At 25, Kurt Gödel proved there can never be a mathematical “theory of everything.” Columnist Natalie Wolchover explores the implications. In 1931, by turning logic on itself, Kurt Gödel proved a pair ...

Let’s start with what’s probably the most tired, overused joke in math: A topologist is someone who can’t tell a coffee cup from a doughnut. Both, you see, have a hole in them. Topology is usually ...

A week after OpenAI made headlines with an A.I.-generated proof, a new “declaration” by 16 experts raises concerns that the ...

By encoding mathematical statements into numbers, mathematician Kurt Gödel used ordinary arithmetic to check whether a ...

A new collaboration, publication, and conversation illuminate how a new theory of reality based on consciousness will enable scientific study of the human psychedelic experience.

Mathematician Will Sawin discusses his experience reviewing and refining a mathematical proof devised by OpenAI's internal ...

Psychedelic drug experiences are among the most fascinating but mysterious journeys of the human mind. Long the domain of ...

A statement can be true or false. But as Kurt Gödel demonstrated, there will always be mathematical assumptions that can ...

Artificial intelligence built by OpenAI has cracked a decades-old conjecture by Paul Erdős, which mathematicians have hailed ...

Most people wouldn't think that it would take rigorous mathematical proof to show how many folds it takes to make a donut shape out of paper. Yet, no one could quite figure it out until recently. How ...

The 10th European Set Theory Conference continues a series that began in 2007. Since its first edition, the European Set Theory Conference has been a key venue for advancing research in the field ...

INSTEAD of merely revising his former treatise, Prof. Love has written a new one; the result is that we have two works by the same author, in some ways contrasting, in others complementary. And as in ...