[aaronlevin]

The main objection to computer-aided proofs is not that they are more difficult for humans to understand.

The main objection is that most proof-assistants use a different logical foundation than modern mathematics. Modern mathematics is built on ZFC[0] whereas most proof assistants, such as Coq, Isabelle, Agda, etc use different logical foundations, such as the Calculus of Constructions[1].

Many important results in modern mathematics are not easily stated or proven in systems such as CoC[1]. For example, Brouwer's _Fixed Point Theorem_[2], a pretty bog standard result in Topology that is useful to proof many things in Functional Analysis, has a clear statement in ZFC, but does not, to my knowledge, have an equivalent in CoC (and if it does it will be stated radically different).

[0]: https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_t... [1]: https://en.wikipedia.org/wiki/Calculus_of_constructions [2]: https://en.wikipedia.org/wiki/Brouwer_fixed-point_theorem