The original version of this story appeared in Quanta Magazine. In 2003, a German graduate student named Britta Späth encountered the McKay conjecture, one of the biggest open problems in the ...

All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in general, research mathematicians don’t need to think about it ...

AlphaProof and AlphaGeometry 2 are steps toward building systems that can reason, which could unlock exciting new capabilities. AI models can easily generate essays and other types of text. However, ...

Set theory, the mathematical study of collections of objects, forms a foundation for much of modern mathematics, while cardinal functions provide a means to quantify the sizes of these sets, ...

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...