Zermelo-Fraenkel set theory is so widely accepted that modern mathematicians hardly think about it. But believing in its core ...

Discrete mathematics gets easier when you know how to approach proofs. Direct reasoning, induction, and contradiction each have specific steps that can be learned and practiced. Pairing these methods ...

GPT-5.4 Pro cracked a conjecture in number theory that had stumped generations of mathematicians, using a proof strategy that ...

The Langlands program has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore One of the biggest stories in science has been ...

The one source of truth is mathematics. Every statement is a pure logical deduction from foundational axioms, resulting in absolute certainty. Since Andrew Wiles proved Fermat’s Last Theorem, you’d be ...

Peter Scholze wants to rebuild much of modern mathematics, starting from one of its cornerstones. Now, he has received validation for a proof at the heart of his quest from an unlikely source: a ...

"We have demonstrated that it is impossible to describe all aspects of physical reality using a computational theory of quantum gravity," says Dr. Faizal. "Therefore, no physically complete and ...

To introduce the students to the general theory of sets, as a foundational and as an axiomatic theory. The aim is to make the course of general interest to students who are not planning to specialize ...