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 ...

Can advanced mathematics decode the exotic geometries of a psychedelic trip to unlock a new science of reality?

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 ...

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 ...

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 ...

Liam Price has no formal training in mathematics and has yet to attend university, but last month, he managed to break new ground in mathematical research — with the help of ChatGPT. Posting on the ...