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 ...

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 ...

What patterns can be observed among the mathematical arguments above-average students find convincing and the strategies these students use to learn new mathematical concepts? To investigate this ...

Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach. In 2012, the mathematician Shinichi Mochizuki claimed he had solved the abc conjecture ...

A Japanese mathematician claims to have solved one of the most important problems in his field. The trouble is, hardly anyone can work out whether he's right. Sometime on the morning of 30 August 2012 ...

In 1931, the Austrian logician Kurt Gödel pulled off arguably one of the most stunning intellectual achievements in history. Mathematicians of the era sought a solid foundation for mathematics: a set ...

The next number has to be 32, right? The pattern is clear: To find the next number, double the current one. We have 1 × 2 = 2; 2 × 2 = 4; 4 × 2 = 8; 8 × 2 = 16. The next number should be 16 × 2 = 32.

One of the most famous unsolved problems in mathematics likely remains unsolved. At a hotly-anticipated talk at the Heidelberg Laureate Forum today, retired mathematician Michael Atiyah delivered what ...

Thomas Jefferson’s first draft of the Declaration of Independence read: “We hold these truths to be sacred and undeniable . . . ” It was supposedly Benjamin Franklin who suggested instead announcing ...