By name: math-model-selector
description: Routes problems to appropriate mathematical frameworks using expert heuristics
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
What changes? (discrete vs continuous)
What causes the change? (rate dependencies)
What's random? (uncertainty type)
What's being optimized? (objective function)
How precise? (qualitative vs quantitative)
Output Format
Framework Recommendation:
- Primary: [framework name]
- Why: [one-sentence justification]
Starting Point:
- Key equations: [relevant formulas]
- Initial approach: [first step]
Tools to Use:
- [specific script or computation tool]
Related Skills:
- [domain skill to activate next]
Example Interaction
User: I want to model how a rumor spreads through a population
Claude: Let me help you find the right framework.
Q1: What quantity are we tracking?
> Number of people who heard the rumor over time.
Q2: What causes it to change?
> Spread rate depends on who knows and who doesn't.
Q3: Is there randomness?
> Assume deterministic (average behavior) for now.
Q4: Optimizing anything?
> No, just understanding dynamics.
Q5: What precision?
> Qualitative behavior, maybe predict peak rate.
Framework Recommendation:
- Primary: First-order ODE (logistic growth)
- Why: Rate depends on current state nonlinearly
Starting Point:
- dN/dt = r * N * (1 - N/K)
- N = heard count, K = population, r = spread rate
Tools:
- sympy_compute.py solve (equilibrium)
- Phase line for qualitative behavior
Related Skills:
- math/math-intuition-builder (understand the model)
- odes-pdes/first-order-odes (solve it)
Co-activates
After framework selection, suggest:
math-intuition-builder - to understand the framework
Relevant domain skill - for actual computation
math-mode - for symbolic verification