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

Abstract: This letter presents an output feedback approach to distributed optimal formation control of linear time-invariant multiagent systems. The formation control problem is formulated as a ...

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 ...

For nearly 80 years, mathematicians have struggled to solve a classic geometry puzzle first posed by Paul Erdős in 1946: the ...

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 ...

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 ...

We examine how AI is changing the future of work — and how, in many ways, that future is already here. While the age of sentient robot assistants isn't quite here yet, AI is fast making a bid to be ...

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 ...

In a world where scientific breakthroughs often bring fame, wealth, and global recognition, Grigori Perelman chose a completely different path. The Russian mathematician stunned the academic world ...