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.
Q&A
The Mathematician Who Delights in Building Bridges
Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.
set theory
Mathematicians Solve Decades-Old Classification Problem
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.
Q&A
A Number Theorist Who Connects Math to Other Creative Pursuits
Jordan Ellenberg enjoys studying — and writing about — the mathematics underlying everyday phenomena.
mathematical physics
New Black Hole Math Closes Cosmic Blind Spot
A mathematical shortcut for analyzing black hole collisions works even in cases where it shouldn’t. As astronomers use it to search for new classes of hidden black holes, others wonder: Why?
graph theory
New Proof Reveals That Graphs With No Pentagons Are Fundamentally Different
Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon.
prime numbers
Mathematicians Find a New Class of Digitally Delicate Primes
Despite finding no specific examples, researchers have proved the existence of a pervasive kind of prime number so delicate that changing any of its infinite digits renders it composite.
geometry
After Centuries, a Seemingly Simple Math Problem Gets an Exact Solution
Mathematicians have long pondered the reach of a grazing goat tied to a fence, only finding approximate answers until now.
Q&A
A Scientist Who Delights in the Mundane
From crumpled paper to termite mounds to three-sided coins, L. Mahadevan has turned the whole world into his laboratory.