤᵥ = 8πTᵤᵥ If the stress-energy Tᵤᵥ is made from radiation, then light itself becomes a source of curvature. As more radiation falls inward, the mass aspect grows, the Spacetime fabric tightens, and a clean black horizon appears where escaping paths begin to fail. #GeneralRelativity #EinsteinEquations #BlackHole #Spacetime #Astrophysics #TheoreticalPhysics #Light #Mathematics #Science

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27,760 次观看 • 2 个月前

Yasuke IN REAL LIFE? 🤯 Check out how this fight scene came to life thanks to the incredible work of our Motion Capture actors 🤸‍♂️

Yasuke IN REAL LIFE? 🤯 Check out how this fight scene came to life thanks to the incredible work of our Motion Capture actors 🤸‍♂️

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