Human readable (informal) proofs are full of gaps that all have to be traced back to axioms e.g. gaps that rely on shared intuition, background knowledge and other informal proofs.
It's somewhat like taking rough pseudo code (the informal proof, a mixture of maths and English) and translating that into a bullet-proof production app (the formal proof, in Lean), where you're going to have to specify every step precisely traced back to axioms, handle all the edge causes, fix incorrect assumptions, and fill in the missing parts that were assumed to be straightforward but might not be.
A major part is you also have to formalise all the proofs your informal proof relied on so everything is traced back to the initial axioms e.g. you can't just cite Pythagorus theorem, you have to formalise that too.
So it's an order of magnitude more difficult to write a formal proof compared to an informal one, and even when you have the informal proof it can teams many years of effort.
It's somewhat like taking rough pseudo code (the informal proof, a mixture of maths and English) and translating that into a bullet-proof production app (the formal proof, in Lean), where you're going to have to specify every step precisely traced back to axioms, handle all the edge causes, fix incorrect assumptions, and fill in the missing parts that were assumed to be straightforward but might not be.
A major part is you also have to formalise all the proofs your informal proof relied on so everything is traced back to the initial axioms e.g. you can't just cite Pythagorus theorem, you have to formalise that too.
So it's an order of magnitude more difficult to write a formal proof compared to an informal one, and even when you have the informal proof it can teams many years of effort.