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

The work of Alexandre Grothendieck has transformed math the way the Internet has transformed communication: Once you’re used to it, you can’t imagine what life was like before it.

This year's Abel Prize goes to mathematicians involved in group theory.