Abstractions blog

For a half century, mathematicians have tried to define the exact circumstances under which a black hole is destined to exist. A new proof shows how a cube can help answer the question.

New results break with decades of conventional wisdom for the gradient descent algorithm.

New observations of a faraway rocky world that might have its own magnetic field could help astronomers understand the seemingly haphazard magnetic fields swaddling our solar system’s planets.

Genetic elements called Mavericks that have some viral features could be responsible for the large-scale smuggling of DNA between species.

The numbers count a variety of seemingly unrelated mathematical structures.

A new result shows how much of the plane can be colored by points that are never exactly one unit apart.

In some deep subterranean aquifers, cells have a chemical trick for making oxygen that could sustain whole underground ecosystems.

A new algorithm brings together the advantages of randomness and deterministic processes to reliably construct large prime numbers.

Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big?