This is a preview. Log in through your library . Abstract In 1985 Gabai gave a complete proof of the Simple Loop Conjecture, which states that any map between closed surfaces, which does not induce an ...

In 1990, motivated by applications in the social sciences, Thomas Schwartz made a conjecture about tournaments which would have had numerous attractive consequences. In particular, it implied that ...

One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...

The Kaplansky conjectures are three long-standing open problems on the group rings of torsion-free groups. Last week, Dr. Giles Gardam, postdoc in Mathematics Münster's topology group, announced that ...

Hannah Cairo found herself stuck on a problem that wouldn’t leave her mind. It wasn’t a regular homework assignment—it was a decades-old mathematical puzzle believed to be true by leading experts in ...

A 17-year-old girl, Hannah Cairo, has just conquered everyone with her ability to develop and solve all kinds of mathematical problems. Many call her a genius and many on social networks define her as ...

Innocent-looking problems involving whole numbers can stymie even the most astute mathematicians. As in the case of Fermats last theorem, centuries of effort may go into proving such tantalizing, ...

Conjecture (Berge and Fulkerson): Every 2-connected cubic graph has a collection of six perfect matchings that together cover every edge exactly twice. This conjecture is attributed to Berge in [2].

The Kaplansky conjectures are three long-standing open problems on the group rings of torsion-free groups. Last week, Dr. Giles Gardam, postdoc in Mathematics Münster's topology group, announced that ...