Concerns about the use of computer-aided empirical verification in geometry classes lead to an investigation of students' understandings of the similarities and differences between the measurement of ...

Mathematicians are celebrating a 1000-page proof of the geometric Langlands conjecture, a problem so complicated that even other mathematicians struggle to understand it. Despite that, it is hoped ...

A Sequel to the First Six Books of the Elements of Euclid, containing an Easy Introduction to Modern Geometry, with numerous Examples. By John Casey (Dublin University Press Series, 1881.) ...

Mathematicians Wrote a Proof for a 100-Year-Old Problem—and May Have Just Changed Geometry The work has been deemed “spectacular progress” by giants of the field.

We give a geometric proof of the Berger Holonomy Theorem. The proof uses Euclidean submanifold geometry of orbits and gives a link between Riemannian holonomy groups and normal holonomy groups.

A group of nine mathematicians has proved the geometric Langlands conjecture, a key component of one of the most sweeping paradigms in modern mathematics. The proof represents the culmination of three ...