Computability

Ultrafinitism, a philosophy that rejects the infinite, has long been dismissed as mathematical heresy. But it is also producing new insights in math and beyond.

With a newly discovered mathematical tool, researchers are hoping to gain unprecedented insight into the structure of complex knots.

The quest to find the longest-running simple computer program has identified a new champion. It’s physically impossible to write out the numbers involved using standard mathematical notation.

In math and computer science, researchers have long understood that some questions are fundamentally unanswerable. Now physicists are exploring how even ordinary physical systems put hard limits on what we can predict, even in principle.

By proving a broader version of Hilbert’s famous 10th problem, two groups of mathematicians have expanded the realm of mathematical unknowability.

Researchers got a better look at the thoughts of chatbots, amateurs learned exactly how complicated simple systems can be, and quantum computers passed an essential milestone.

You don’t need 0s and 1s to perform computations, and in some cases it’s better to avoid them.

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

Two mathematicians have shown that origami can, in principle, be used to perform any possible computation.