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 ...

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OpenAI released GPT-4o, its latest chatbot technology, in a partly finished state. It has much to prove. ChatGPT-4o trying to solve a geometry problemCredit...Arsenii Vaselenko for The New York Times ...

After cracking an unsolvable mathematics problem last year, AI is back to tackle geometry. Developed by Google DeepMind, a new algorithm, AlphaGeometry, can crush problems from past International ...

Dive into one of the most wicked geometry problems and see it explained step by step in a clear, intuitive way. This lesson breaks down the hidden structure, key insights, and clever reasoning that ...

An AI system developed by Google DeepMind, Google’s leading AI research lab, appears to have surpassed the average gold medalist in solving geometry problems in an international mathematics ...