In work that has been 30 years in the making, mathematicians have proved a major part of a profound mathematical vision called the Langlands program. A group of nine mathematicians has proved the ...

Though pictures are often used to present mathematical arguments, they are not typically thought to be an acceptable means for presenting mathematical arguments rigorously. With respect to the proofs ...

A system developed by Google’s DeepMind has set a new record for AI performance on geometry problems. DeepMind’s AlphaGeometry managed to solve 25 of the 30 geometry problems drawn from the ...

This is a preview. Log in through your library . Abstract We give a geometric proof of the Berger Holonomy Theorem. The proof uses Euclidean submanifold geometry of orbits and gives a link between ...

Abstract: There are several methods used to construct curves in CAGD, e.g., the de Casteljau's algorithm, Wang algorithm, Said-Ball algorithm. However, they are represented in the forms that are not ...

A 125-page proof posted to arXiv may represent a huge breakthrough in geometric measure theory. This problem has implications in fields like encryption, computer science, and number theory. How much ...

Mathematicians say that they have solved a major, decades-old problem in geometry: how to reconstruct the inner structure of a mystery object ‘X’ from knowing only how fast waves travel between any ...