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# Elliptic curves

## Latest Articles

### Elliptic Curve ‘Murmurations’ Found With AI Take Flight

Mathematicians are working to fully explain unusual behaviors uncovered using artificial intelligence.

### The Year in Math

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

### 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.

### 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?

### 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.

### Mathematical Trio Advances Centuries-Old Number Theory Problem

The work — the first-ever limit on how many whole numbers can be written as the sum of two cubed fractions — makes significant headway on “a recurring embarrassment for number theorists.”

### A Mathematician Dancing Between Algebra and Geometry

Wei Ho, the first director of the Women and Mathematics program at the Institute for Advanced Study, combines algebra and geometry in her work on an ancient class of curves.

### ‘Post-Quantum’ Cryptography Scheme Is Cracked on a Laptop

Two researchers have broken an encryption protocol that many saw as a promising defense against the power of quantum computing.

### Mathematicians Prove 30-Year-Old André-Oort Conjecture

A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.