Notes for MATH700132 (Mathematical Logic) taught by David Evans at Imperial in Spring 2025. They are a work in progress. These notes are primarily based on the content covered in lectures, with some ...

All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in general, research mathematicians don’t need to think about it ...

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 ...

Physicists present evidence that the universe is not a computer simulation. Credit: Amanclos / CC BY 2.0 / Flickr A team of physicists has presented new mathematical evidence that challenges the ...

The idea that we might be living inside a vast computer simulation, much like in The Matrix, has fascinated philosophers and scientists for years. But a new study from researchers at the University of ...

"We have demonstrated that it is impossible to describe all aspects of physical reality using a computational theory of quantum gravity," says Dr. Faizal. "Therefore, no physically complete and ...

Abstract: The paper is about formalization of Set Theory and Elementary Algebra theorems in mathematics and their proofs in a new programming language called LEAN 4 Theorem Prover. The paper describes ...

Terence Tao, one of the world’s foremost mathematicians, who is often called the “Mozart of Math,” would rather not talk politics. “I do scientific research,” Tao said. “I vote, I sign a petition, but ...

Russell has a PhD in the history of medicine, violence, and colonialism. His research has explored topics including ethics, science governance, and medical involvement in violent contexts. Russell has ...

The original version of this story appeared in Quanta Magazine. In 1994, an earthquake of a proof shook up the mathematical world. The mathematician Andrew Wiles had finally settled Fermat’s Last ...