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…