Large language models (LLMs), artificial intelligence (AI) systems that can process and generate texts in various languages, ...

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 ...

Here's a basic example using the statement, "This true statement is not provable." If it were provable, it would be false, making logic inconsistent. If it's not provable, then it's true, but that ...

President Donald Trump keeps making a mathematically impossible promise. At event after event this month and last, Trump has declared that the “most favored nation” policy he unveiled in an executive ...

In mathematics, some theorems seem self‑evident yet remain unproven. Explore the story of the “obviously true” statement that has baffled experts for decades. 'No idea what you have unleashed': ...

High schoolers’ reading and math scores dropped to the lowest level in decades, along with declines in science scores from eighth graders, according to the National Assessment of Education Progress ...

TOPEKA, Kan. (WIBW) - Kansas Senate Democratic Leader Dinah Sykes released a statement Saturday, Aug 10, in response to calls for Congressional Redistricting in Kansas. “Every ten years, the Kansas ...

The original version of this story appeared in Quanta Magazine. At the turn of the 20th century, the renowned mathematician David Hilbert had a grand ambition to bring a more rigorous, mathematical ...