Manu Prakash works on the world’s most urgent problems and seemingly frivolous questions at the same time. They add up to a philosophy he calls “recreational biology.”

Black hole and Big Bang singularities break our best theory of gravity. A trilogy of theorems hints that physicists must go to the ends of space and time to find a fix.

A new proof illuminates the hidden patterns that emerge when addition becomes impossible.

One computer scientist’s “stunning” proof is the first progress in 50 years on one of the most famous questions in computer science.

Slight changes in the number, shape, efficiency and interconnectedness of organelles in the cells of flight muscles provide extra energy for birds’ continent-spanning feats.

Turbulence is a notoriously difficult phenomenon to study. Mathematicians are now starting to untangle it at its smallest scales.

Geometry may have its origins thousands of years ago in ancient land surveying, but it has also had a surprising impact on modern physics. In the latest episode of The Joy of Why, Yang-Hui He explores geometry’s evolution and its future potential through AI.

From living matter to molecules to elementary particles, the world is made of “chiral” objects that differ from their reflected forms.

Researchers have devised a scheme for painting the edges of a graph that’s almost as speedy as possible.