## Latest Articles

### New Proof Finds the ‘Ultimate Instability’ in a Solar System Model

For the first time, mathematicians have proved that planetary orbits in a solar system will always be unstable.

### Mathematicians Find Hidden Structure in a Common Type of Space

In 50 years of searching, mathematicians found only one example of a “subspace design” in a vector space. A new proof reveals that there are infinitely more out there.

### New Proof Distinguishes Mysterious and Powerful ‘Modular Forms’

Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical physics.

### Mathematicians Complete Quest to Build ‘Spherical Cubes’

Is it possible to fill space “cubically” with shapes that act like spheres? A proof at the intersection of geometry and theoretical computer science says yes.

### ‘Nasty’ Geometry Breaks Decades-Old Tiling Conjecture

Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong.

### Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations

For more than 250 years, mathematicians have wondered if the Euler equations might sometimes fail to describe a fluid’s flow. A new computer-assisted proof marks a major breakthrough in that quest.

### A Mathematician Who Fled to Freedom but Still Stares Down Doubts

Svetlana Jitomirskaya was born in Ukraine, but left the Soviet Union to escape sexism and antisemitism. Even though her work in mathematical physics has now been honored with one of the field’s top prizes, she finds herself still fighting old battles.

### Teenager Solves Stubborn Riddle About Prime Number Look-Alikes

In his senior year of high school, Daniel Larsen proved a key theorem about Carmichael numbers — strange entities that mimic the primes.

### How Mathematical Curves Enable Advanced Communication

A simple geometric idea has been used to power advances in information theory, cryptography and even blockchain technology.