refactor(topics): 멀티 에이전트용 지식 재편 — _Common(공통 기본기) + Domain_* 구조
에이전트 8종(대화형/프로그래머 C·S/디자이너/설계자/기획자/QA/PD/PM)에게 [공통 기본 능력 + 롤별 Specialty] 2층으로 지식을 주입하기 위한 재분류. 문서 내용·포맷은 무수정, 폴더 이동만 (6,372개 문서 수 보존 확인). - Topic_Programming → Domain_Programming (내부 구조 보존) - Topic_Graphic → Domain_Design - Topic_Business → Domain_Product - Topic_General → Domain_General - _Common 신설: Math(구 Topic_Math_Specialty), Reasoning(구 General/From_Thinking & Reasoning), Reasoning_Creativity(구 General/From_창의성), Communication(Poetic_Blog_Writing + From_writing) - 타 도메인의 From_* 폴더는 유지 (출처 표기일 뿐, 이미 도메인에 맞게 분류된 문서) - 빈 폴더 정리 (memory/procedures) - 에이전트→폴더 매핑은 workspace의 .astra/agent-knowledge-map.json (9개 에이전트) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Antigravity Agent
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---
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id: wiki-2026-0508-problem-solving-process
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title: Problem Solving Process
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category: 10_Wiki/Topics
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status: verified
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canonical_id: self
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aliases: [Problem Solving, Polya Method, Engineering Problem Solving]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.9
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verification_status: applied
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tags: [cognition, engineering, methodology, debugging]
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raw_sources: []
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last_reinforced: 2026-05-10
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github_commit: pending
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tech_stack:
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language: multi
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framework: structured-problem-solving
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---
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# Problem Solving Process
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## 매 한 줄
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> **"매 a problem well-stated is half-solved."**. 매 Polya 1945 *How to Solve It* 의 4단계 (understand → plan → carry out → look back) 가 매 modern engineering, debugging, AI agent design 의 backbone. 매 2026 LLM agent (Claude, OpenAI Operator) 의 ReAct/CoT 도 매 본질적으로 Polya 의 자동화.
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## 매 핵심
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### 매 Polya 4 stages
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- **Understand**: 매 restate, 매 identify knowns/unknowns/constraints.
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- **Plan**: 매 decompose, 매 analogous problems, 매 work backwards.
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- **Carry Out**: 매 execute, 매 verify each step.
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- **Look Back**: 매 check, 매 generalize, 매 alternate methods.
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### 매 strategies
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- **Decomposition**: 매 break into sub-problems (divide & conquer).
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- **Analogy**: 매 find similar solved problem (case-based reasoning).
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- **Inversion**: 매 work backwards from goal.
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- **Specialization**: 매 try simpler instance (n=1, n=2 first).
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- **Generalization**: 매 solve more general version sometimes easier.
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- **Symmetry / Invariants**: 매 find quantity that doesn't change.
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### 매 응용
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1. Debugging: 매 reproduce → bisect → fix → verify → write test.
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2. System design: 매 understand requirements → decompose → component design.
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3. LLM agent: 매 ReAct loop = Polya in code.
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4. Math/algorithms: 매 examples → conjecture → prove → optimize.
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## 💻 패턴
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### Pattern 1: Debugging as Polya
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```python
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def debug(bug_report):
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# 1. UNDERSTAND
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repro = build_minimal_repro(bug_report)
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# 2. PLAN
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suspected_modules = trace_stack(repro)
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plan = git_bisect_plan(repro, suspected_modules)
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# 3. CARRY OUT
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bad_commit = git_bisect(plan)
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fix = author_fix(bad_commit)
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# 4. LOOK BACK
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add_regression_test(repro)
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update_runbook(bug_report.symptom)
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return fix
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```
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### Pattern 2: ReAct LLM agent (Polya 자동화)
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```python
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SYSTEM = """For each task, follow:
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1. THOUGHT: restate the problem and constraints (UNDERSTAND).
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2. PLAN: decompose into 1-3 next actions.
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3. ACTION: call exactly one tool.
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4. OBSERVE: read result.
