Revelations in the field of quantum physics have resulted in the discovery of the Amplituhedron, a jewel-like higher dimensional object whose volume elegantly predicts fundamental physical processes that took the brilliant Dr. Richard Feynman hundreds of pages of abstruse mathematics to describe. The theoretical manifold not only enables simple pen-and-paper calculation of physics that would normally require supercomputers to work out, but also challenges basic assumptions about the nature of reality -- forgoing the core concepts of locality and unitarity and suggesting that space and time are merely emergent properties of a timeless, infinitely-sided "master amplituhedron," whose geometry represents the sum total of all physical interactions. More: The 152-page source paper on arXiv [PDF] - Lead author Nima Arkani-Hamed's hour-long lecture at SUSY 2013 - Scans of Arkani-Hamed's handwritten lecture notes - A far more detailed lecture series "Scattering Without Space Time": one, two, three - Arkani-Hamed previously on MeFi - A hot-off-the-presses Wikipedia page (watch this space)
Every film Pixar has produced has landed in the top fifty highest-grossing animated films of all time. What's their secret? Mathematics. Oh, and 22 Rules of Storytelling. [more inside]
You and Your Research was a talk given by Richard Hamming in 1986. Read it if you have an interest in doing first-class work.
Proofs and Pictures: The Role of Visualization in Mathematical and Scientific Reasoning [video] "The picture is a telescope for looking into Plato's heaven." -- James Brown [cached]