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, ...

We continue the study of the Bochner-Riesz family of conjectures. In particular, the weak-type endpoint Bochner-Riesz conjecture is shown to be equivalent to the standard Bochner-Riesz conjecture, and ...

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 ...

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 ...

This is a preview. Log in through your library . Abstract We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the ...

Dr. Chandrashekhar B. Khare, a mathematician by qualification and music aficionado at heart, creatively recounts his ...

Kyoto University Research Institute for Mathematical Sciences professor Shinichi Mochizuki. (Photo courtesy of Kyoto University) A paper by a Kyoto University mathematician that claims to have proven ...