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 ...

Brain-imaging techniques have made it possible to explore the neural foundations of logical and mathematical cognition. These techniques are revealing more than simply where these high-order processes ...

David E. Dunning explores how mathematical notation is a social, world-building technology. It’s natural to think of math as being fundamentally abstract. Whether it’s invented or discovered, its ...

Logical reasoning is a crucial skill for math success. It helps understand concepts and solve problems. This skill builds strong arguments and reduces errors. It improves problem-solving across ...