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# Mathematics

## Latest Articles

### 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.

### 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.

### The Hidden Connection That Changed Number Theory

Quadratic reciprocity lurks around many corners in mathematics. By proving it, number theorists reimagined their whole field.

### A Brief History of Tricky Mathematical Tiling

The discovery earlier this year of the “hat” tile marked the culmination of hundreds of years of work into tiles and their symmetries.

### A New Generation of Mathematicians Pushes Prime Number Barriers

New work attacks a long-standing barrier to understanding how prime numbers are distributed.

### The Mathematician Who Sculpted the Shape of Space

Eugenio Calabi, who died on September 25, conceived of novel geometric objects that later became fundamental to string theory.

### Echoes of Electromagnetism Found in Number Theory

A new magnum opus posits the existence of a hidden mathematical link akin to the connection between electricity and magnetism.

### The Deep Link Equating Math Proofs and Computer Programs

Mathematical logic and the code of computer programs are, in an exact way, mirror images of each other.

### How Simple Math Moves the Needle

The spatial intuition behind a three-point turn offers an on-ramp to a century-old geometry problem.