Researchers have just released hacker-proof cryptographic code — programs with the same level of invincibility as a mathematical proof.

These games combine quantum entanglement, infinity and impossible-to-calculate winning probabilities. But if researchers can crack them, they’ll reveal deep mathematical secrets.

Two new studies show that the brain’s navigation system changes how it represents physical space to reflect personal experience.

All descriptions of change are a unique blend of chance and determinism, according to the sweeping mathematical proof of the “weak Pinsker conjecture.”

A number theorist with programming prowess has found a solution to 33 = x³ + y³ + z³, a much-studied equation that went unsolved for 64 years.

Neuroscience has found that gestures are not merely important as tools of expression but as guides of cognition and perception.

Puzzle solvers used “imaginary” numbers to solve a real world problem: finding long-lost treasure.

By reconstructing prehistoric food webs and analyzing the diverse interactions of humans with other species, the ecologist Jennifer Dunne is developing a new understanding of sustainability through network science.

One of the first quantum simulators has produced a puzzling phenomenon: a row of atoms that repeatedly pops back into place.