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 ...

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 ...

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 ...

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.

The big thinkers at Aperture explore infinity and the different ways it appears in mathematics and physics. Suspected ...

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 ...