## Latest Articles

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### New Math Proves That a Special Kind of Space-Time Is Unstable

Einstein’s equations describe three canonical configurations of space-time. Now one of these three — important in the study of quantum gravity — has been shown to be inherently unstable.

### Black Hole Singularities Are as Inescapable as Expected

For the first time, physicists have calculated exactly what kind of singularity lies at the center of a realistic black hole.