OpenAI claims its model solved a famous geometry problem that has eluded the world’s greatest mathematicians for 80 years — a breakthrough hailed as evidence of the bot’s creativity and “intuition.” ...

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 ...

Artificial intelligence is mastering the kinds of projects that have long helped to build the careers of young mathematicians. What does that mean for their future? Credit...Illustrations by Yoshi ...