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