theorem
Let an agent explain theorems by statement, proof, history and use, distinguish related terms, and point to formal verification resources.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Statement What it says.
State
Precise statement.
State
Statement.
- What exactly does the theorem state, including all hypotheses? definition
- What happens if a hypothesis is dropped? boundary
Meaning
Intuition.
Meaning
Intuition.
- How can the theorem be explained intuitively? action
- Which example illustrates it? action
Proof Why it is true.
Outline
Proof sketch.
Outline
Proof outline.
- What are the main steps of a standard proof? definition
- Which earlier results does it use? provenance
Check
Verifying.
Check
Checking proofs.
- Is this proposed proof correct, and where might it fail? boundary
- Is there a formalised proof in a proof assistant? provenance
Terms Related terms.
Lemma
Lemmas and corollaries.
Lemma
Lemmas and corollaries.
- Is this result a lemma, corollary or main theorem? definition
- Why is it labelled that way? definition
Conjecture
Unproved statements.
Conjecture
Conjectures.
- Has this statement actually been proved, or is it still a conjecture? provenance
- Which source confirms its status? provenance
History Origins.
Who
Discoverers.
Who
Attribution.
- Who first proved the theorem, according to historians of mathematics? provenance
- Is the naming historically accurate? boundary
Uses
Applications.
Uses
Applications.
- Where is the theorem used in mathematics or applications? provenance
- Which fields depend on it? provenance
Classifiers Filled
- Family
- Thing Registry
- Category
- Information and virtual systems
- Entry kind
- thing
- Plane
- INF
- Domain
- INF.KNW
- Other names and narrower kinds
- Johnson bound, differentiation rule, lemma, pumping lemma, isomorphism theorem, Jacobi–Anger expansion, Serre duality, Newton's inequalities, unexpected hanging paradox, Mertens' theorems, Abelian theorem, Tauberian theorem
What it is Filled
A mathematical statement proved true by logical deduction from axioms and previously established results, such as the Pythagorean theorem or the fundamental theorem of arithmetic; related terms include lemma, corollary and proposition.
Why it exists Filled
Let an agent explain theorems by statement, proof, history and use, distinguish related terms, and point to formal verification resources.
Distinguishing features Filled
- Proved statement
- Depends on axioms
- Builds on earlier results
- Can be formally verified
What robots and AI may and may not do Filled
Must not
- Present a conjecture or unproved claim as a theorem.
- Drop hypotheses of a theorem so that it appears to apply where it does not.
- Attribute a theorem or proof to the wrong person.
- Pass off machine-generated proofs as a student's own work in assessed settings.
Only with a human decision
- Accepting a machine-checked proof as the basis for a safety-critical system.
May
- State a theorem with its hypotheses and cite where it is proved.
- Check or help write proofs at the request of the person doing the work.
Moral aspects Filled
- Credit for results matters to mathematicians' careers and has often been denied to some groups.
- Misapplied theorems can make flawed engineering or statistics look rigorous.
Who is affected
- Mathematicians and students
- Users of results in science and engineering
Owners Filled
Steward
Nobody owns a theorem; it belongs to mathematics, and its discoverers are credited.
Links to other meta-models Filled
parent
- Q108163 - registry parent class
- Q20665666 - registry parent class
related
- proposition - category
- mathematical proof - method
- conjecture - unproved statement
- axiom - foundation
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.theorem
- Wikidata: Q65943 (https://www.wikidata.org/wiki/Q65943)
Direct properties not applicable Not applicable
Not applicable
Plane INF: no invented physical properties.
Recognition optional Filled
- Named results with proofs
- Lemmas and corollaries
- Conjectures are unproved
- Not physical; statements and proofs in texts and formal libraries.
Capabilities and actions required Filled
- state and explain a theorem
- outline or check a proof
- distinguish lemma, corollary and conjecture
- find formalised proofs
Hazards and failure modes required Filled
- Misstating hypotheses
- Misattributing theorems
- Treating conjectures as proved
Standards and interfaces required Filled
- No specific regulation
Context of use required Filled
- Building mathematical knowledge.
- major named theorems
- lemmas
- corollaries
- existence and classification theorems
- formally verified theorems
Sources Filled
- Wikidata item Q65943: theorem - identity and sense of the item
- Wikipedia: Theorem - general description of the item
Open questions
- Should each theorem be a separate entry?
- How should formal libraries be linked?
- How should naming disputes be recorded?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q65943/spec.json