The Greek philosopher Plato wrote about Socrates challenging a student with the "doubling the square" problem in about 385 B.C.E. When asked to double the area of a square, the student doubled 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 ...

How to safely reopen offices, schools and other public spaces while keeping people six feet apart comes down to a question mathematicians have been studying for centuries. Sphere packing might seem ...

We've wondered for centuries whether knowledge is latent and innate or learned and grasped through experience, and a new research project is asking the same question about AI. When you purchase ...