The article reconsiders the position of the foundations of mathematics after
the discovery of HoTT. Discussion that this discovery has generated in the
community of mathematicians, philosophers and computer scientists might
indicate a new crisis in the foundation of mathematics. By examining the
mathematical facts behind HoTT and their relation with the existing
foundations, we conclude that the present crisis is not one. We reiterate a
pluralist vision of the foundations of mathematics. The article contains a
short survey of the mathematical and historical background needed to understand
the main tenets of the foundational issues.Comment: Final versio