Latest Articles
Mathematicians Eliminate Long-Standing Threat to Knot Conjecture
A new proof shows that a knot some thought would contradict the famed slice-ribbon conjecture doesn’t.
Probability and Number Theory Collide — in a Moment
Mathematicians are taking ideas developed to study random numbers and applying them to a broad range of categories.
From Systems in Motion, Infinite Patterns Appear
Mathematicians are finding inevitable structures in sufficiently large sets of integers.
Cryptography’s Future Will Be Quantum-Safe. Here’s How It Will Work.
Lattice cryptography promises to protect secrets from the attacks of far-future quantum computers.
Mathematicians Discover the Fibonacci Numbers Hiding in Strange Spaces
Recent explorations of unique geometric worlds reveal perplexing patterns, including the Fibonacci sequence and the golden ratio.
A Numerical Mystery From the 19th Century Finally Gets Solved
Two mathematicians have proven Patterson’s conjecture, which was designed to explain a strange pattern in sums involving prime numbers.
Hypergraphs Reveal Solution to 50-Year-Old Problem
In 1973, Paul Erdős asked if it was possible to assemble sets of “triples” — three points on a graph — so that they abide by two seemingly incompatible rules. A new proof shows it can always be done.
Mathematical Connect-the-Dots Reveals How Structure Emerges
A new proof identifies precisely how large a mathematical graph must be before it contains a regular substructure.
Surfaces Beyond Imagination Are Discovered After Decades-Long Search
Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.