For ages, countless mathematicians have advanced mathematics through proofs. This is because proof is a key tool for developing new theories and solving problems. That’s why a discussion about proofs ...

Paul Erdős, the famously eccentric, peripatetic and prolific 20th-century mathematician, was fond of the idea that God has a celestial volume containing the perfect proof of every mathematical theorem ...

The process of proofs and refutations described by Lakatos is essential in school mathematics to provide students with an opportunity to experience how mathematical knowledge develops dynamically ...

Educational Studies in Mathematics, Vol. 94, No. 1 (January 2017), pp. 37-54 (18 pages) This paper reports the results of an international comparative study on the nature of proof to be taught in ...

Every day, dozens of like-minded mathematicians gather on an online forum called Zulip to build what they believe is the future of their field. They’re all devotees of a software program called Lean.

Every day, dozens of like-minded mathematicians gather on an online forum called Zulip to build what they believe is the future of their field. They’re all devotees of a software program called Lean.

What makes a proof stronger than a guess? What does evidence look like in the realm of mathematical abstraction? Hear the mathematician Melanie Matchett Wood explain how probability helps to guide ...

Two years ago, a couple of high school classmates each composed a mathematical marvel, a trigonometric proof of the Pythagorean theorem. Now, they’re unveiling 10 more. For over 2,000 years, such ...

Forbes contributors publish independent expert analyses and insights. Dr. Lance B. Eliot is a world-renowned AI scientist and consultant. In today’s column, I examine an insightful AI research study ...