Kevin Hartnett

Senior Writer

Art for "Proof Finds That All Change Is a Mix of Order and Randomness"
dynamical systems

Proof Finds That All Change Is a Mix of Order and Randomness

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

Art for "The Universe’s Ultimate Complexity Revealed by Simple Quantum Games"
quantum information theory

The Universe’s Ultimate Complexity Revealed by Simple Quantum Games

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

Art for "Smaller Is Better: Why Finite Number Systems Pack More Punch"
Abstractions blog

Smaller Is Better: Why Finite Number Systems Pack More Punch

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

number theory

How a Strange Grid Reveals Hidden Connections Between Simple Numbers

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

artificial intelligence

Foundations Built for a General Theory of Neural Networks

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.

Art for "Milestone Experiment Proves Quantum Communication Really Is Faster"
quantum computing

Milestone Experiment Proves Quantum Communication Really Is Faster

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

Illustration of lock with polynomials surrounding it
Abstractions blog

Mathematicians Seal Back Door to Breaking RSA Encryption

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

Art for "In the Universe of Equations, Virtually All Are Prime"
number theory

In the Universe of Equations, Virtually All Are Prime

Equations, like numbers, cannot always be split into simpler elements.

Art for "With Ruler and Compass, Amateur Mathematician Tames Fiendish Problem"
geometry

Amateur Mathematician Finds Smallest Universal Cover

Through exacting geometric calculations, Philip Gibbs has found the smallest known cover for any possible shape.