How do people write 50-page long proofs (and longer)? So they have a target in mind, but I can't get my head around them foreseeing that these 50 pages of work will actually lead them to exactly their target.
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There are two cases:
Of course, often when writing complicated proofs one may feel the need to add some less trivial introductory parts, which take more pages.
All in all mathematics is not something that you do from one day to the next, but rather a huge project that you never finish in your lifetime. And the proofs just accumulate.
When I hear extremely long proofs mentioned, the classification of finite simple groups comes to my mind. One often hears that the complete proof is some 15000 pages long! But note that this is not a single contiguous piece of work, but rather some 500 published articles by more than 100 mathematicians over a period of half a century. So this is an excellent example of a proof
I know three ways to build long proofs.
The most direct is a work of the mathematical intuition. It is considered by Henri Poincaré in the beginning of “Mathematical Creation”.
The another way is to expand, to generalize our knowledge.
And the third way is used when results obtained by many authors during many years already imply the searched result. Then you can construct a proof of the searched result, looking from the height over the ways by the authors, and creating a systematical way, proof.