A Computer-Assisted Proof Solves the ‘Packing Coloring’ Problem
There’s a surprisingly straightforward answer to how many numbers are needed to fill an infinite grid so that identical numbers never get too close together. ..
There’s a surprisingly straightforward answer to how many numbers are needed to fill an infinite grid so that identical numbers never get too close together. ..
After decades of frustration, researchers have determined how an airborne scent molecule links to shapeshifting olfactory receptors in the nose. ..
A new theory describes how particle interactions fuel fast magnetic reconnection, the process behind solar flares and other astrophysical jets. ..
By imbuing enormous vectors with semantic meaning, we can get machines to reason more abstractly—and efficiently—than before. ..
In 50 years of searching, mathematicians found only one example of a “subspace design” that fit their criteria. A new proof reveals that there are infinitely ..
The quantum energy teleportation protocol was proposed in 2008 and largely ignored. Now two independent experiments have shown that it works. ..
As researchers race to cultivate these intriguing cells from the deep seafloor, the few growing in labs are our best glimpses of the forerunners of complex ..
The first large-scale comparison of DNA mutation rates in 68 different vertebrate species gives insights into how quickly life can evolve. ..
A decades-old conjecture about the best way to minimize the surface area of a three-bubble cluster seemed unprovable—until a breakthrough result. ..
Richard Feynman’s path integral is a powerful prediction machine and a philosophy. Physicists still struggle to figure out how to use it, and what it means. ..