In ancient Greece, Euclid showed that if you agree on a small list of preliminary principles, or axioms, you can use deductive reasoning to reveal all sorts of new mathematical truths. But although ...

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

Computers are extremely good with numbers, but they haven’t gotten many human mathematicians fired. Until recently, they could barely hold their own in high school-level math competitions. But now ...

Yesterday I was doing some literature review for an article I’m writing about my inverted transition-to-proof class, and I got around to reading a paper by Guershon Harel and Larry Sowder¹ about ...

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

Discrete mathematics is about precision in reasoning as much as it is about solving problems. Proof techniques like induction, contradiction, and direct reasoning are used to establish results in ...