Historically we have abused the word proof to mean three different things:
- proof (human understanding of mathematical fact). A human working in the traditional way proves a mathematical statement.
- verification (mechanical checking of correctness). A computer verifies that a sequence of logical steps is correct.
- revelation (knowing something is true on authority). An oracle reveals that a given mathematical statement is true.
In the age of computers, we witnessed verification without proof. In the age of AI, we witnessed revelation without proof.
However, our institutional infrastructure is based on the assumption that these three are the same. The great question of our time is: how can we disentangle this conflation, in such a way that mathematics as a human practice continues to exist?
This thought is not mine: it is among many other observations due to Alexander Gamburd in his beautiful article on Navier–Stokes and mathematics in the age of AI.