Can one hear the shape of a drum?
E92906
"Can one hear the shape of a drum?" is a famous 1966 paper by mathematician Mark Kac that explores whether the geometric shape of a domain can be uniquely determined from the spectrum of its Laplacian, encapsulated in the question of whether one can infer a drum’s shape from the sound it makes.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Can one hear the shape of a drum? canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T787788 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Can one hear the shape of a drum? Context triple: [Mark Kac, notableWork, Can one hear the shape of a drum?]
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A.
Israel–Carter–Robinson uniqueness theorems
The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
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B.
The Science of Musical Sound
The Science of Musical Sound is a book by engineer and acoustics researcher John R. Pierce that explains the physical and perceptual principles underlying how music and sound are produced, transmitted, and heard.
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C.
Euler’s polyhedron formula
Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
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D.
Theorema Egregium
Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
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E.
Hilbert problems
The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Can one hear the shape of a drum? Target entity description: "Can one hear the shape of a drum?" is a famous 1966 paper by mathematician Mark Kac that explores whether the geometric shape of a domain can be uniquely determined from the spectrum of its Laplacian, encapsulated in the question of whether one can infer a drum’s shape from the sound it makes.
-
A.
Israel–Carter–Robinson uniqueness theorems
The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
-
B.
The Science of Musical Sound
The Science of Musical Sound is a book by engineer and acoustics researcher John R. Pierce that explains the physical and perceptual principles underlying how music and sound are produced, transmitted, and heard.
-
C.
Euler’s polyhedron formula
Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
-
D.
Theorema Egregium
Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
-
E.
Hilbert problems
The Hilbert problems are a famous list of 23 unsolved mathematical problems presented by David Hilbert in 1900 that profoundly influenced the development of 20th-century mathematics.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical paper
ⓘ
research article ⓘ |
| addresses | relationship between physical sound and mathematical spectrum ⓘ |
| asksWhether | the spectrum of the Laplacian uniquely determines the shape of a domain ⓘ |
| associatedWith | Mark Kac's work in probability and analysis ⓘ |
| author | Mark Kac ⓘ |
| context |
Dirichlet eigenvalues of the Laplacian
ⓘ
Laplacian on bounded planar domains ⓘ |
| field |
mathematical physics
ⓘ
mathematics ⓘ partial differential equations ⓘ spectral geometry ⓘ |
| historicalSignificance |
became a central question in spectral geometry
ⓘ
stimulated the search for non-isometric isospectral domains ⓘ |
| influencedField |
Riemannian manifolds
ⓘ
surface form:
Riemannian geometry
mathematical analysis ⓘ quantum mechanics ⓘ spectral geometry ⓘ |
| inspired | construction of planar isospectral domains by Gordon, Webb, and Wolpert ⓘ |
| involves |
eigenvalue problem for the Laplace operator
ⓘ
inverse spectral problem ⓘ relationship between geometry and spectrum ⓘ spectral invariants ⓘ |
| language | English ⓘ |
| mainConcept |
Dirichlet conditions
ⓘ
surface form:
Dirichlet boundary conditions
Laplacian spectrum ⓘ eigenvalues of the Laplacian ⓘ isospectral domains ⓘ vibrating membrane ⓘ |
| mainQuestion | whether the geometric shape of a domain is determined by the spectrum of its Laplacian ⓘ |
| medium | journal article ⓘ |
| notableFor |
connecting physical intuition about sound with abstract spectral theory
ⓘ
formulating the phrase "Can one hear the shape of a drum?" ⓘ popularizing inverse spectral problems ⓘ |
| popularizedQuestion | Can one determine the shape of a drum from the sound it makes? ⓘ |
| publicationYear | 1966 ⓘ |
| questionType | inverse spectral question ⓘ |
| relatedTo |
eigenvalue spectra of differential operators
ⓘ
hearing the shape of a Riemannian manifold ⓘ inverse problems in mathematical physics ⓘ |
| timePeriod | 20th century ⓘ |
| titleQuestion | Can one hear the shape of a drum? ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Can one hear the shape of a drum? Description of subject: "Can one hear the shape of a drum?" is a famous 1966 paper by mathematician Mark Kac that explores whether the geometric shape of a domain can be uniquely determined from the spectrum of its Laplacian, encapsulated in the question of whether one can infer a drum’s shape from the sound it makes.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.