For four decades, a quiet boundary in pure mathematics kept a powerful theorem locked inside the safe world of finite quantities. Now a new result known as Sebestyen’s theorem has pushed that boundary ...

At the University of Vaasa in Finland, mathematician Yosra Barkaoui has successfully generalized a fundamental theorem that had remained confined to “bounded” systems for more than 40 years.

For centuries, the concept of infinity has captivated mathematicians and philosophers alike, stretching far beyond the simple idea of endless counting. Recent groundbreaking discoveries, however, have ...

When mathematician Georg Cantor first glimpsed the true nature of infinity, it changed mathematics forever. He demonstrated that infinity isn’t just endless—it exists in different sizes, each opening ...

The original version of this story appeared in Quanta Magazine. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in ...

The “ultrafinitists” who seek to abolish the use of infinity in mathematics reminded me of the influential Dutch mathematician L. E. J. Brouwer, renowned for proving Brouwer’s fixed-point theorem. He ...

India has a rich ancient history of great achievements in mathematics which has been disseminated in the world and has led different civilisations. Since Indian mathematicians came up with the ...

Mathematics is, at its core, an art. Like painters, musicians or writers, mathematicians create and explore new worlds. They test, and then push past, the limits of their imagination. They engage with ...