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.

Is artificial intelligence replacing human genius in mathematics, or redefining it? From the Navier-Stokes mystery to ...

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 ...

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 ...

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Mathematicians have discovered a pattern known as the einstein tile — a single shape that can cover an infinite plane without ever repeating. Long thought impossible, the discovery rewrote what ...