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 $6$?
2026-04-06 04:52:32.1775451152
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On a long proof
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Math can be very difficult.
There are famous long proofs, like that of the Feit-Thompson theorem, whose initial proof took 255 pages of very intrincate arguments, or the classification of quasi-thin simple groups done by Aschbacher and Smith in 1221 pages, or well, the whole classification of simple finite groups —which is estimated in the tens of thousands of pages— of which the result of Aschbacher and Smith is a very small part.
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.