Abstractions blog

“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.

By resolving a paradox about light in a box, researchers hope to clarify the concept of energy in quantum theory.

In 2019, the Event Horizon Telescope released a historic image of a supermassive black hole in another galaxy. The follow-up — an image of Sagittarius A* — shows it shimmering at the center of our own.

Several projects are aiming to bring back mammoths and other species that have vanished from the planet. Whether that’s technically possible is beside the point.

Throwing out data seems to make measurements of distances and angles more precise. The reason why has been traced to Heisenberg’s uncertainty principle.

The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.

Van der Waerden’s conjecture mystified mathematicians for 85 years. Its solution shows how polynomial roots relate to one another.

Cryptographers want to know which of five possible worlds we inhabit, which will reveal whether truly secure cryptography is even possible.

Language processing programs are notoriously hard to interpret, but smaller versions can provide important insights into how they work.