Math is not about proofing something, or creating a as big as possible collection of lemmas. Math is about creating structures that can use as tools to solve problems. And problem solving is a task done by humans, so math is only useful if humans understand it and have a intuition.

These are not mere calculations. See, an understandable proof has more structure than plain first order logic alone. This allows such proofs to be extended and worked upon as well as real life implications to be discovered.