The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. A mathematician has now all but solved it.
Like a perpetual motion machine, a time crystal forever cycles between states without consuming energy. Physicists claim to have built this new phase of matter inside a quantum computer.
A newfound hub of immune system activity at the back of the brain solves a century-old puzzle.
In a landmark series of calculations, physicists have proved that black holes can shed information — an apparent violation of Einstein’s theory of relativity.
Physicists have reached a long-sought goal. The catch is that their room-temperature superconductor requires crushing pressures to keep from falling apart.
It took Lisa Piccirillo less than a week to answer a long-standing question about a strange knot discovered over half a century ago by the legendary John Conway.
By chopping up large numbers into smaller ones, researchers have rewritten a fundamental mathematical speed limit.
New experimental results simultaneously advance and challenge the theory that the brain’s network of neurons balances on the knife-edge between two phases.
A new proof from the Australian science fiction writer Greg Egan and a 2011 proof anonymously posted online are now being hailed as significant advances on a puzzle mathematicians have been studying for at least 25 years.
The mathematicians Günter Ziegler and Martin Aigner have spent the past 20 years collecting some of the most beautiful proofs in mathematics.
In new computer experiments, artificial-intelligence algorithms can tell the future of chaotic systems.
The Navier-Stokes equations describe simple, everyday phenomena, like water flowing from a garden hose, yet they provide a million-dollar mathematical challenge.
For centuries, mathematicians tried to solve problems by adding new values to the usual numbers. Now they’re investigating the unintended consequences of that tinkering.
By reimagining the kinks and folds of origami as atoms in a lattice, researchers are uncovering strange behavior hiding in simple structures.
Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.
A new theory explains how fragile quantum states may be able to exist for hours or even days in our warm, wet brain. Experiments should soon test the idea.
