Kelsey Houston-Edwards

The mathematician David Bessis claims that everyone is capable of, and can benefit greatly from, mathematical thinking.

Four mathematicians broke a 75-year-old record by finding a denser way to pack high-dimensional spheres.

Just as ice melts to water, graphs undergo phase transitions. Two mathematicians showed that they can pinpoint such transitions by examining only local structure.

Two recent collaborations between mathematicians and DeepMind demonstrate the potential of machine learning to help researchers generate new mathematical conjectures.

More than 30 years ago, Andreas Floer changed geometry. Now, two mathematicians have finally figured out how to extend his revolutionary perspective.

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them.

Originally devised as a rigorous means of counting holes, homology provides a scaffolding for mathematical ideas, allowing for a new way to analyze the shapes within data.

Fifty years ago, Paul Erdős and two other mathematicians came up with a graph theory problem that they thought they might solve on the spot. A team of mathematicians has finally settled it.

A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems.