The following are two closely related questions.
What was Bourbaki's position on the ontological status of mathematical objects? Were they some kind of Realist/Platonist or were they Formalist?
Dieudonne, a Bourbaki, provides a confusing answer stating that they "act" like realists. It is unclear whether they actually adhere to that position. Is the realist position, or some variant, Bourbaki's philosophical position?
Furthermore, Pierre Deligne a major successor of the school claims that he uses the Axiom of Choice for convenience but does not believe in it. What does he mean by that statement? For example, does it mean to reject certain results based on AC like the embedding of the p-adic field onto the complex plane because they are counterintuitive? Are there any sources where he elaborates this position? Does this imply that he is not a Realist/Platonist?
I hope my questions make sense. Thank you so much.