Leila Sloman

A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.”

High-dimensional spheres can have a much wider variety of structures than mathematicians thought possible.

A new paper establishes a long-conjectured bound about the size of the overlap between sets of lines and points.

A new proof breaks a decades-long drought of progress on the problem of estimating the size of triangles created by cramming points into a square.

The proof establishes new conditions that cause connected oscillators to sway in sync.

Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big?

Four mathematicians have found a new upper limit to the “Ramsey number,” a crucial property describing unavoidable structure in graphs.

For decades, mathematicians have been inching forward on a problem about which sets contain evenly spaced patterns of three numbers. Last month, two computer scientists blew past all of those results.

In a recent paper, two mathematicians showed that a particular pattern is unavoidable when fractions are categorized.