The question is too vague -- what you mean by 'innate ideas' needs further specification -- presumably, you mean to question whether the innateness is 'scientifically proven', and not to question whether those ideas which are by some imputed to be innate, are themselves 'scientifically proven'.
Some behaviors evidently require ideation, and some of those have been shown to not require post-natal learning, but that's a fairly narrowly-focused remark.
Perhaps if you try to formulate some claim that's specific enough to be testable, you can find out about how similar ideas have fared when subjected to scientific method.
Innate meaning, i think, born with: we are born with certain reflexes.
The question is are we born with certain abstract ideas rigth or wrong such as, but not necessarely that one, geometric shapes.
An experiment to prove an innate idea? That was my question: has it been attempted? Succesfuly?
One can imagine showing images to babies as soon as they can see and recording their reaction etc...