Mathematical logic and set theory provide the foundational language for modern mathematics, articulating precise notions of proof, computability and the hierarchy of infinities. Central themes include ...

Zermelo-Fraenkel set theory is so widely accepted that modern mathematicians hardly think about it. But believing in its core principles didn’t come easily. How do mathematicians decide that something ...

Descriptive set theory examines the structure and classification of definable sets within topological spaces, with a particular focus on Polish spaces—those that are separable and completely ...

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

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

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 ...

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

Health and Human Services Secretary Robert F. Kennedy Jr. told a Senate Finance Committee hearing on 22 April 2026 that President Donald Trump uses a 'different way' of calculating drug price ...

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 ...

Physicists are making new inroads into the world of post-quantum theories, uncovering what reality may look like on a level deeper and stranger than the already infamously odd quantum theory. In the ...