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# Number theory

## Latest Articles

### The Year in Math

Landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.

### 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.

### 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.