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New Proof Shows That ‘Expander’ Graphs Synchronize
The proof establishes new conditions that cause connected oscillators to sway in sync.
Math That Lets You Think Locally but Act Globally
Knowing a little about the local connections on flight maps and other networks can reveal a lot about a system’s global structure.
Mathematicians Solve Long-Standing Coloring Problem
A new result shows how much of the plane can be colored by points that are never exactly one unit apart.
How to Build a Big Prime Number
A new algorithm brings together the advantages of randomness and deterministic processes to reliably construct large prime numbers.
New Proof Threads the Needle on a Sticky Geometry Problem
A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures.
The Lawlessness of Large Numbers
Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big?
Elliptic Curves Yield Their Secrets in a New Number System
Ana Caraiani and James Newton have extended an important result in number theory to the imaginary realm.
How Math Achieved Transcendence
Transcendental numbers include famous examples like e and π, but it took mathematicians centuries to understand them.
Computer Scientists Inch Closer to Major Algorithmic Goal
A new paper finds a faster method for determining when two mathematical groups are the same.