To explain it to other people, understand the implications for future results, to know what it really means, is now even more important.

I think the thing a lot of the non-mathematical community doesn't understand is why this is important. I suspect a lot of people imagine a future where AI can build one result on another into a tower of useful math, and the math produced being incomprehensible is a human limitation, not a fundamental problem.

What they don't understand is that the LLMs aren't really much better at understanding these messy sorts of proofs than we are. They're able to move forward one step because the foundation they're building on is solid, but what they're building isn't that useful even to future LLM work.

I'm a software engineer by trade, and I work with LLMs daily. Give them a solid codebase, and a plan, and they will implement features at an impressive rate. But the architecture will be haphazard, and if you just let them keep going without a well understood structure to the code, eventually they'll hit the point where they're introducing more bugs than fixes, and the whole process falls apart.

I think we're going to see an analogous situation with mathematics. LLMs are great at building the next floor of the tower, but to make real progress we have to build those into a solid foundation before we can build higher.