Geometry

Eric Larson and Isabel Vogt have solved the interpolation problem — a centuries-old question about some of the most basic objects in geometry. Some credit goes to the chalkboard in their living room.

The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true.

June Huh wasn’t interested in mathematics until a chance encounter during his sixth year of college. Now his profound insights connecting combinatorics and geometry have led to math’s highest honor.

With her homeland mired in war, the sphere-packing number theorist Maryna Viazovska has become the second woman to win a Fields Medal in the award’s 86-year history.

The quest to solve cubic equations led to duels, betrayals — and modern mathematics.

For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them.

Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.

The result could help researchers answer a larger question about flattening objects from the fourth dimension to the third dimension.

Three mathematicians show, for the first time, how to form a square with the same area as a circle by cutting them into interchangeable pieces that can be visualized.