What's up in

# algebraic geometry

## Latest Articles

### A Mathematician’s Unanticipated Journey Through the Physical World

Lauren Williams has charted an adventurous mathematical career out of the pieces of a fundamental object called the positive Grassmannian.

### Conducting the Mathematical Orchestra From the Middle

Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.

### Mathematicians Will Never Stop Proving the Prime Number Theorem

Why do mathematicians enjoy proving the same results in different ways?

### The Map of Mathematics

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

### Mathematicians Cut Apart Shapes to Find Pieces of Equations

New work on the problem of “scissors congruence” explains when it’s possible to slice up one shape and reassemble it as another.

### With Category Theory, Mathematics Escapes From Equality

Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.

### Big Question About Primes Proved in Small Number Systems

The twin primes conjecture is one of the most important and difficult questions in mathematics. Two mathematicians have solved a parallel version of the problem for small number systems.

### A Movement to Close the Gender Gap in Mathematics

The Brazilian mathematician Carolina Araujo, who calls herself “a bit of an anarchist,” is organizing meetings and building a support network to study and solve the problems women face in mathematics.

### New Proof Shows Infinite Curves Come in Two Types

Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.