The original version of this story appeared in Quanta Magazine. In 1876, Peter Guthrie Tait set out to measure what he called the “beknottedness” of knots. The Scottish mathematician, whose research ...

The original version of this story appeared in Quanta Magazine. One July afternoon in 2024, Ryan Williams set out to prove himself wrong. Two months had passed since he’d hit upon a startling ...

One July afternoon in 2024, Ryan Williams set out to prove himself wrong. Two months had passed since he’d hit upon a startling discovery about the relationship between time and memory in computing.

Developing, deploying, and supporting artificial intelligence can be a daunting venture that calls for an often-confusing array of new skills and technologies. Yet, ostensibly, it's supposed to reduce ...

Anyone who has seen the classic rabbit-duck optical illusion knows the magic and confusion of duality. One might see a duck facing to the left with its bill hanging slightly open or a rabbit with its ...