Reading source record observed-2026-10-01. View default cited record →
Seven Millennium Prize Problems; five selected here
The exact passages cited in OpenMath. Each passage identifies how its wording was recorded.
For an elliptic curve over the rational numbers, does the rank of its rational points equal the order of vanishing of its L-function at s = 1?
Passage ID: birch-and-swinnerton-dyer-conjecture:entry:0:v1
Source item: https://www.claymath.org/millennium/birch-and-swinnerton-dyer-conjecture/
Source record: clay-millennium@observed-2026-10-01
On a smooth complex projective variety, is every rational Hodge class a rational linear combination of classes of algebraic cycles?
Passage ID: hodge-conjecture:entry:0:v1
Source item: https://www.claymath.org/millennium/hodge-conjecture/
Source record: clay-millennium@observed-2026-10-01
Is every decision problem with solutions verifiable in polynomial time also solvable in polynomial time?
Passage ID: p-vs-np:entry:0:v1
Source item: https://www.claymath.org/millennium/p-vs-np/
Source record: clay-millennium@observed-2026-10-01
Is every closed, simply connected three-dimensional manifold homeomorphic to the three-sphere?
Passage ID: poincare-conjecture:entry:0:v1
Source item: https://www.claymath.org/millennium/poincare-conjecture/
Source record: clay-millennium@observed-2026-10-01
Do all nontrivial zeros of the Riemann zeta function have real part 1/2?
Passage ID: riemann-hypothesis:entry:0:v1
Source item: https://www.claymath.org/millennium/riemann-hypothesis/
Source record: clay-millennium@observed-2026-10-01
Explicit citations in versioned problem publications. A citation records a use; it does not confer proof or independent verification.
Problem publication v17
Source assessment · superseded assessment
Open
Unsolved
The cited source item and version only; this is not an independent OpenMath assessment.
Observed Oct 1, 2026
Question
Birch and Swinnerton-Dyer conjecture
Problem publication v15
Source assessment · superseded assessment
Open
Unsolved
The cited source item and version only; this is not an independent OpenMath assessment.
Observed Oct 1, 2026
Problem publication v14
Source assessment · superseded assessment
Open
Unsolved
The cited source item and version only; this is not an independent OpenMath assessment.
Observed Oct 1, 2026
Problem publication v13
Source assessment
Proved
Solved
The cited source item and version only; this is not an independent OpenMath assessment.
Observed Oct 1, 2026
Scope
The topological three-dimensional Poincaré theorem
Question
Poincaré conjecture
Problem publication v13
Source assessment · superseded assessment
Open
Unsolved
The cited source item and version only; this is not an independent OpenMath assessment.
Observed Oct 1, 2026
Question
Riemann hypothesis
Clay Mathematics Institute
OpenMath source records preserve exact citations. Observation dates order these records; they do not establish the latest upstream paper or proof.
Clay · Millennium Problems
Clay · Millennium Problems
Store metadata and original OpenMath paraphrases; follow the original source for authoritative wording.
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