🎮 Interactive Visualizations
Explore Z₂ groups, torus topology, wave functions & more
📖 Notation Reference
Symbols used in the notes, with a searchable index
📚 How to Learn
- • Complete Math first, then Physics
- • Each topic builds on the previous
- • Work through examples with pen and paper
- • Background only: the notes make no claims about the current framework
20
Documents
~50
Hours Total
100+
Concepts
1
Prerequisites
Algebra, calculus, complex numbers, Euler's formula
2
Linear Algebra
Vectors, matrices, eigenvalues, trace
3
Group Theory
Lie groups, SU(2), SU(3), U(1), discrete symmetries
4
Topology Basics
Manifolds, compactness, continuity
5
Differential Geometry
Metrics, curvature, geodesics
6
Algebraic Topology
Homology, Betti numbers
7
Orbifolds
Quotient spaces and their singular points
8
Index Theory
Atiyah–Singer and APS index theorems
9
Intersection Theory
Intersection numbers on manifolds
10
Classical Mechanics
Lagrangian, Hamiltonian, Noether's theorem
11
Special Relativity
Lorentz transformations, GPS proof
12
Quantum Mechanics
Wave functions, spin, uncertainty
13
Quantum Field Theory
Feynman diagrams, propagators, vacuum
14
Gauge Theory
Standard Model gauge structure
15
General Relativity
Einstein equations, curved spacetime
16
ADM Formalism
3+1 decomposition, Hamiltonian gravity
17
Cosmology
Friedmann equations, dark energy, the cosmological constant
18
String Theory
Strings, D-branes, compactification
19
Holography
AdS/CFT, entropy bounds
These are general study notes in mathematics and physics. An earlier version of this page listed formulas linking a geometric constant to the fine-structure constant, the Weinberg angle, the strong coupling, the Higgs scale and ΩΛ. Those claims were publicly retracted in June 2026 and are not part of the current work; see Retracted work. The current claim is only a₀ = κ c √(GρΛ) with κ = ½ fitted; see the status board.