Arithmetic geometry is a vibrant field at the intersection of number theory and algebraic geometry, focussing on the study of polynomial equations and the distribution of their rational solutions.

One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...

The Collatz Conjecture is a deceptively simple math problem. It has only two rules. First, pick any number. If it's even, divide it by two. If it's odd, multiply it by three and add one. This will ...

After over three decades, five academic studies and one thousand pages, a team led by Yale Professor Sam Raskin has solved a part of what some consider math’s “Rosetta Stone.” Raskin led a nine-person ...

The artificial intelligence (AI) program DeepMind has gotten closer to proving a math conjecture that's bedeviled mathematicians for decades and revealed another new conjecture that may unravel how ...

Despite multiple conferences dedicated to explicating Mochizuki’s proof, number theorists have struggled to come to grips with its underlying ideas. His series of papers, which total more than 500 ...

We present a numerical method for finding extreme examples of identities related to the uniform abc-conjecture for algebraic number fields. Journal Information This journal, begun in 1943 as ...

This summer, as part of the Department's Summer Research Experience for Undegraduates and First-Year Graduate Students, graduate student Summer Haag, undergraduate Clyde Kertzer, postdoc James ...

A team of mathematicians has solved a math problem first posed more than 40 years ago. It took three mathematicians almost 15 years to solve the famous Rota’s Conjecture – a theory first posed by ...