The world may seem orderly, but randomness and chaos shape everything in the universe, from enormous galaxies all the way down to subatomic particles. Take a chilly window sheeting over with ice: even ...

When Hannah Cairo was 17 years old, she disproved the Mizohata-Takeuchi conjecture, a long-standing guess in the field of harmonic analysis about how waves behave on curved surfaces. The conjecture ...

Mathematicians thought they were on the cusp of proving a conjecture about the ancient structures known as Apollonian circles. But a summer project would lead to its downfall. Summer Haag and Clyde ...

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 ...

A pair of mathematicians has solved the first chunk of one of the most famous conjectures about the additive properties of whole numbers. Proposed more than 60 years ago by the legendary Hungarian ...

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 ...

Two mathematicians have proven Patterson’s conjecture, which was designed to explain a strange pattern in sums involving prime numbers. In the early 1950s, a group of researchers at the Institute for ...

Using a limited set of mathematical equations, a mathematical sciences professor said he has confirmed a 224-year-old math conjecture about the origins of our solar system, providing insights about ...