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5. REFLECT: did this advance? if not, revise plan (LOOK BACK).
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Repeat until done.
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"""
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```
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### Pattern 3: Decomposition tree
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```python
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@dataclass
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class Problem:
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statement: str
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children: list["Problem"] = field(default_factory=list)
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solved: bool = False
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solution: Optional[str] = None
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def solve(p: Problem):
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if can_solve_directly(p):
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p.solution = direct(p); p.solved = True; return
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p.children = decompose(p)
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for c in p.children: solve(c)
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p.solution = combine([c.solution for c in p.children])
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p.solved = all(c.solved for c in p.children)
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```
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### Pattern 4: Five-Whys root cause
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```text
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Symptom: 매 dashboard p99 latency 5x baseline.
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Why? — 매 DB queries slow.
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Why? — 매 missing index.
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Why? — 매 migration didn't add it.
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Why? — 매 PR template doesn't require index check.
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Why? — 매 no automated linter.
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→ 매 Root: missing tooling, not "lazy engineer".
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```
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### Pattern 5: Pre-mortem (inverted planning)
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```python
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def pre_mortem(plan):
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# 매 imagine the plan failed in 6 months
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# 매 ask team: what went wrong?
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failure_modes = team_brainstorm("It's 6mo from now. Project failed. Why?")
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return prioritize_mitigations(failure_modes)
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```
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### Pattern 6: Working-memory checkpoint
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```markdown
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<!-- 매 problem_log.md while solving -->
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## 매 KNOWN
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- API returns 500 on POST /orders > 1000 items.
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## 매 UNKNOWN
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- Is it timeout, memory, or DB lock?
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## 매 TRIED
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- [x] Reproduce locally → reproduces at 1500.
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- [x] Add timing logs → DB INSERT is slow.
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- [ ] Check lock contention.
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## 매 NEXT
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- pg_stat_activity during repro.
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```
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### Pattern 7: Solution generalization (look back)
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```python
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# 매 after fixing one instance — 매 ask: where else does this pattern occur?
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def generalize(fix):
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pattern = abstract(fix) # e.g., "missing pagination in list endpoints"
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similar = scan_codebase_for(pattern)
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return apply_fix_to_all(similar)
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```
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## 매 결정 기준
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| 상황 | Strategy |
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|---|---|
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| 매 stuck at "understand" | Restate problem to rubber duck / LLM |
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| 매 plan unclear | Try simpler case (n=1) first |
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| 매 carry-out fails | Bisect; isolate variable |
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| 매 done — but is it right? | Look back; alt method; edge cases |
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| 매 recurring class of bugs | Generalize the fix; tooling |
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| 매 LLM agent loop stuck | Force REFLECT step; reduce action set |
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**기본값**: 매 always do Look Back — 매 most engineers skip it; 매 90% of compounding leverage lives there.
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## 🔗 Graph
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- 부모: [[Cognitive Psychology]]
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- 변형: [[Polya Method]] · [[Debugging]] · [[Root Cause Analysis]]
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- Adjacent: [[ReAct]] · [[Chain of Thought]]
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## 🤖 LLM 활용
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**언제**: 매 system-prompt scaffolds, 매 incident runbooks, 매 onboarding docs, 매 interview prep.
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**언제 X**: 매 trivial 1-line tasks — 매 over-formalization slows.
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## ❌ 안티패턴
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- **Skip understanding**: 매 jump to coding → 매 wrong problem solved.
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- **Skip looking back**: 매 ship fix, never abstract → 매 same bug class returns.
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- **No working-memory log**: 매 forget what you tried.
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- **One strategy only**: 매 if decomposition fails, try inversion / analogy.
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- **LLM as oracle**: 매 use as plan-critic, not plan-author.
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## 🧪 검증 / 중복
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- Verified (Polya 1945, Newell & Simon 1972, Yao et al. 2022 ReAct).
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- 신뢰도 A (foundational).
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## 🕓 Changelog
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| 날짜 | 변경 |
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|---|---|
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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — Polya 4단계 + ReAct + 7 패턴 |
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