Kevin Hartnett

Senior Writer

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.

abstractions blog

New Proof Shows Infinite Curves Come in Two Types

Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.

number theory

Without a Proof, Mathematicians Wonder How Much Evidence Is Enough

A new statistical model appears to undermine long-held assumptions in number theory. How much should it be trusted when all that really matters is proof?

Art for "A Proof About Where Symmetries Can’t Exist"
geometry

A Proof About Where Symmetries Can’t Exist

In a major mathematical achievement, a small team of researchers has proven Zimmer’s conjecture.

Art for "Machine Learning Confronts the Elephant in the Room"
artificial intelligence

Machine Learning Confronts the Elephant in the Room

A visual prank exposes an Achilles’ heel of computer vision systems: Unlike humans, they can’t do a double take.