## Latest Articles

### Never-Repeating Tiles Can Safeguard Quantum Information

Two researchers have proved that Penrose tilings, famous patterns that never repeat, are mathematically equivalent to a kind of quantum error correction.

### ‘Magical’ Error Correction Scheme Proved Inherently Inefficient

Locally correctable codes need barely any information to fix errors, but they’re extremely long. Now we know that the simplest versions can’t get any shorter.

### The ‘Accidental Activist’ Who Changed the Face of Mathematics

Throughout her 60-year career, Lenore Blum has developed new perspectives on logic and computation while championing women in mathematics and computer science. Now consciousness is on her mind.

### An Easy-Sounding Problem Yields Numbers Too Big for Our Universe

Researchers prove that navigating certain systems of vectors is among the most complex computational problems.

### Thirty Years Later, a Speed Boost for Quantum Factoring

Shor’s algorithm will enable future quantum computers to factor large numbers quickly, undermining many online security protocols. Now a researcher has shown how to do it even faster.

### Tiny Language Models Come of Age

To better understand how neural networks learn to simulate writing, researchers trained simpler versions on synthetic children’s stories.

### Alan Turing and the Power of Negative Thinking

Mathematical proofs based on a technique called diagonalization can be relentlessly contrarian, but they help reveal the limits of algorithms.

### Complexity Theory’s 50-Year Journey to the Limits of Knowledge

How hard is it to prove that problems are hard to solve? Meta-complexity theorists have been asking questions like this for decades. A string of recent results has started to deliver answers.

### To Move Fast, Quantum Maze Solvers Must Forget the Past

Quantum algorithms can find their way out of mazes exponentially faster than classical ones, at the cost of forgetting the path they took. A new result suggests that the trade-off may be inevitable.