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# logic

## Latest Articles

### The Deep Link Equating Math Proofs and Computer Programs

Mathematical logic and the code of computer programs are, in an exact way, mirror images of each other.

### 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.

### Why Mathematical Proof Is a Social Compact

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.

### 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.

### Ninth Dedekind Number Found by Two Independent Groups

The numbers count a variety of seemingly unrelated mathematical structures.

### ‘Nasty’ Geometry Breaks Decades-Old Tiling Conjecture

Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong.

### Proof Assistant Makes Jump to Big-League Math

Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics.

### How the Slowest Computer Programs Illuminate Math’s Fundamental Limits

The goal of the “busy beaver” game is to find the longest-running computer program. Its pursuit has surprising connections to some of the most profound questions and concepts in mathematics.

### Inside the Secret Math Society Known Simply as Nicolas Bourbaki

For almost a century, the anonymous members of Nicolas Bourbaki have written books intended as pure expressions of mathematical thought.