[creata]

You're exaggerating the significance of HoTT. Mathematics is already on a pretty firm foundation. And I somehow doubt Bauer meant any ill intent with that line...[0][1]

[0]: https://en.wikipedia.org/wiki/Homotopy_type_theory#Special_Y...

[1]: http://math.andrej.com/2016/10/10/five-stages-of-accepting-c...