This is an updated version of a story first published on May 5, 2024. For many high school students returning to class, it may seem like geometry and trigonometry were created by the Greeks as a form ...

An artificial-intelligence (AI) tool can rigorously prove whether geometric facts — statements about two-dimensional shapes such as triangles or polygons — are true, just as well as competitors in the ...

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 ...