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.

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

A two-player game can reveal whether the universe has an infinite amount of complexity.

Recent progress on the “sum product” problem recalls a celebrated mathematical result that revealed the power of miniature number systems.

A graduate student has helped illuminate a long-suspected connection between addition and multiplication.

Neural networks can be as unpredictable as they are powerful. Now mathematicians are beginning to reveal how a neural network’s form will influence its function.

In a Paris lab, researchers have shown for the first time that quantum methods of transmitting information are superior to classical ones.

Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work.