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A proposition which is consistent with known data, but has neither been verified nor shown to be false. It is synonymous with hypothesis.

In its original form, the Poincaré conjecture states that every simply connected closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense) S^3, ...

Every closed three-manifold with finite fundamental group has a metric of constant positive scalar curvature, and hence is homeomorphic to a quotient S^3/Gamma, where Gamma ...

The only Wiedersehen surfaces are the standard round spheres. The conjecture was proven by combining the Berger-Kazdan comparison theorem with A. Weinstein's results for n ...

Thurston's conjecture proposed a complete characterization of geometric structures on three-dimensional manifolds. Before stating Thurston's geometrization conjecture in ...

A conjecture due to M. S. Robertson in 1936 which treats a univalent power series containing only odd powers within the unit disk. This conjecture implies the Bieberbach ...

Let lambda_1, ..., lambda_n in C be linearly independent over the rationals Q, then Q(lambda_1,...,lambda_n,e^(lambda_1),...,e^(lambda_n)) has transcendence degree at least n ...

The conjecture that Frey's elliptic curve was not modular. The conjecture was quickly proved by Ribet (Ribet's theorem) in 1986, and was an important step in the proof of ...

A conjecture that, as proved by Parshin (1968), implies the Mordell conjecture.

The Cramér conjecture is the unproven conjecture that lim sup_(n->infty)(p_(n+1)-p_n)/((lnp_n)^2)=1, where p_n is the nth prime.