Some mathematical statements feel undeniably true the moment you hear them. Yet proving them can be impossible. This theorem has convinced generations of mathematicians without ever yielding a formal ...

Since the start of the 20th century, the heart of mathematics has been the proof — a rigorous, logical argument for whether a given statement is true or false. Mathematicians’ careers are measured by ...

A mathematician will turn a groundbreaking 100-page proof into computer code. The proof tool, Lean, lets users turn proofs written in prose into rules and logic for testing. Kevin Buzzard already uses ...

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 ...

IT is recorded that when a pupil asked Confucius what he would do first if he had absolute power, the Master replied “I should reform language”. (The development of the theme in the text of the ...

THE HISTORY Of computers is often told as a history of objects, from the abacus to the Babbage engine up through the code-breaking machines of World War II. In fact, it is better understood as a ...

To determine the nature of infinity, mathematicians face a choice between two new logical axioms. What they decide could help shape the future of mathematical truth. In the course of exploring their ...

I consider the idea of a propositional logic of location based on the following semantic framework, derived from ideas of Prior. We have a collection L of the locations and a collection S of ...

Ever stared at a math problem feeling completely lost, even when you've memorised all the formulas? Or maybe you've wondered why certain math rules even exist? The true secret weapon that unlocks ...