Yang–Mills existence and mass gap problem
E173924
The Yang–Mills existence and mass gap problem is a fundamental unsolved question in mathematical physics that asks for a rigorous proof that quantum Yang–Mills theory exists and exhibits a positive mass gap, and is one of the seven Millennium Prize Problems.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Yang–Mills existence and mass gap problem canonical | 2 |
| Jaffe–Witten problem statement | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1523325 — 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: Yang–Mills existence and mass gap problem Context triple: [Millennium Prize Problem, hasProblem, Yang–Mills existence and mass gap problem]
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A.
Millennium Prize Problem
The Millennium Prize Problem is one of seven famous unsolved mathematical problems designated by the Clay Mathematics Institute, each carrying a $1 million reward for a correct solution.
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B.
Poincaré conjecture
The Poincaré conjecture is a landmark problem in topology that characterizes the three-dimensional sphere among three-dimensional manifolds and was famously solved by Grigori Perelman in the early 2000s.
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C.
Atiyah–Singer index theorem
The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
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D.
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.
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E.
P versus NP problem
The P versus NP problem is a central unsolved question in theoretical computer science that asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
- 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: Yang–Mills existence and mass gap problem Target entity description: The Yang–Mills existence and mass gap problem is a fundamental unsolved question in mathematical physics that asks for a rigorous proof that quantum Yang–Mills theory exists and exhibits a positive mass gap, and is one of the seven Millennium Prize Problems.
-
A.
Millennium Prize Problem
The Millennium Prize Problem is one of seven famous unsolved mathematical problems designated by the Clay Mathematics Institute, each carrying a $1 million reward for a correct solution.
-
B.
Poincaré conjecture
The Poincaré conjecture is a landmark problem in topology that characterizes the three-dimensional sphere among three-dimensional manifolds and was famously solved by Grigori Perelman in the early 2000s.
-
C.
Atiyah–Singer index theorem
The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
-
D.
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.
-
E.
P versus NP problem
The P versus NP problem is a central unsolved question in theoretical computer science that asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
Millennium Prize Problem
ⓘ
open problem in mathematical physics ⓘ |
| asksFor |
proof of existence of a nontrivial quantum Yang–Mills theory with compact simple gauge group
ⓘ
proof of existence of a positive mass gap ⓘ proof that the least nonzero energy of an excitation above the vacuum is strictly positive ⓘ proof that the theory satisfies the standard axioms of quantum field theory ⓘ rigorous construction of quantum Yang–Mills theory on four-dimensional Minkowski space ⓘ |
| concerns |
Yang–Mills theory
ⓘ
existence of quantum Yang–Mills theory ⓘ mass gap in quantum Yang–Mills theory ⓘ |
| difficulty | very hard ⓘ |
| dimension | 4-dimensional spacetime ⓘ |
| field |
mathematical physics
ⓘ
mathematics ⓘ quantum field theory ⓘ theoretical physics ⓘ |
| formalizedBy |
Yang–Mills existence and mass gap problem
self-linksurface differs
ⓘ
surface form:
Jaffe–Witten problem statement
|
| hasConsequence |
insight into strong coupling behavior of quantum fields
ⓘ
mathematical understanding of confinement in QCD ⓘ rigorous foundation for non-abelian gauge theories ⓘ |
| hasNoKnown | complete rigorous solution ⓘ |
| hasPrize | US$1,000,000 ⓘ |
| involves |
Wightman axioms
ⓘ
surface form:
Wightman axioms or Osterwalder–Schrader axioms
existence of a vacuum state ⓘ local gauge invariance ⓘ non-abelian gauge symmetry ⓘ renormalization in quantum field theory ⓘ spectral properties of the Hamiltonian ⓘ |
| namedAfter | Yang–Mills theory ⓘ |
| partOf | list of seven Millennium Prize Problems ⓘ |
| relatedConcept |
lattice gauge theory
ⓘ
mass gap ⓘ nonperturbative quantum field theory ⓘ quantum chromodynamics ⓘ spectral gap ⓘ |
| relatedTo |
Millennium Prize Problem
ⓘ
surface form:
Clay Millennium Prize Problems
confinement in quantum chromodynamics ⓘ non-abelian gauge theories ⓘ |
| requires |
compact simple gauge group such as SU(3)
ⓘ
nontrivial quantum field theory distinct from the free theory ⓘ |
| requiresProofIn |
Minkowski space-time
ⓘ
surface form:
Minkowski spacetime
four-dimensional Euclidean space (via Wick rotation) ⓘ |
| sponsor | Clay Mathematics Institute ⓘ |
| status | unsolved ⓘ |
| typicalGaugeGroup |
rotation group SU(2)
ⓘ
surface form:
SU(2)
SU(3) ⓘ special unitary group SU(n) ⓘ
surface form:
SU(N)
|
| yearProposed | 2000 ⓘ |
How these facts were elicited
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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: Yang–Mills existence and mass gap problem Description of subject: The Yang–Mills existence and mass gap problem is a fundamental unsolved question in mathematical physics that asks for a rigorous proof that quantum Yang–Mills theory exists and exhibits a positive mass gap, and is one of the seven Millennium Prize Problems.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
Yang–Mills existence and mass gap problem
→
formalizedBy
→
Yang–Mills existence and mass gap problem
self-linksurface differs
ⓘ
this entity surface form:
Jaffe–Witten problem statement