Physics

"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 some mathematicians say it—or some aspect of it—belongs in the esteemed ranks of the Millennium Prize Problems, a list of the top open questions in math. Edward Frenkel, a mathematician at the University of California, Berkeley, has even dubbed the Langlands program 'a Grand Unified Theory of Mathematics.'"

"Natalie Paquette spends her time thinking about how to grow an extra dimension. Start with little circles, scattered across every point in space and time—a curlicue dimension, looped back onto itself. Then shrink those circles down, smaller and smaller, tightening the loop, until a curious transformation occurs: the dimension stops seeming tiny and instead becomes enormous, like when you realize something that looks small and nearby is actually huge and distant."

"Edward Witten has spent almost 50 years at the forefront of theoretical and mathematical physics. Here he describes how the LHC and other recent results have impacted his view on nature, and asks whether naturalness is still a useful guide for the field."