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Two young mathematicians have astonished their colleagues with a full proof of the Kahn-Kalai conjecture — a sweeping statement about how structure emerges in random sets and graphs.

Play this simple math game with your friends to gain insights into fundamental principles of graph theory.

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.

A new result shows that quantum information can theoretically be protected from errors just as well as classical information can.

Decades ago, a mathematician posed a warmup problem for some of the most difficult questions about prime numbers. It turned out to be just as difficult to solve, until now.

By carefully constructing a multidimensional and well-connected graph, a team of researchers has finally created a long-sought locally testable code that can immediately betray whether it’s been corrupted.

Researchers are turning to the mathematics of higher-order interactions to better model the complex connections within their data.

A pair of researchers has shown that trying to classify groups of numbers called “torsion-free abelian groups” is as hard as it can possibly be.

A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections.

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