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# Logic

## Latest Articles

### What Makes for ‘Good’ Mathematics?

Terence Tao, who has been called the “Mozart of Mathematics,” wrote an essay in 2007 about the common ingredients in “good” mathematical research. In this episode, the Fields Medalist joins Steven Strogatz to revisit the topic.

### How to Build an Origami Computer

Two mathematicians have shown that origami can, in principle, be used to perform any possible computation.

### 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.