Math Foundation

---
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.
---

# 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*