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logic

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
Read Later

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
Read Later

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
Read Later

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

Illustration of researchers building and writing a digital library, which helps a humanoid robot do advanced math
foundations of mathematics

Building the Mathematical Library of the Future

By Kevin Hartnett
October 1, 2020
Read Later

A small community of mathematicians is using a software program called Lean to build a new digital repository. They hope it represents the future of their field.

Photo of students sitting at desks competing in the International Mathematical Olympiad
Abstractions blog

At the Math Olympiad, Computers Prepare to Go for the Gold

By Kevin Hartnett
September 21, 2020
Read Later

Computer scientists are trying to build an AI system that can win a gold medal at the world’s premier math competition.

Illustration of a robot and a human furiously doing math next to each other
artificial intelligence

How Close Are Computers to Automating Mathematical Reasoning?

By Stephen Ornes
August 27, 2020
Read Later

AI tools are shaping next-generation theorem provers, and with them the relationship between math and machine.

Micrograph of a cortical neuron, showing its many dendrites.
neuroscience

Hidden Computational Power Found in the Arms of Neurons

By Jordana Cepelewicz
January 14, 2020
Read Later

The dendritic arms of some human neurons can perform logic operations that once seemed to require whole neural networks.

Illustration of Fermat's Last Theorem
Quantized Columns

Why the Proof of Fermat’s Last Theorem Doesn’t Need to Be Enhanced

By Michael Harris
June 3, 2019
Read Later

Decades after the landmark proof of Fermat’s Last Theorem, ideas abound for how to make it even more reliable. But such efforts reflect a deep misunderstanding of what makes the proof so important.

Measuring tapes
infinity

Mathematicians Measure Infinities and Find They’re Equal

By Kevin Hartnett
September 12, 2017
Read Later

Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.


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