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proofs

computational complexity

How Computer Scientists Learned to Reinvent the Proof

By Mordechai Rorvig
May 23, 2022
Read Later

Why verify every line of a proof, when just a few checks will do?

Outdoor photo of Leslie Lamport wearing a blue shirt with his hand up to his shoulder
Q&A

How to Write Software With Mathematical Perfection

By Sheon Han
May 17, 2022
Read Later

Leslie Lamport revolutionized how computers talk to each other. Now he’s working on how engineers talk to their machines.

Q&A

In Music and Math, Lillian Pierce Builds Landscapes

By Jordana Cepelewicz
March 30, 2022
Read Later

Lillian Pierce wants to transform access to the world of mathematics, while making headway on problems that bridge the discrete and continuous.

A fictitious 8-bit video game called “counterexample quest.”
machine learning

In New Math Proofs, Artificial Intelligence Plays to Win

By Leila Sloman
March 7, 2022
Read Later

A new computer program fashioned after artificial intelligence systems like AlphaGo has solved several open problems in combinatorics and graph theory.

machine learning

Machine Learning Becomes a Mathematical Collaborator

By Kelsey Houston-Edwards
February 15, 2022
Read Later

Two recent collaborations between mathematicians and DeepMind demonstrate the potential of machine learning to help researchers generate new mathematical conjectures.

geometry

An Ancient Geometry Problem Falls to New Mathematical Techniques

By Steve Nadis
February 8, 2022
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Three mathematicians show, for the first time, how to form a square with the same area as a circle by cutting them into interchangeable pieces that can be visualized.

topology

How Tadayuki Watanabe Disproved a Major Conjecture About Spheres

By Kevin Hartnett
October 26, 2021
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Watanabe invented a new way of distinguishing shapes on his way to solving the last open case of the Smale conjecture, a central question in topology about symmetries of the sphere.

topology

New Math Book Rescues Landmark Topology Proof

By Kevin Hartnett
September 9, 2021
Read Later

Michael Freedman’s momentous 1981 proof of the four-dimensional Poincaré conjecture was on the verge of being lost. The editors of a new book are trying to save it.

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.


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