Here’s the rule: To assure cards get sufficiently mixed up, shuffle a deck about seven times. Mathematician, magician and card shark Persi Diaconis of Stanford University, along with David Bayer of Columbia University, created shock waves in Las Vegas when he figured that out back in 1992. Most dealers had been shuffling much less. But now Diaconis and his colleagues are issuing an update. When dealing many gambling games, like blackjack, about four shuffles are enough. The reason for the lower number is that many games require randomness for only a few specific aspects of the cards, not al...

New techniques are beginning to unravel the mysteries of knots, revealing a great mathematical superstructure in the process.

In the 1980s, an inkling emerged among some scientists that very disparate phenomena might on some deep level be related. The weather, protein folding, computers, evolution, the stock market, the immune system … each shows complex behavior arising from fairly simple interactions among its parts. For the past 20 years, researchers have labored to understand how these and other “complex systems” work. But there’s still no agreement about even the most basic of questions: What is a complex system? The frustration of this enduring question has led one researcher to a ...

The U.S. News & World Report rankings of colleges and universities are largely arbitrary, according to a new mathematical analysis.

Featured Math Trek column: The Great Internet Mersenne Prime Search, a cooperative computing project, helps find a prime that has nearly 13 million digits.

The mathematics of dynamical systems reveals ocean dynamics, an understanding that could improve the monitoring of ocean processes.

The Great Internet Mersenne Prime Search, a cooperative computing project, helps find a prime that has nearly 13 million digits.

Imagine twisting a beam of light into a knot, as if it were a piece of a string. Now grab another light beam and tie it around the first, forming its own loop. Tie on another and another, until all of space is filled up with loops of light. Sounds preposterous, but a pair of physicists has shown that light can do just this — at least in theory. Visible light, along with all other forms of electromagnetic radiation, is governed by Maxwell’s equations, and the researchers have found a new solution to these equations in which light forms linked knots. The team is now working to...

Mathematicians create videos that help in visualizing four-dimensional objects.

Math Trek: If we have free will, so do subatomic particles, mathematicians claim to prove.

Quasicrystals are bizarre, rare, mysterious materials blending mathematical order and irregularity. A new, unexpected material halfway between a regular crystal and a quasicrystal may help reveal their secrets.

Math Trek: The National Aquatics Center in Beijing, newly built for the Olympics, is a glowing cube of bubbles. The mathematics behind it are built around Lord Kelvin's tetrakaidecahedra and the physics of foam.