Preprint in the OpenAI Math release
Hilbert’s tenth problem over the rational numbers
OpenAI
Abstract
We give a negative answer to Hilbert's tenth problem over the rational numbers: no algorithm decides whether a polynomial with integer coefficients has a rational zero. The number of variables is part of the input.
open until 1 Jan 2028
est. 50% chance this result is independently verified by the end of 2027.
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