At sea, biologists discovered microbial partners that together produce nitrogen, a nutrient essential for life. The pair are in the process of merging into a single organism.

The proof creates stricter limits on potential exceptions to the famous Riemann hypothesis.

Physicists have ruled out a mundane explanation for the strange findings of an old Soviet experiment, leaving open the possibility that the results point to a new fundamental particle.

Number theorist Ken Ono is teaching Olympians to swim more efficiently.

Neural networks and other forms of machine learning ultimately learn by trial and error, one improvement at a time.

If you cover a surface with tiles, repetitive patterns always emerge — or do they? In this week’s episode, mathematician Natalie Priebe Frank and co-host Janna Levin discuss how recent breakthroughs in tiling can unlock structural secrets in the natural world.

After decades of uncertainty, a motley team of programmers has proved precisely how complicated simple computer programs can get.

Susan Clark is helping to unravel the mysterious workings of the Milky Way’s magnetic field, a critical missing piece of the galactic puzzle.

Two mathematicians have proved a long-standing conjecture that is a step on the way toward finding the worst shape for packing the plane.