Biophysicists Uncover Powerful Symmetries in Living Tissue
After identifying interlocking symmetries in mammalian cells, scientists describe some tissues as liquid crystals. That lays the groundwork for a fluid-dynamic ..
After identifying interlocking symmetries in mammalian cells, scientists describe some tissues as liquid crystals. That lays the groundwork for a fluid-dynamic ..
Mathematical proofs based on a technique called diagonalization can be relentlessly contrarian, but they help reveal the limits of algorithms. ..
A deceptively simple math proposition known as the Kakeya conjecture underpins a tower of other questions in physics, number theory, and harmonic analysis. ..
Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big? ..
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. ..
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 ..
A decades-old conjecture about the best way to minimize the surface area of a three-bubble cluster seemed unprovable—until a breakthrough result. ..
Researchers have uncovered a surprising wealth of “intransitive” patterns in randomly chosen dice. ..
Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. They ..