What's up in

# algebraic geometry

## Latest Articles

### 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.

### Without a Proof, Mathematicians Wonder How Much Evidence Is Enough

A new statistical model appears to undermine long-held assumptions in number theory. How much should it be trusted when all that really matters is proof?

### Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years.

### Why Mathematicians Can’t Find the Hay in a Haystack

In math, sometimes the most common things are the hardest to find.

### Tinkertoy Models Produce New Geometric Insights

An upstart field that simplifies complex shapes is letting mathematicians understand how those shapes depend on the space in which you visualize them.