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.

Two professional poker players will take on a computer, and this year the computer could win.

MATH TREK: The mathematicians thought they'd just extended a fundamental result in algebra, but it turns out that they'd also proven a conjecture in astrophysics.

A new approach to network theory focusing on the subcommunities within networks may shed light on everything from food webs to terrorist cells. It may even act as an oracle, helping scientists identify connections within a network they haven’t yet seen.

Deep inside our cells, the DNA that encodes the mysteries of our individuality twines into tidy little spiral staircases neatly side by side — or so we might imagine. Consider, though, that if you scale up the nucleus of a cell to the size of a basketball, each molecule of DNA inside it would resemble fishing line more than four miles long. And now consider what happens to your iPod headphones when you cram them into a pocket: Invariably, it seems, they tangle. And they’re only a foot long! Now you have a picture of the gargantuan task your cells face in managing the ...

Mathematicians discover a Klein bottle hidden within the data underlying photographs