Mathematics

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

Knowing a little about the local connections on flight maps and other networks can reveal a lot about a system’s global structure.

A new result shows how much of the plane can be colored by points that are never exactly one unit apart.

A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures.

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

Ana Caraiani and James Newton have extended an important result in number theory to the imaginary realm.

Transcendental numbers include famous examples like e and π, but it took mathematicians centuries to understand them.

Mathematicians probe the limits of randomness in new work estimating quantities called Ramsey numbers.

A series of new papers describes how to fully characterize key dynamical systems with relatively little data.