Manifesto -- uber-polya

You have a scheduling conflict. You need to split costs fairly. You're deciding which projects to fund. You're routing deliveries. You're figuring out whether that A/B test result is real or noise.

These feel like different problems. They're not. They all have the same shape: Given some constraints, find the best answer. That's a math problem. And math problems have solvers.

The Hidden Structure

Every hard decision you make is secretly one of a small number of mathematical structures wearing a real-world disguise.

"Schedule 12 nurses across 3 shifts so nobody works more than 5 days" is not a scheduling problem. It is an integer linear program with 252 binary variables and 48 constraints. It has an optimal solution. A solver can find it in 0.3 seconds and prove that no better answer exists.

"Split rent fairly among 3 roommates with different-sized rooms" is not a negotiation. It is a fair division problem. There exists a provably fair allocation.

"Pick the best 5 of 20 projects given a $500K budget" is not a meeting. It is a knapsack optimization.

You don't need to know any of this to solve these problems. You just need a tool that does.

The Gap

Today, when people face hard decisions, they do one of four things:

They wing it. Gut feeling, experience, intuition.
They use spreadsheets. Works for simple problems. Falls apart with combinatorial search spaces.
They ask AI. ChatGPT or Claude gives a plausible-sounding answer. But it's not verified.
They hire a consultant. Expensive, slow.

All four approaches share the same flaw: they skip the modeling step.

What Modeling Does

When you formalize a problem into a mathematical model, three things happen:

Ambiguity disappears.
The solution space becomes searchable.
The answer comes with a guarantee.

Polya's Insight

In 1945, George Polya published How to Solve It. His four phases:

Understand the problem.
Devise a plan.
Execute the plan.
Look back.

This method is 80 years old. We now have AI that understands natural language, solver libraries that process millions of variables, and verification methods that prove correctness.

The Universal Algorithm

UBER-POLYA(problem):

1. UNDERSTAND -- Socratic dialogue

2. CLASSIFY -- Map to mathematical structure

3. SELECT -- Pick algorithm for structure and instance size

4. EXECUTE -- Run it, verify independently

5. INTERPRET -- Translate back with sensitivity analysis

This is a compiler for problems.

What This Means in Practice

For the operations manager: 6 hours becomes 2 minutes
For the startup founder: ranked list with explicit trade-offs
For the student: provably conflict-free timetable
For the data scientist: right hypothesis test, three methods, plain-English interpretation

Why Verification Matters

LLMs are confident whether they're right or wrong. uber-polya doesn't trust itself. Every solution includes:

Feasibility check
Optimality certificate
Cross-validation
Sensitivity analysis

The Expansion

Today: discrete optimization, continuous optimization, statistical inference, time series, survival analysis, machine learning, simulation, game theory, decision analysis, and 15 more domains. 305 algorithms across 24 domains. Professional PDF reports with branded styling.

Coming: partial differential equations, dynamical systems, spatial statistics, option pricing, and more.

The Invitation

uber-polya is free, open-source, and available today. Every problem has a mathematical structure. uber-polya finds it, solves it, and proves the answer is right.