Diophantine equations: a systematic approach

By combining computer assistance with human reasoning, we have solved the Hilbert's tenth problem for all polynomial Diophantine equations of size at most $28$, where the size is defined in (Zidane, 2018). In addition, we have solved this problem for all two-variable Diophantine equations of size at most $31$, all symmetric equations of size at most $36$, and all three-monomial equations of size at most $45$. In each category, we identified the smallest equations for which the Hilbert's tenth problem remains open. This answers the question asked in (Zidane, 2018).