Geometry's least-packable shapes

If you've ever struggled to pack a bunch of suitcases into the trunk of your car, you've got some idea of a basic problem in materials science: if you throw a bunch of atoms or molecules together, how do they fit together, ...

Mathematicians prove the Umbral Moonshine Conjecture

Monstrous moonshine, a quirky pattern of the monster group in theoretical math, has a shadow - umbral moonshine. Mathematicians have now proved this insight, known as the Umbral Moonshine Conjecture, offering a formula with ...

Conjecture on the lateral growth of Type I collagen fibrils

Whatever the origin and condition of extraction of type I collagen fibrils, in vitro as well as in vivo, the radii of their circular circular cross sections stay distributed in a range going from 50 to 100 nm for the most ...

An old mathematical puzzle soon to be unraveled?

(Phys.org) —It is one the oldest mathematical problems in the world. Several centuries ago, the twin primes conjecture was formulated. As its name indicates, this hypothesis, which many science historians have attributed ...

Indian researcher helps prove math conjecture from the 1950s

On June 18, Adam Marcus and Daniel A. Spielman of Yale University, along with Nikhil Srivastava of Microsoft Research India, announced a proof of the Kadison-Singer conjecture, a question about the mathematical foundations ...

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