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proofs

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explainers

Alan Turing and the Power of Negative Thinking

By Ben Brubaker
September 5, 2023
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Mathematical proofs based on a technique called diagonalization can be relentlessly contrarian, but they help reveal the limits of algorithms.

Q&A

Why Mathematical Proof Is a Social Compact

By Jordana Cepelewicz
August 31, 2023
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Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.

computational complexity

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

By Ben Brubaker
August 17, 2023
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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.

Quantized Columns

How Math Achieved Transcendence

By David S. Richeson
June 27, 2023
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Transcendental numbers include famous examples like e and π, but it took mathematicians centuries to understand them.

Quantized Columns

The Colorful Problem That Has Long Frustrated Mathematicians

By David S. Richeson
March 29, 2023
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The four-color problem is simple to explain, but its complex proof continues to be both celebrated and despised.

cryptography

How Do You Prove a Secret?

By Sheon Han
October 11, 2022
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Zero-knowledge proofs allow researchers to prove their knowledge without divulging the knowledge itself.

Red particles with varying spins and some entanglement
computational complexity

Computer Science Proof Unveils Unexpected Form of Entanglement

By Mordechai Rorvig
July 18, 2022
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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.

The Joy of Why

How Do Mathematicians Know Their Proofs Are Correct?

By Steven Strogatz
July 13, 2022
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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.

Computers doing mathematics.
The Joy of Why

Can Computers Be Mathematicians?

By Steven Strogatz
June 29, 2022
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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.


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