“relying on” is misleading here relative to what the researchers have said.

If I write a book and pass it through a spelling and polish checker, I still wrote the book and its core IP. I didn’t “rely on” the tool to create the IP.

it’s much more like you come up with the premise and someone else writes the book. the released prompts for other foundational problems (like unit distance) prove that.

The tools the researchers used though was much more than an spellchecker, because spellcheckers don't come up with chains of reasoning for the arguments in the book. The LLMs did in the case of the Navier-Stokes problem.

If this were the case the problem would not have remained unsolved for this long. A new spell checker is not what cracked the problem.