uber-polya

The math problem-solver for every AI coding assistant

Don't guess. Solve.

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$ /uber-polya Schedule 12 nurses across 3 shifts

1. Understands → "Constraint satisfaction problem"

2. Models → ILP with 252 variables, 48 constraints

3. Solves → Optimal schedule in 0.3 seconds

4. Verifies → All constraints satisfied, optimality proven

5. Delivers → A shift schedule you can use today

6. Reports → Professional PDF report (optional)

Claude Code Anthropic

Codex OpenAI

Copilot GitHub

Cursor

Windsurf Codeium

Kiro Amazon

Qoder Alibaba

Antigravity Google

How it works

Three steps. One command.

uber-polya implements George Polya's four-phase problem-solving cycle as an executable algorithm. You describe the problem in plain English. It does the rest.

You describe your problem

In plain English. "Schedule 12 nurses across 3 shifts so nobody works more than 5 days." No math required.

uber-polya finds the math, solves it, and verifies

Classifies the problem, selects the right algorithm from 305 options, writes solver code, runs it, and independently verifies the answer.

You get a usable result

A schedule, a plan, a decision, a budget, a ranking, a proof -- whatever you need. With sensitivity analysis, visualizations, and optional PDF reports.

What can it solve?

Every hard decision is secretly a math problem.

uber-polya finds the mathematical structure hiding inside your problem and solves it with the right algorithm. Here is a sample of what it handles today.

Business Problems 18

Shift Scheduling

Assign staff to shifts respecting constraints and preferences

Project Selection

Pick the best projects under a budget to maximize ROI

Task Assignment

Assign people to tasks minimizing cost or travel

Route Planning

Optimize delivery routes across multiple vehicles and stops

Pricing

Find the price point that maximizes revenue given demand

A/B Testing

Determine if a test result is statistically significant

Portfolio Allocation

Allocate investments to minimize risk for a target return

Build vs. Buy

Compare long-term expected value of building or purchasing

Sales Forecasting

Forecast next quarter's revenue from historical data

Customer Churn

Predict which customers will leave and why

Training Impact

Measure whether a training program actually boosted sales

Call Center Staffing

Size your team for a 95% service level agreement

Subscriber Retention

Predict when customers will cancel their subscriptions

Inventory Ordering

Calculate how much to order and when to reorder

Container Loading

Pack shipments into the fewest trucks possible

Vendor Ranking

Rank vendors balancing cost, quality, and delivery speed

Product Configuration

Check if all customer requirements can be satisfied at once

Demand Patterns

Model customer arrival patterns for capacity planning

Personal Problems 21

Meal Planning

Plan a week of meals within budget and nutrition targets

Rent Splitting

Divide rent fairly among roommates with different-sized rooms

Study Schedule

Schedule study sessions across subjects with no conflicts

Apartment Ranking

Rank apartments by multiple criteria weighted to your priorities

Expense Splitting

Split group trip expenses so everyone pays their fair share

Refinancing

Calculate if refinancing your mortgage saves money and when

Budget Forecasting

Predict whether you'll stay within budget this year

Garden Fencing

Maximize garden area with a fixed amount of fencing

Room Painting

Calculate how much paint for oddly-shaped rooms

Solar Payback

Find when your solar panel investment pays for itself

Recipe Scaling

Scale a recipe for 50 people keeping proportions right

Raffle Odds

Calculate your chances of winning a raffle or lottery

Medication Timing

Find when drug levels peak and trough for optimal dosing

Moving Logistics

Fit all furniture into the fewest truck loads

Carpool Scheduling

Rotate school drop-offs among 4 families minimizing total drives

Workout Plan

Design a 5-day exercise schedule hitting all muscle group targets

Trip Itinerary

Pick the best city attractions within your time and budget

Debt Payoff

Optimal payment strategy across 4 debts to minimize total interest

Energy Bill

Schedule appliances to off-peak hours to cut electricity costs

Potluck Planning

Assign dishes to guests matching skills and covering all categories

House Hunting

Balance commute, price, and schools across 15 houses

What's included

Free and open source. Apache 2.0 licensed.

Everything you need to turn real-world problems into verified mathematical solutions.

Skills

uber-polya orchestrator + uber-model, uber-solve, uber-interpret

305

Algorithms

Across 24 mathematical domains with cross-referenced selection

Structures

Across 24 mathematical domains with pattern matching

Worked Examples

With runnable solver code, verification, and visualizations

Solver Libraries

PuLP, NetworkX, Z3, SymPy, SciPy, cvxpy, statsmodels, and more

PDF

Report Output

Professional branded PDF reports with equations, tables, and figures. No LaTeX install needed.

Platforms

Claude Code, Codex, Copilot, Cursor, Windsurf, Kiro, Qoder, Antigravity

Start Now

The story

80 years in the making.

In 1945, George Polya published How to Solve It -- a universal method for solving mathematical problems. Understand the problem. Make a plan. Execute the plan. Look back and verify.

For 80 years, that method lived in textbooks. It was a framework for humans, not machines. But the method was always algorithmic at its core: classify the problem, select a strategy, execute, verify.

uber-polya makes it executable. You describe a real-world problem in plain English. The system finds the hidden mathematical structure, selects the right algorithm from a curated catalog of 305 options, writes verified solver code, and translates the answer back into something you can act on.

One algorithm. Any problem. Verified.

Read the full manifesto →

Research benchmark

First Proof Challenge: 10/10 solved.

uber-polya autonomously solved all 10 research-level problems from the First Proof challenge -- unpublished problems by Hairer, Spielman, Srivastava, Weinberger, and others -- with novel proof strategies distinct from both OpenAI's and the authors' own solutions.

Problem	Domain	uber-polya's Novel Approach	Confidence
P1: Φ⁴₃ Measure	Stochastic analysis	Relative entropy + Kakutani dichotomy	HIGH
P2: Rankin–Selberg	Representation theory	Hecke algebra truncation + conjugation formula	HIGH
P3: Markov Chain	Algebraic combinatorics	Hecke-algebraic zero-range process	HIGH
P4: Stam Inequality	Algebraic combinatorics	Cauchy–Schwarz duality + V_n-additivity	HIGH
P5: Slice Filtration	Equivariant homotopy	Equivariant Postnikov towers + geometric fixed points	HIGH
P6: ε-Light Subsets	Spectral graph theory	Sparse–dense dichotomy, c = 1/8 (better than authors' 1/42)	MED-HIGH
P7: Lattices + 2-Torsion	Geometric topology	Representation-ring character obstruction (1 = 0)	HIGH
P8: Lagrangian Smoothing	Symplectic geometry	Gromov–Lees h-principle + Moser trick	MEDIUM
P9: Tensor Relations	Tensor algebra	Exterior algebra + Segre + Plücker syzygies	HIGH
P10: CP-ALS PCG	Numerical linear algebra	Gather/scatter + Cholesky Kronecker + Nyström	HIGH

Each solution was generated by the uber-polya pipeline (Phase A: Model → Phase B: Solve → Phase C: Interpret) with Python/SymPy verification scripts and iteration on failure. All 10 approaches are genuinely novel -- we blacklisted both OpenAI's and the authors' known strategies, forcing the pipeline to discover alternative mathematical frameworks.

Highlights: Problem 7's representation-ring argument (Maschke's theorem → 1 = 0 contradiction) is simpler than both alternatives. Problem 6 achieves a better constant (c = 1/8) than the authors' c = 1/42. The full 92-page PDF includes proofs, 3-way comparison appendix, and layman explanations.

View the First Proof submission on GitHub →