In short, the solution to Gödel’s incompleteness was computing.
(Church / Post / Turing)
Here’s the thing about this:
“Gödel’s incompleteness result is widely regarded as the most remarkable achievement of 20th century mathematics, although some mathematicians say it is logic, not math, and others call it the fundamental result of theoretical computer science (reformulated by Church & Post & Turing around 1936), a discipline that did not yet officially exist back then but was effectively created through Gödel’s work. It had enormous impact not only on computer science but also on philosophy and other fields. ”