mathematical physics
At Long Last, Mathematical Proof That Black Holes Are Stable
The solutions to Einstein’s equations that describe a spinning black hole won’t blow up, even when poked or prodded.
general relativity
Mass and Angular Momentum, Left Ambiguous by Einstein, Get Defined
Surprising as it may sound, 107 years after the introduction of general relativity, the meanings of basic concepts are still being worked out.
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.