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.
number theory
Mathematicians Open a New Front on an Ancient Number Problem
For millennia, mathematicians have wondered whether odd perfect numbers exist, establishing an extraordinary list of restrictions for the hypothetical objects in the process. Insight on this question could come from studying the next best things.
Q&A
He Found ‘Islands of Fertility’ Beneath Antarctica’s Ice
John Priscu’s search for life that thrives under ice took him to subglacial lakes at the South Pole. Now he has his eye on Mars and Europa.