  A proof is one of the most important concepts of mathematics. However, there
is a striking difference between how a proof is defined in theory and how it is
used in practice. This puts the unique status of mathematics as exact science
into peril. Now may be the time to reconcile theory and practice, i.e.
precision and intuition, through the advent of computer proof assistants. For
the most time this has been a topic for experts in specialized communities.
However, mathematical proofs have become increasingly sophisticated, stretching
the boundaries of what is humanly comprehensible, so that leading
mathematicians have asked for formal verification of their proofs. At the same
time, major theorems in mathematics have recently been computer-verified by
people from outside of these communities, even by beginning students. This
article investigates the gap between the different definitions of a proof and
possibilities to build bridges. It is written as a polemic or a collage by
different members of the communities in mathematics and computer science at
different stages of their careers, challenging well-known preconceptions and
exploring new perspectives.
