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New Proofs Expand the Limits of What Cannot Be Known newsthirst.

In other words, Hilbert’s 10th problem is undecidable. Mathematicians hoped to follow the same approach to prove the extended, rings-of-integers version of the problem—but they hit a snag. Gumming Up the Works The useful correspondence between Turing machines and Diophantine equations falls apart when the equations are allowed to have non-integer solutions. For instance, consider…

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U.S. lawmakers in ‘uncharted waters’ as DeepSeek tests limits of American trade restrictions newsthirst.

The DeepSeek AI application is seen on a mobile phone in this photo illustration taken in Warsaw, Poland on 27 January, 2025.  Jaap Arriens | Nurphoto | Getty Images Chinese artificial intelligence startup DeepSeek could face curbs from the U.S. government as it upends the U.S. AI ecosystem, though enforcing restrictions on an open-source technology…

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