A new paper shows how to create longer disordered strings than mathematicians had thought possible, proving that a well-known recent conjecture is “spectacularly wrong.”

Inside the symmetries of a crystal shape, a postdoctoral researcher has unearthed a counterexample to a basic conjecture about multiplicative inverses.

To the surprise of experts in the field, a postdoctoral statistician has solved one of the most important problems in high-dimensional convex geometry.

A cryptographic master tool called indistinguishability obfuscation has for years seemed too good to be true. Three researchers have figured out that it can work.

After 44 years, there’s finally a better way to find approximate solutions to the notoriously difficult traveling salesperson problem.

Three mathematicians have resolved a fundamental question about straight paths on the 12-sided Platonic solid.

Two mathematicians have proved the first leg of Paul Erdős’ all-time favorite problem about number patterns.

In his rapid ascent to the top of his field, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.

To distinguish between fundamentally different objects, mathematicians turn to invariants that encode the objects’ essential features.

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