Artificial intelligence has formally verified the prizewinning proof that solved the sphere packing problem in eight dimensions, a result closely tied to Maryna Viazovska’s Fields Medal. The ...

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 ...

When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to rewrite the ...

Mathematical logic, set theory, lattices and universal algebra form an interconnected framework that underpins much of modern mathematics. At its heart, mathematical logic provides rigorous formal ...

For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise. In October 2018, David Asperó was on holiday in Italy, gazing out a car ...

After an eight-year struggle, embattled Japanese mathematician Shinichi Mochizuki has finally received some validation. His 600-page proof of the abc conjecture, one of the biggest open problems in ...

Earlier this month the math world turned toward the University of Oxford, looking for signs of progress on a mystery that has gripped the community for three years. Within days it was clear that ...

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 ...

On a recent train trip from Lyon to Paris, Vladimir Voevodsky sat next to Steve Awodey and tried to convince him to change the way he does mathematics. Voevodsky, 48, is a permanent faculty member at ...