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logic

Latest Articles

foundations of mathematics

The Deep Link Equating Math Proofs and Computer Programs

By Sheon Han
October 11, 2023
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Mathematical logic and the code of computer programs are, in an exact way, mirror images of each other.

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.

set theory

Ninth Dedekind Number Found by Two Independent Groups

By Rachel Crowell
August 1, 2023
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The numbers count a variety of seemingly unrelated mathematical structures.

geometry

‘Nasty’ Geometry Breaks Decades-Old Tiling Conjecture

By Jordana Cepelewicz
December 15, 2022
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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.

Illustration of colorful flowchart using raised blocks against a black background
proofs

Proof Assistant Makes Jump to Big-League Math

By Kevin Hartnett
July 28, 2021
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Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics.

Abstractions blog

How the Slowest Computer Programs Illuminate Math’s Fundamental Limits

By John Pavlus
December 10, 2020
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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.

Black and white historical photo of eight men in front of a building, including Henri Cartan, André Weil and Szolem Mandelbrojt.
Abstractions blog

Inside the Secret Math Society Known Simply as Nicolas Bourbaki

By Kevin Hartnett
November 9, 2020
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For almost a century, the anonymous members of Nicolas Bourbaki have written books intended as pure expressions of mathematical thought.


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