mathematical-proof-logic
The logical structure of mathematical proof -- how first-order logic, natural deduction, and semantic reasoning combine to produce rigorous mathematical arguments. Covers the logical skeleton of direct proof, contraposition, contradiction, cases, and induction; the role of definitions, lemmas, and theorems; how informal mathematical prose maps to formal deductive structure; and the difference between proof-as-object and proof-as-activity. Use when the question is "why is this a valid proof?" rather than "what proof technique applies?
npx skills add majiayu000/claude-skill-registry --skill mathematical-proof-logic --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Mathematical Proof Logic Mathematical proof is the oldest and most rigorous form of argumentation humans have developed. Its rigor comes from logic: every legitimate step in a proof must correspond to a rule of inference in some underlying logical system -- usually first-order logic with a background theory like ZFC set theory or Peano arithmetic. This skill is about the logical structure of proof, not the pragmatic heuristics for finding one. It answers the question "what makes this sequence of sentences a valid proof?" rather than "what trick should I try?" The complementary `proof-techniques` skill in the math department covers the latter. **Agent affinity:** godel (metamathematics), tarski (semantic grounding), russell (Principia heritage) **Concept IDs:** log-predicate-logic, log-proof-techniques, log-deductive-reasoning, log-mathematical-proof ## Proof as Logical Object A mathematical proof is, formally, a finite sequence of sentences in a formal language such that every sentence is either: 1. An axiom of the background theory, 2. A previously established theorem (lemma), or 3. Inferred from earlier sentences by an inference rule of the logic. The final sentence is the theo
- Proof as Logical Object
- The Underlying Logic
- Proof Structures as Logical Patterns
- Direct proof
- Proof by contrapositive
- Proof by contradiction (reductio ad absurdum)
- Proof by cases
- Proof by induction
- Existence proofs
- Uniqueness proofs
- Definitions, Axioms, Lemmas, Theorems
- Informal Prose and Its Formal Shadow
- Worked Example: A Classical Proof
- Common Errors in Proofs
What does the mathematical-proof-logic skill do?
The logical structure of mathematical proof -- how first-order logic, natural deduction, and semantic reasoning combine to produce rigorous mathematical arguments. Covers the logical skeleton of direct proof, contraposition, contradiction, cases, and induction; the role of definitions, lemmas, and theorems; how informal mathematical prose maps to formal deductive structure; and the difference between proof-as-object and proof-as-activity. Use when the question is "why is this a valid proof?" rather than "what proof technique applies?
How do I install it?
Run `npx skills add majiayu000/claude-skill-registry --skill mathematical-proof-logic --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From majiayu000/claude-skill-registry, a repository with 534 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.