# On a long proof

On wikipedia there is a claim that the Abel–Ruffini theorem was nearly proved by Paolo Ruffini, and that his proof spanned over $500$ pages, is this really true? I don’t really know much abstract algebra, and I know that the length of a paper will vary due to the size of the font, but what could possibly take $500$ pages to explain? Did he have to introduce a new subject part way through the paper or what? It also says Niels Henrik Abel published a proof that required just six pages, how can someone jump from $500$ pages to $6$?

## Answer

Not only true, but not unique. The abc conjecture has a recent (2012) proposed proof by Shinichi Mochizuki that spans over 500 pages, over 4 papers. The record is the classification of finite simple groups which consists of tens of thousands of pages, over hundreds of papers. Very few people have read all of them, although the result is important and used frequently.

Attribution
Source : Link , Question Author : Ethan , Answer Author : vadim123