Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. They were wrong.

A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures.

Arithmetic Geometry and Manin's Conjecture Publication Trend The graph below shows the total number of publications each year in Arithmetic Geometry and Manin's Conjecture.

Strangely Curved Shapes Break 50-Year-Old Geometry Conjecture Mathematicians have disproved a major conjecture about the relationship between curvature and shape.