Personally I find this more mind boggling than that it can't be communicated easily. Clearly, a proof of 500 pages will be extremely difficult to verify or even understand.
However... That a concept taking just a paragraph to explain* for people who know math requires a proof of over 500 pages. THAT is what I find mind boggling and I find hard to understand. That it can just balloon in size like that, especially given that mathematics is a language of logic.
The halting problem proves that mathematics is hard. There is no algorithm that can prove/disprove any decidable statement. Not even a a superslow algorithm.
However... That a concept taking just a paragraph to explain* for people who know math requires a proof of over 500 pages. THAT is what I find mind boggling and I find hard to understand. That it can just balloon in size like that, especially given that mathematics is a language of logic.
* https://en.wikipedia.org/wiki/Abc_conjecture