Every now and again, a tardy student writes down an impossible to solve problem and solves it because he thought it was just homework.

> Every now and again

As far as I can tell, this has only happened once, in 1939 [1].

[1]: https://www.snopes.com/fact-check/the-unsolvable-math-proble...

Depends what you mean by advance. If nobody but those few hundred mathematicians was even aware of mathematics then what would be the point?