【文小刚：物理学的新革命——凝聚态物理中的近代数学 | 众妙之门】

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**Keywords**:

**Quantum Entanglement**(QE) : 量子纠缠**Topological Order**(Long-range QE) : 拓扑序**Topological Insulator**(Short-range QE) : 拓扑绝缘体**Rigid State**: 凝聚态**Cohomology**: 上同调**Tensor**: 张量**Category Theory**: 范畴学**Group Theory**: 群论**Algebraic Topology**: 代数拓扑

….

1. **Four “Physics” Revolutions aided by Math**

Math is applied to explain the Nature (Physics) :

**Calculus (Differential Equation)** : Newtonian Physics

**Riemann Geometry** : Einstein General Relativity

**Partial Differential Equation**: Maxwell Electro-Magnetic Field

**Linear Algebra** (Matrix) : Quantum Mechanics

**Group Theory**: Physics / Chemistry Symmetry

Next…

**Category Theory** : Topological Order of the long-range Quantum Entanglement

**Algebraic Topology**: Topological Insulator (**2016** Nobel Prize Physcis)

**2. The 5th Physics Revolution aided by New Math tool : Category Theory**

**3. Category Theory = “Structural Relationship” **Math

**4. Algebraic Topology**

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