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.”
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.
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.
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.
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.
number theory
In the Universe of Equations, Virtually All Are Prime
Equations, like numbers, cannot always be split into simpler elements.
geometry
Amateur Mathematician Finds Smallest Universal Cover
Through exacting geometric calculations, Philip Gibbs has found the smallest known cover for any possible shape.