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 ...

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 ...

Here’s a simple-sounding problem: Imagine a circular fence that encloses one acre of grass. If you tie a goat to the inside of the fence, how long a rope do you need to allow the animal access to ...

Meta's work made headlines and raised a possibility once considered pure fantasy: that AI could soon outperform the world's best mathematicians by cracking math's marquee "unsolvable" problems en ...

"Even the +, −, =, and x signs we take for granted only came into widespread use in the 17th century. Which means that the earlier algebraists we know of … all had expressed their equations mostly in ...

During the 18th century the denizens of the Prussian city of Königsberg wrestled with a puzzle: How could they find a walking path through the city that crossed each of its storied seven bridges ...

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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 ...

For thousands of years, mathematicians have adapted to the latest advances in logic and reasoning. Are they ready for artificial intelligence? By Siobhan Roberts In the collection of the Getty museum ...

Mathematicians have long pondered the reach of a grazing goat tied to a fence, only finding approximate answers until now. Here’s a simple-sounding problem: Imagine a circular fence that encloses one ...