Abstractions blog

In 1973, Paul Erdős asked if it was possible to assemble sets of “triples” — three points on a graph — so that they abide by two seemingly incompatible rules. A new proof shows it can always be done.

Computer scientists have found a new type of problem that quantum computers can solve dramatically faster than their classical counterparts.

A new origins-based system for classifying minerals reveals the huge geochemical imprint that life has left on Earth. It could help us identify other worlds with life too.

A new proof identifies precisely how large a mathematical graph must be before it contains a regular substructure.

Quantum computers may derive their power from the “magical” way that properties of particles change depending on the context.

For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them.

The lush biodiversity of the Amazon may be due in part to the dynamics of branching rivers, which serve as invisible fences that continuously barricade and merge bird populations.

Jared Duker Lichtman, 26, has proved a longstanding conjecture relating prime numbers to a broad class of “primitive” sets. To his adviser, it came as a “complete shock.”

Some animal neuropeptides have been around longer than nervous systems.