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 ...

Artificial intelligence is mastering the kinds of projects that have long helped to build the careers of young mathematicians ...

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 ...

In mid-May, OpenAI announced that an internal AI model had disproved the Erdős unit distance conjecture, a famous problem in ...

Investopedia contributors come from a range of backgrounds, and over 25 years there have been thousands of expert writers and editors who have contributed. Eric's career includes extensive work in ...

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 ...