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# proofs

## Latest Articles

### 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.

### How Math Achieved Transcendence

Transcendental numbers include famous examples like e and π, but it took mathematicians centuries to understand them.

### The Colorful Problem That Has Long Frustrated Mathematicians

The four-color problem is simple to explain, but its complex proof continues to be both celebrated and despised.

### How Do You Prove a Secret?

Zero-knowledge proofs allow researchers to prove their knowledge without divulging the knowledge itself.

### Computer Science Proof Unveils Unexpected Form of Entanglement

Three computer scientists have posted a proof of the NLTS conjecture, showing that systems of entangled particles can remain difficult to analyze even away from extremes.

### How Do Mathematicians Know Their Proofs Are Correct?

What makes a proof stronger than a guess? What does evidence look like in the realm of mathematical abstraction? Hear the mathematician Melanie Matchett Wood explain how probability helps to guide number theorists toward certainty.

### Can Computers Be Mathematicians?

Artificial intelligence has bested humans at problem-solving challenges like chess and Go. Is mathematics research next? Steven Strogatz speaks with mathematician Kevin Buzzard to learn about the effort to translate math into language that computers understand.