## Latest Articles

### Mathematicians Crack a Simple but Stubborn Class of Equations

Ever since Archimedes, mathematicians have been fascinated by equations that involve a difference between squares. Now two mathematicians have proven how often these equations have solutions, concluding a decades-old quest.

### For His Sporting Approach to Math, a Fields Medal

With Hugo Duminil-Copin, thinking rarely happens without moving. His insights into the flow-related properties of complex networks have earned him the Fields Medal.

### He Dropped Out to Become a Poet. Now He’s Won a Fields Medal.

June Huh wasn’t interested in mathematics until a chance encounter during his sixth year of college. Now his profound insights connecting combinatorics and geometry have led to math’s highest honor.

### Graduate Student’s Side Project Proves Prime Number Conjecture

Jared Duker Lichtman, 26, has proved a longstanding conjecture relating prime numbers to a broad class of “primitive” sets. To his adviser, it came as a “complete shock.”

### Elegant Six-Page Proof Reveals the Emergence of Random Structure

Two young mathematicians have astonished their colleagues with a full proof of the Kahn-Kalai conjecture — a sweeping statement about how structure emerges in random sets and graphs.

### Deep Learning Poised to ‘Blow Up’ Famed Fluid Equations

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near.

### In Music and Math, Lillian Pierce Builds Landscapes

Lillian Pierce wants to transform access to the world of mathematics, while making headway on problems that bridge the discrete and continuous.

### Dennis Sullivan, Uniter of Topology and Chaos, Wins the Abel Prize

The American mathematician invented entire new ways to understand shapes and spaces.

### This Animal’s Behavior Is Mechanically Programmed

Biomechanical interactions, rather than neurons, control the movements of one of the simplest animals. The discovery offers a glimpse into how animal behavior worked before neurons evolved.