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 ...

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 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 ...

Although it has ancient roots, the meaning of infinity remains baffling, and it seems to have absolutely no bearing on everyday life. The mathematics of infinity is complex, but it isn’t simply a very ...

In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides ...