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How to Solve It — Pólya's Method, Wired Into My AI

2026-07-27

A friend recommended a book to me. I bought it, started reading, and immediately wired it into my AI. Haven't looked back.

The book is How to Solve It, by George Pólya, published in 1945. It's about math. But the principles are about everyday problem solving — and they work on machines just as well as they work on people.

My AI systems now have a framework for attacking problems and requests from me. Before, they'd jump straight to an answer. Now they take steps to understand the problem first. They assume less.

The Four Steps

Pólya broke problem solving into four steps.

1. UNDERSTAND the problem 2. DEVISE A PLAN connect data → unknown 3. CARRY OUT the plan 4. LOOK BACK audit the result loop back — use what you learned on the next problem
  1. Understand the problem. Isolate the unknown, the data, the conditions. What are you trying to solve? What do you know? What constrains you?
  2. Devise a plan. Find the connection between the data and the unknown. Find an analogous problem. Solve a simpler version. Work backward. Decompose it into smaller parts.
  3. Carry out the plan. Execute each step. Check correctness at each step. Can you prove it?
  4. Look back. Audit the result. Can you check it? Can you derive it differently? Can you use this for other problems?

Step four is where most people — and most AI — stop. They get an answer and move on. Pólya says: stop and look at what you just did. That's where one-off work turns into a repeatable process.

Every Agent Runs It

Each of my agents runs Pólya's system end to end, with every request.

Hermes chief of staff 1 · Understand 2 · Plan 3 · Execute 4 · Look Back repeats every request Pi coding agent 1 · Understand 2 · Plan 3 · Execute 4 · Look Back repeats every request Paseo autonomous daemon 1 · Understand 2 · Plan 3 · Execute 4 · Look Back repeats every request

Hermes is my chief of staff. Runs on my Mac, manages my life, builds things — this blog post, a drill timer, a game called Pocket Golf. The Pólya framework lives in its system prompt.

Pi is my coding agent. Deterministic work. HTML generation, filling templates, making commits.

Paseo is a local daemon. Autonomous workflows that run without me watching.

Different jobs. Same loop. Every time.

The Agent Writing This Post Is Doing Step One

The agent interviewing me to write this post is doing step one right now. It's asking me questions because its goal is to understand the problem first — not to fire off a guess and hope.

That's the whole shift. The framework forces the AI to slow down before it speeds up.

The Actual Prompt

This is what's in my agent's system prompt. Not paraphrased. Not cleaned up. This is the actual text.

## How to Solve It

[ UNDERSTAND ] ➔ Isolate the Unknown, the Data, and the Constraints
       ↓
[ DEVISE PLAN ] ➔ Find an Analogous Problem or Work Backward
       ↓
[ EXECUTE IT ]  ➔ Take Action and Verify the Logic of Each Step
       ↓
[ LOOK BACK ]   ➔ Audit the Outcome and Generalize the Lesson

### 1. Understand the problem
You cannot solve a problem if you do not know exactly what it is. Brutally isolate the core issue:
- What is the unknown? Define what a perfect outcome looks like.
- What are the data? List concrete, unchangeable facts, assets, and current realities.
- What is the condition? Identify the rules or constraints tying data to the unknown.

### 2. Devise a plan
A plan is born when you find the connection between current data and the unknown outcome. If stuck:
- Find an analogous problem — Have you, a friend, or a competitor faced something similar? Reuse their method or result.
- Solve a simpler version — If the goal is a massive business, get one customer this weekend first.
- Work backward — Imagine it already solved. Step back day by day to the milestones that made it so.
- Decompose — Break the obstacle into independent chunks; solve them one by one.

### 3. Carry out the plan
Patience and strict focus. Avoid messy unforced errors.
- Check each step — Verify each move is grounded in reality, not wishful thinking.
- Can you prove it? — Can you clearly explain why this action moves toward the goal?

### 4. Look back
Most people stop when the fire is out. This is where wisdom is built.
- Can you check the result? Did it fix the root cause, or only hide symptoms?
- Can you derive it differently? Cleaner, cheaper, or faster path?
- Can you use this for other problems? Turn the fix into a permanent rule, habit, checklist, skill, or memory.

Default loop for strategy, product, code, family logistics, and content: understand → plan → execute with proof → look back and generalize.

Copy it. Paste it into your own system prompt. Adapt the examples to your domain. That's all I did.

What Changed

The biggest surprise has been the efficiency and the quality of outputs.

The AI takes steps to understand the problem first. It assumes less. That alone changes what comes back.

I haven't done a side-by-side — same prompt, with and without the framework — to measure the gap. That'd be interesting. For now, the difference is obvious enough that I'm not going back.

If you're building with AI agents, give Pólya a read. The book is from 1945. It costs twelve dollars. It changed how my AI works more than any prompt engineering trick I've learned.

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— Jon