Poincaré conjecture

[ pwahn-kah-rey kuhn-jek-cher ]

noun

1. Mathematics. the question of whether a compact, simply connected three-dimensional manifold is topologically equivalent to a three-dimensional sphere.

Word History and Origins

Origin of Poincaré conjecture¹

Named after J. H. Poincaré

Example Sentences

The 2000 proclamation gave $7 million worth of reasons for people to work on the seven problems: the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, the P versus NP problem, the Yang-Mills existence and mass gap problem, the Poincaré conjecture, the Navier-Stokes existence and smoothness problem, and the Hodge conjecture.

From Scientific American

Yet despite the fanfare and monetary incentive, after 21 years, only the Poincaré conjecture has been solved.

From Scientific American

In 2002 and 2003 Grigori Perelman, a Russian mathematician then at the St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences, shared work connected to his solution of the Poincaré conjecture online.

From Scientific American

According to CMI, the Poincaré conjecture focuses on a topological question about whether spheres with three-dimensional surfaces are “essentially characterized” by a property called “simple connectivity.”

From Scientific American

In topology, his proof of the Poincare´ Conjecture in dimension 1, showing that the unit circle is the only simply connected compact 1-manifold without boundary, sent topology into a decade-long tailspin.

From Scientific American