  AlphaZero learns to play go, chess and shogi at a superhuman level through
self play given only the rules of the game. This raises the question of whether
a similar thing could be done for mathematics -- a MathZero. MathZero would
require a formal foundation and an objective. We propose the foundation of
set-theoretic dependent type theory and an objective defined in terms of the
classification problem -- the problem of classifying concept instances up to
isomorphism. The natural numbers arise as the solution to the classification
problem for finite sets. Here we generalize classical Bourbaki set-theoretic
isomorphism to set-theoretic dependent type theory. To our knowledge we give
the first isomorphism inference rules for set-theoretic dependent type theory
with propositional set-theoretic equality. The presentation is intended to be
accessible to mathematicians with no prior exposure to type theory.
