Abstractions blog

Three mathematicians have resolved a fundamental question about straight paths on the 12-sided Platonic solid.

A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot.

Studies suggest that self-disseminating vaccines could prevent the “spillover” of animal viruses into humans as pandemic diseases.

Physicists have identified an algebraic structure underlying the messy mathematics of particle collisions. Some hope it will lead to a more elegant theory of the natural world.

Emperor penguins display rigorously geometric spacing and mathematical efficiency when they huddle together for warmth, which may reveal secrets to their overall health.

An 18th-century physicist first predicted the existence of a chorus of atmospheric waves that swoop around Earth. Scientists have finally found them.

A new model shows that the denizens of a vast, ancient biome beneath the seafloor use barely enough energy to stay alive — and broadens understanding of what life can look like.

The unintentional creation of “sturddlefish” hybrids may illuminate the genomic mechanisms that govern whether species can interbreed.

Detailed computer simulations have found that a cosmic contraction can generate features of the universe that we observe today.