Math Model Selector

# Math Model Selector

## When to Use

Trigger on phrases like:
- "what math should I use"
- "which mathematical framework"
- "how do I model this"
- "what kind of problem is this"
- "formalize this problem"

Use when user has a problem but doesn't know which mathematical domain applies.

## Process

Guide user through decision tree using Polya-style questions:

### 1. Identify the quantity
**Ask:** "What quantity or phenomenon are you trying to understand?"
- Physics problem -> conservation laws, differential equations
- Economics -> equilibrium, optimization
- Data patterns -> statistics, regression

### 2. Characterize change
**Ask:** "What changes, and how does it change?"
- Discrete steps -> difference equations, recurrences
- Continuous rate -> ODEs
- Rate of rate matters -> 2nd order ODEs
- Spatial variation -> PDEs

### 3. Check for uncertainty
**Ask:** "Is there randomness or uncertainty involved?"
- Deterministic -> standard analysis
- Epistemic uncertainty -> Bayesian methods
- Random process -> probability theory, stochastic processes

### 4. Optimization check
**Ask:** "Are you optimizing something?"
- Convex objective -> linear/quadratic programming
- Non-convex -> gradient descent, evolutionary methods
- Discrete choices -> combinatorics, integer programming

### 5. Answer precision
**Ask:** "What level of answer do you need?"
- Rough estimate -> dimensional analysis
- Qualitative behavior -> phase portraits, stability
- Numerical answer -> simulation
- Exact closed form -> analytical methods

## Key Questions to Ask