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# mathematics

## Latest Articles

### A Close-Up View Reveals the ‘Melting’ Point of an Infinite Graph

Just as ice melts to water, graphs undergo phase transitions. Two mathematicians showed that they can pinpoint such transitions by examining only local structure.

### A Triplet Tree Forms One of the Most Beautiful Structures in Math

The Markov numbers reveal the secrets of irrational numbers and the patterns of the Fibonacci sequence. But there’s one question about them that has resisted proof for over a century.

### ‘A-Team’ of Math Proves a Critical Link Between Addition and Sets

A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.”

### An Easy-Sounding Problem Yields Numbers Too Big for Our Universe

Researchers prove that navigating certain systems of vectors is among the most complex computational problems.

### A Century Later, New Math Smooths Out General Relativity

Mathematicians prove a theorem that illuminates the geometry of universes with tiny amounts of mass.

### Pierre de Fermat’s Link to a High School Student’s Prime Math Proof

How Fermat’s less famous “little theorem” got mathematicians young and old to play with prime-like Carmichael numbers.

### The Astonishing Behavior of Recursive Sequences

Some strange mathematical sequences are always whole numbers — until they’re not. The puzzling patterns have revealed ties to graph theory and prime numbers, awing mathematicians.

### Why the Human Brain Perceives Small Numbers Better

The discovery that the brain has different systems for representing small and large numbers provokes new questions about memory, attention and mathematics.

### In the ‘Wild West’ of Geometry, Mathematicians Redefine the Sphere

High-dimensional spheres can have a much wider variety of structures than mathematicians thought possible.