The original version of this story appeared in Quanta Magazine. Nearly a century ago, the physicist Erwin Schrödinger called attention to a quirk of the quantum world that has fascinated and vexed researchers ever since. When quantum particles such as atoms interact, they shed their individual identities in favor of …

The original version of this story appeared in Quanta Magazine. Say you want to send a private message, cast a secret vote, or sign a document securely. If you do any of these tasks on a computer, you’re relying on encryption to keep your data safe. That encryption needs to …

The original version of this story appeared in Quanta Magazine. If you want to tile a bathroom floor, square tiles are the simplest option—they fit together without any gaps in a grid pattern that can continue indefinitely. That square grid has a property shared by many other tilings: Shift the …

The original version of this story appeared in Quanta Magazine. Algorithms have become ubiquitous. They optimize our commutes, process payments, and coordinate the flow of internet traffic. It seems that for every problem that can be articulated in precise mathematical terms, there’s an algorithm that can solve it, at least …