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 ...

Some scientific discoveries matter because they reveal something new — the double helical structure of DNA, for example, or the existence of black holes. However, some revelations are profound because ...

The race is on to develop an artificial intelligence that can do pure mathematics, and top mathematicians just threw down the gauntlet with an exam of actual, unsolved problems that are relevant to ...

Since the start of the 20th century, the heart of mathematics has been the proof — a rigorous, logical argument for whether a given statement is true or false. Mathematicians’ careers are measured by ...

Mathematician Kevin Buzzard of Imperial College London is training computers how to prove one of the most famous problems in math history: Fermat’s last theorem. Resolving the problem isn’t the point.

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 ...

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 ...

It’s difficult to get computers to think like humans, so mathematicians are trying the opposite. A proposed mathematical framework forces humans to think more like machines in order to harness the ...