By extending the scope of the key insight behind Fermat’s Last Theorem, four mathematicians have made great strides toward building a “grand unified theory” of math.

Reversible programs run backward as easily as they run forward, saving energy in theory. After decades of research, they may soon power AI.

Promise and controversy continues to surround string theory as a potential unified theory of everything. In the latest episode of The Joy of Why, Cumrun Vafa discusses his progress in trying to find good, testable models hidden among the ‘swampland’ of impossible universes.

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.