But the bigger point is how foundational these stories are to how we narrate struggle and resilience. Middle school teaches ...

If you want to disagree “most vehemently and logically,” this is the clean core: 1. The new structure explicitly shields low ...

A 2,000-year-old loom found in a Chinese tomb may hold the key to the origins of computing.

You’d be surprised how many young people can’t read this. One of its conclusions tells the sad tale. “Between 2020 and 2025, the number of students whose math skills fall below high school level has ...

Hallucination is fundamental to how transformer-based language models work. In fact, it’s their greatest asset: this is the method by which language models find links between sometimes disparate ...

When engineers build AI language models like GPT-5 from training data, at least two major processing features emerge: memorization (reciting exact text they’ve seen before, like famous quotes or ...

Given the importance of recursion in modern linguistics, there ought to be much to commend in Watumull et al.'s (2014) attempt to clarify what recursion is (or ought to be); I have trudged this very ...

The original version of this story appeared in Quanta Magazine. In 1974, five years before he wrote his Pulitzer Prize–winning book Gödel, Escher, Bach: An Eternal Golden Braid, Douglas Hofstadter was ...

They used powerful mathematical theorems—including Gödel's incompleteness theorem—to prove that a complete and consistent description of everything requires what they call "non-algorithmic ...

Once a century, a very special day comes along. That day is today — 9/16/25. Pi Day (3/14) often comes with sweet treats; Square Root Day (4/4/16 or 5/5/25, for example) has a certain numerical rhyme.

In his decades-long career in tech journalism, Dennis has written about nearly every type of hardware and software. He was a founding editor of Ziff Davis’ Computer Select in the 1990s, senior ...