In 1946, the mathematician Paul Erdős posed the unit distance problem—and suggested a winning strategy. An A.I. model has now ...

P vs. NP asks: are these two classes actually the same? If P = NP, then every “hard” problem is secretly fast to solve; we ...

Abstract: In traditional binary classification tasks, learning algorithms conventionally distinguish positive and negative samples by leveraging fully labeled training data. However, in practical ...

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The puzzle poses a deceptively simple question that boils down to: How many pairs of dots on a piece of paper can be the same distance apart?

Company says work on Paul Erdős planar unit distance problem shows advance in AI reasoning OpenAI has claimed a further advance in AI reasoning after its technology successfully tackled an 80-year-old ...

OpenAI has said that its unreleased AI reasoning model solved a decades-old mathematical problem that had remained unsolved for nearly 80 years. The model produced an original mathematical proof ...

After 80 years of fruitless struggle by human mathematicians, a major geometry conjecture has at last been solved—via a straightforward query to a chatbot. “No previous AI-generated proof has come ...

For nearly 80 years, mathematicians believed they understood the limits of a famous geometry puzzle first posed by legendary Hungarian mathematician Paul Erdős. Now, an AI model developed by OpenAI ...

OpenAI claims its new reasoning model has produced an original mathematical proof disproving a famous unsolved conjecture in geometry, which was first posed by Paul Erdős in 1946. If this sounds ...

Abstract: The existing priority-based current limiting control (CLC) for grid-forming (GFM) inverters may lead to failures in fault recovery, including being locked in CLC and mode oscillation between ...

Cold case of woman’s murder in seaside town solved after 20 years due to DNA found on cigarette butt The latest headlines from our reporters across the US sent straight to your inbox each weekday Your ...