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proofs
The Joy of Why
Can Computers Be Mathematicians?
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.
Q&A
The Computer Scientist Who Parlays Failures Into Breakthroughs
Daniel Spielman solves important problems by thinking hard — about other questions.
computational complexity
How Computer Scientists Learned to Reinvent the Proof
Why verify every line of a proof, when just a few checks will do?
Q&A
How to Write Software With Mathematical Perfection
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
Lillian Pierce wants to transform access to the world of mathematics, while making headway on problems that bridge the discrete and continuous.
machine learning
In New Math Proofs, Artificial Intelligence Plays to Win
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
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
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
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.