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Computer-assisted proofs

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With Fifth Busy Beaver, Researchers Approach Computation’s Limits

July 2, 2024

After decades of uncertainty, a motley team of programmers has proved precisely how complicated simple computer programs can get.

‘A-Team’ of Math Proves a Critical Link Between Addition and Sets

December 6, 2023

A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.”

The Deep Link Equating Math Proofs and Computer Programs

October 11, 2023

Mathematical logic and the code of computer programs are, in an exact way, mirror images of each other.

Q&A

Why Mathematical Proof Is a Social Compact

August 31, 2023

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.

The Number 15 Describes the Secret Limit of an Infinite Grid

April 20, 2023

The “packing coloring” problem asks how many numbers are needed to fill an infinite grid so that identical numbers never get too close to one another. A new computer-assisted proof finds a surprisingly straightforward answer.

The Colorful Problem That Has Long Frustrated Mathematicians

March 29, 2023

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

Proof Assistant Makes Jump to Big-League Math

July 28, 2021

Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics.

Building the Mathematical Library of the Future

October 1, 2020

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.

How Close Are Computers to Automating Mathematical Reasoning?

August 27, 2020

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

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