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# number theory

## Latest Articles

### 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 Hidden Connection That Changed Number Theory

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

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

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

### 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.

### Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math

Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?

### A Tower of Conjectures That Rests Upon a Needle

On its surface, the Kakeya conjecture is a simple statement about rotating needles. But it underlies a wealth of mathematics.

### Why Mathematical Proof Is a Social Compact

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.

### Two Students Unravel a Widely Believed Math Conjecture

Mathematicians thought they were on the cusp of proving a conjecture about the ancient structures known as Apollonian circles. But a summer project would lead to its downfall.

### Elliptic Curves Yield Their Secrets in a New Number System

Ana Caraiani and James Newton have extended an important result in number theory to the imaginary realm.