I think the current fundamental structures are influenced by the Bourbaki group, however it has gaps. Category Theory is likely able to fill those gaps and I guess it will end up as the foundational layer of both mathematics, computer science, and pretty much everything else. David Aubin wrote about this in https://press.princeton.edu/books/hardcover/9780691118802/th... (VI.96) Some discussions too here https://math.stackexchange.com/questions/25761/introduction-....