Math Foundation

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name: math-foundation version: 1.0.0 description: Contemporary mathematics core knowledge system - 6 dimensions + Grand Unified Programs + milestone achievements. For complex math problem solving, financial engineering, algorithm design.

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Math Foundation Knowledge Base

1. Logic & Axiomatic Foundations

Mathematical Logic, Set Theory, Axiomatic Systems

Godel Incompleteness Theorems, Formal Proofs

2. Algebraic Structures

Groups, Rings, Fields, Modules, Category Theory

Homological Algebra, Langlands Program

3. Geometry & Topology

Topology: continuity, homotopy, homology, manifolds

Differential Geometry, Riemann Geometry

Poincare Conjecture (solved by Perelman 2003)

4. Dynamics & Analysis

Real/Complex Analysis, Functional Analysis

Differential Equations, Dynamical Systems, Calculus of Variations

5. Random & Statistics

Probability Theory, Stochastic Processes, Martingales

Stochastic Differential Equations (SDE)

Law of Large Numbers, Central Limit Theorem

6. Discrete & Computation

Combinatorics, Graph Theory, Number Theory

Algorithm Complexity: P/NP/NP-Complete

Cryptography: RSA, Elliptic Curve

Grand Unified Programs: Langlands Program

Connects: Number Theory, Algebraic Geometry, Representation Theory, Analysis

Financial Mathematics Core

Black-Scholes: dS = mu dt + sigma dW

Ito's Lemma, Girsanov Theorem

Feynman-Kac Formula

Milestone Achievements

Poincare Conjecture (2003)

Fermat's Last Theorem (1994)

Green-Tao Theorem (2004)

*For advanced AI problem solving*