Latest Articles
From Systems in Motion, Infinite Patterns Appear
Mathematicians are finding inevitable structures in sufficiently large sets of integers.
How Cryptography’s Quantum-Safe Future 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.
Unimaginable Surfaces Discovered After Decades-Long Search
Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.
How Complex Is a Knot? New Proof Reveals Ranking System That Works.
“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.
Mathematicians Coax Fluid Equations Into Nonphysical Solutions
The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.