Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong. One of the oldest and simplest ...

Consider a pencil lying on your desk. Try to spin it around so that it points once in every direction, but make sure it sweeps over as little of the desk’s surface as possible. You might twirl the ...

The Latin root of the word conjecture, conicere, means to throw things together. Think of Jackson Pollock splashing different paints onto a canvas and hoping for some kind of coherent result. In ...

We are also interested in the formalized statements of solved variants of open conjectures and solved statements from dedicated problem lists. While the main goal is to collect conjecture statements, ...

Within mathematics, there is a vast and ever expanding web of conjectures, theorems and ideas called the Langlands program. That program links seemingly disconnected subfields. It is such a force that ...

The Nature Index 2024 Research Leaders — previously known as Annual Tables — reveal the leading institutions and countries/territories in the natural and health sciences, according to their output in ...

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 ...