combinatorics
Mathematician Hurls Structure and Disorder Into Century-Old Problem
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.”
group theory
Mathematician Disproves 80-Year-Old Algebra Conjecture
Inside the symmetries of a crystal shape, a postdoctoral researcher has unearthed a counterexample to a basic conjecture about multiplicative inverses.
geometry
Statistics Postdoc Tames Decades-Old Geometry Problem
To the surprise of experts in the field, a postdoctoral statistician has solved one of the most important problems in high-dimensional convex geometry.
computer security
Computer Scientists Achieve ‘Crown Jewel’ of Cryptography
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.
algorithms
Computer Scientists Break Traveling Salesperson Record
After 44 years, there’s finally a better way to find approximate solutions to the notoriously difficult traveling salesperson problem.
Abstractions blog
Mathematicians Report New Discovery About the Dodecahedron
Three mathematicians have resolved a fundamental question about straight paths on the 12-sided Platonic solid.
number theory
Landmark Math Proof Clears Hurdle in Top Erdős Conjecture
Two mathematicians have proved the first leg of Paul Erdős’ all-time favorite problem about number patterns.
profiles
A Number Theorist Who Solves the Hardest Easy Problems
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.
Abstractions blog
In a Single Measure, Invariants Capture the Essence of Math Objects
To distinguish between fundamentally different objects, mathematicians turn to invariants that encode the objects’ essential features.