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 ...

To determine the nature of infinity, mathematicians face a choice between two new logical axioms. What they decide could help shape the future of mathematical truth From Quanta (Find original story ...

Set theory underpins modern mathematical logic by providing a unified language for defining fundamental mathematical objects and analysing their properties. At its core lies the Zermelo–Fraenkel ...

Jacob Aron says that if one of the Turing machines simulated by Adam Yedidia and Scott Aaronson halts, it would prove the set of axioms of mathematics called ZFC to be inconsistent, but mathematicians ...

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