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 ...

But now, two mathematician friends have used their quarantine time to crack a variation of the age-old geometry problem. They analyzed a set of loopy shapes called smooth, continuous curves to prove ...

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 ...

Long before robots could run or cars could drive themselves, mathematicians contemplated a simple mathematical question. They figured it out, then laid it to rest—with no way of knowing that the ...

DeepMind, the Google AI R&D lab, believes that the key to more capable AI systems might lie in uncovering new ways to solve challenging geometry problems. To that end, DeepMind today unveiled ...

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The study of condition numbers and perturbation analysis in least squares problems has become a cornerstone in numerical linear algebra, underpinning the reliability and accuracy of solutions to ...